Superparamagnetism : Theory and Applications · Superparamagnetism : Theory and Applications-Discussion of Two Papers on Magnetic Nanoparticles Manuel Benz December 14, 2012

Superparamagnetism : Theory and Applications-

Discussion of Two Papers on Magnetic Nanoparticles

Manuel Benz

December 14, 2012

Contents

1 Introduction 3

2 Basic Concepts 32.1 An Introduction to Superparamagnetism . . . . . . . . . . . . 32.2 Bulk to Nano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 The Energy Barrier ∆E . . . . . . . . . . . . . . . . . . . . . . . 72.4 M-H Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Forces on Magnetic Nanoparticles . . . . . . . . . . . . . . . . . 11

3 Application of Magnetic Nanoparticles in Biomedicine 123.1 Magnetic Separation . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.1 Cell Labelling & Magnetic Separation . . . . . . . . . . 123.1.2 Separator Design . . . . . . . . . . . . . . . . . . . . . . 133.1.3 Applications of Magnetic Separation . . . . . . . . . . . 14

3.2 Drug Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 Basic Understanding & Motivation . . . . . . . . . . . . 153.2.2 Magnetic Carriers . . . . . . . . . . . . . . . . . . . . . . 153.2.3 Applications of Drug Delivery . . . . . . . . . . . . . . . 153.2.4 Radionuclide and Gene Delivery . . . . . . . . . . . . . 16

3.3 Hyperthermia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.1 Basic Understanding & Motivation . . . . . . . . . . . . 163.3.2 Heating Mechanism . . . . . . . . . . . . . . . . . . . . . 17

3.4 MRI Contrast Enhancement . . . . . . . . . . . . . . . . . . . . 193.4.1 Basic Understanding . . . . . . . . . . . . . . . . . . . . 193.4.2 Contrast Enhancement trough SPM Particles . . . . . 21

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Nanoparticle Magnetism 224.1 Intrinsic Spin Structure and Dynamic Spin Relaxation . . . . 224.2 Applications: Current Trends and Future Directions . . . . . . 26

References 27

1 Introduction

This script’s intention is to give a brief overview of two papers studying thebehaviour of magnetic nanoparticles and its possible applications. Nanopar-ticles, from a certain size on and smaller, can show a special magnetic prop-erty called superparamagnetism.

The first paper “Applications of magnetic nanoparticles in biomedicine”introduces the basic concepts of superparamagnetism and then presents thefollowing applications in biomedicine [1]:

• Magnetic separation of labelled cells and other biological entities;

• Drug, gene and radionuclide delivery;

• Artificial hyperthermia treatments of tumours;

• Contrast enhancement agents for magnetic resonance imaging appli-cations (MRI).

The second paper “Nanoparticle magnetism” presents a discussion onthe following topics [2]:

• In how far do bulk particles behave differently from nanoparticles;

• How can spin reversal in uniaxial magnetic nanoparticles be explained;

• How is the intrinsic spin structure of nanoparticles to be explained;

• And last but not least: Current trends and future directions of appli-cations through these findings.

But before starting the discussion on the papers, a phenomenological intro-duction to the theory of superparamagnetism is given.

2 Basic Concepts

2.1 An Introduction to Superparamagnetism

Superparamagnetism (SPM) is a type of magnetism that occurs in smallferromagnetic or ferrimagnetic nanoparticles. This implies sizes around afew nanometers to a couple of tenth of nanometers, depending on the ma-terial. Additionally, these nanoparticles are single-domain particles. In asimple approximation, the total magnetic moment of the nanoparticle canbe regarded as one giant magnetic moment, composed of all the individualmagnetic moments of the atoms which form the nanoparticle.

Since these nanoparticles may be used in different applications, the sizesof a few relevant entities are given[1]:

3

• Size of a cell: 10 to 100 µm.

• Size of a virus: 20 to 450 nm.

• Size of a protein: 5 to 50 nm.

• Size of a gene: 2 nm wide and 10 to 100 nm long.

Very often, nanoparticles show a certain preference for the direction, alongwhich their magnetization aligns to. These nanoparticles are said to havean anisotropy in these directions. If it is mainly one preferred direction, wespeak of uniaxial anisotropy1.

Nanoparticles with an uniaxial anisotropy randomly flip the direction oftheir magnetization. This effect is induced by thermal energy. The averagetime to perform such a flip is given by the relaxation time:

τ = τ0 exp( ∆E

kBT) (1)

with

• τ0: The length of time characteristic of the probed material. Often itis of a magnitude of around 10−9 to 10−12 s [2].

• ∆E: The energy barrier the magnetization flip has to overcome bythermal energy. See figure 3 for more details.

• kB: The Boltzmann constant.

• T : The temperature.

The observation of nanoparticles in a superparamagnetic state however doesnot only depend on the temperature T and the energy barrier ∆E: Each ex-perimental technique comes with its own measurement time τm. Dependingon the measurement time, the following two scenarios can occur:

1Magnetic anisotropies imply a directional dependence of the material’s magnetic be-haviour. The following anisotropies can be distinguished [4]:

• Magnetocrystalline anisotropy: A preference in direction from the atomicstructure of the crystal.

• Shape anisotropy: Arising from the fact that particles may not be perfectlyspherical.

• Magnetoelasticanisotropy: Arising from tensions within the nanoparticle.

• Exchange anisotropy: Arising from interactions between antiferromagnetic andferromagnetic materials.

4

Topical Review

volume. This direct proportionality between !E and V isthe reason that superparamagnetism—the thermally activatedflipping of the net moment direction—is important for smallparticles, since for them !E is comparable to kBT at, say,room temperature. However, it is important to recognize thatobservations of superparamagnetism are implicitly dependentnot just on temperature, but also on the measurement time "m

of the experimental technique being used (see figure 2). If" ! "m the flipping is fast relative to the experimental timewindow and the particles appear to be paramagnetic (PM);while if " " "m the flipping is slow and quasi-static propertiesare observed—the so-called ‘blocked’ state of the system. A‘blocking temperature’ TB is defined as the mid-point betweenthese two states, where " = "m. In typical experiments "m

can range from the slow to medium timescales of 102 s for DCmagnetization and 10#1–10#5 s for AC susceptibility, throughto the fast timescales of 10#7–10#9 s for 57Fe Mossbauerspectroscopy.

All of the different magnetic responses discussed aboveare illustrated in figure 1 for the case of ferromagneticor ferrimagnetic nanoparticles injected into a blood vessel.Depending on the particle size, the injected material exhibitseither a multi-domain, single-domain or superparamagnetic(SPM) M–H curve. The magnetic response of the bloodvessel itself includes both a PM response—for example, fromthe iron-containing haemoglobin molecules, and a diamagnetic(DM) response—for example, from those intra-vessel proteinsthat comprise only carbon, hydrogen, nitrogen and oxygenatoms. It should be noted that the magnetic signal from theinjected particles, whatever their size, far exceeds that fromthe blood vessel itself. This heightened selectivity is one of theadvantageous features of biomedical applications of magneticnanoparticles.

Returning to the hysteresis which gives rise to the openM–H curves seen for ferromagnets and antiferromagnets,it is clear that energy is needed to overcome the barrier to

(a) (b)

Figure 2. Illustration of the concept of superparamagnetism, wherethe circles depict three magnetic nanoparticles, and the arrowsrepresent the net magnetization direction in those particles.In case (a), at temperatures well below themeasurement-technique-dependent blocking temperature TB of theparticles, or for relaxation times " (the time between momentreversals) much longer than the characteristic measurement time "m,the net moments are quasi-static. In case (b), at temperature wellabove TB, or for " much shorter than "m, the moment reversals are sorapid that in zero external field the time-averaged net moment on theparticles is zero.

domain wall motion imposed by the intrinsic anisotropy andmicrostructural impurities and grain boundaries in the material.This energy is delivered by the applied field, and can becharacterized by the area enclosed by the hysteresis loop.This leads to the concept that if one applies a time-varyingmagnetic field to a ferromagnetic or ferrimagnetic material,one can establish a situation in which there is a constant flowof energy into that material, which will perforce be transferredinto thermal energy. This is the physical basis of hyperthermiatreatments, which are discussed further in section 5. Note thata similar argument regarding energy transfer can be made forSPM materials, where the energy is needed to coherently alignthe particle moments to achieve the saturated state; this also isdiscussed in more detail in section 5.

2.2. Forces on magnetic nanoparticles

To understand how a magnetic field may be used to manipulatemagnetic nanoparticles, we need to recall some elements ofvector field theory. This is not always intuitive, and the readeris directed to recent reviews for further details [5–7]. It is alsoimportant to recognize that a magnetic field gradient is requiredto exert a force at a distance; a uniform field gives rise to atorque, but no translational action. We start from the definitionof the magnetic force acting on a point-like magnetic dipole m:

Fm = (m · !)B, (4)

which can be geometrically interpreted as differentiation withrespect to the direction of m. For example, if m = (0, 0, mz)then m ·! = mz(#/#z) and a force will be experienced on thedipole provided there is a field gradient in B in the z-direction.In the case of a magnetic nanoparticle suspended in a weaklyDM medium such as water, the total moment on the particlecan be written m = VmM, where Vm is the volume of theparticle and M is its volumetric magnetization, which in turnis given by M = !$H, where !$ = $m # $w is the effectivesusceptibility of the particle relative to the water. For the caseof a dilute suspension of nanoparticles in pure water, we canapproximate the overall response of the particles plus watersystem by B = µ0H, so that equation (4) becomes:

Fm = Vm!$

µ0(B · !)B. (5)

Furthermore, provided there are no time-varying electric fieldsor currents in the medium, we can apply the Maxwell equation! $ B = 0 to the following mathematical identity:!(B · B) = 2B $ (! $ B) + 2(B · !)B = 2(B · !)B, (6)to obtain a more intuitive form of equation (5):

Fm = Vm!$%!

B2

2µ0

"or

Fm = Vm!$%# 1

2 B · H$,

(7)

in which the magnetic force is related to the differential of themagnetostatic field energy density, 1

2 B · H. Thus, if !$ > 0the magnetic force acts in the direction of steepest ascent of theenergy density scalar field. This explains why, for example,when iron filings are brought near the pole of a permanentbar magnet, they are attracted towards that pole. It is also thebasis for the biomedical applications of magnetic separationand drug delivery, as will be discussed in sections 3 and 4.

R169

(a)

Topical Review

volume. This direct proportionality between !E and V isthe reason that superparamagnetism—the thermally activatedflipping of the net moment direction—is important for smallparticles, since for them !E is comparable to kBT at, say,room temperature. However, it is important to recognize thatobservations of superparamagnetism are implicitly dependentnot just on temperature, but also on the measurement time "m

of the experimental technique being used (see figure 2). If" ! "m the flipping is fast relative to the experimental timewindow and the particles appear to be paramagnetic (PM);while if " " "m the flipping is slow and quasi-static propertiesare observed—the so-called ‘blocked’ state of the system. A‘blocking temperature’ TB is defined as the mid-point betweenthese two states, where " = "m. In typical experiments "m

can range from the slow to medium timescales of 102 s for DCmagnetization and 10#1–10#5 s for AC susceptibility, throughto the fast timescales of 10#7–10#9 s for 57Fe Mossbauerspectroscopy.

All of the different magnetic responses discussed aboveare illustrated in figure 1 for the case of ferromagneticor ferrimagnetic nanoparticles injected into a blood vessel.Depending on the particle size, the injected material exhibitseither a multi-domain, single-domain or superparamagnetic(SPM) M–H curve. The magnetic response of the bloodvessel itself includes both a PM response—for example, fromthe iron-containing haemoglobin molecules, and a diamagnetic(DM) response—for example, from those intra-vessel proteinsthat comprise only carbon, hydrogen, nitrogen and oxygenatoms. It should be noted that the magnetic signal from theinjected particles, whatever their size, far exceeds that fromthe blood vessel itself. This heightened selectivity is one of theadvantageous features of biomedical applications of magneticnanoparticles.

Returning to the hysteresis which gives rise to the openM–H curves seen for ferromagnets and antiferromagnets,it is clear that energy is needed to overcome the barrier to

(a) (b)

Figure 2. Illustration of the concept of superparamagnetism, wherethe circles depict three magnetic nanoparticles, and the arrowsrepresent the net magnetization direction in those particles.In case (a), at temperatures well below themeasurement-technique-dependent blocking temperature TB of theparticles, or for relaxation times " (the time between momentreversals) much longer than the characteristic measurement time "m,the net moments are quasi-static. In case (b), at temperature wellabove TB, or for " much shorter than "m, the moment reversals are sorapid that in zero external field the time-averaged net moment on theparticles is zero.

domain wall motion imposed by the intrinsic anisotropy andmicrostructural impurities and grain boundaries in the material.This energy is delivered by the applied field, and can becharacterized by the area enclosed by the hysteresis loop.This leads to the concept that if one applies a time-varyingmagnetic field to a ferromagnetic or ferrimagnetic material,one can establish a situation in which there is a constant flowof energy into that material, which will perforce be transferredinto thermal energy. This is the physical basis of hyperthermiatreatments, which are discussed further in section 5. Note thata similar argument regarding energy transfer can be made forSPM materials, where the energy is needed to coherently alignthe particle moments to achieve the saturated state; this also isdiscussed in more detail in section 5.

2.2. Forces on magnetic nanoparticles

To understand how a magnetic field may be used to manipulatemagnetic nanoparticles, we need to recall some elements ofvector field theory. This is not always intuitive, and the readeris directed to recent reviews for further details [5–7]. It is alsoimportant to recognize that a magnetic field gradient is requiredto exert a force at a distance; a uniform field gives rise to atorque, but no translational action. We start from the definitionof the magnetic force acting on a point-like magnetic dipole m:

Fm = (m · !)B, (4)

which can be geometrically interpreted as differentiation withrespect to the direction of m. For example, if m = (0, 0, mz)then m ·! = mz(#/#z) and a force will be experienced on thedipole provided there is a field gradient in B in the z-direction.In the case of a magnetic nanoparticle suspended in a weaklyDM medium such as water, the total moment on the particlecan be written m = VmM, where Vm is the volume of theparticle and M is its volumetric magnetization, which in turnis given by M = !$H, where !$ = $m # $w is the effectivesusceptibility of the particle relative to the water. For the caseof a dilute suspension of nanoparticles in pure water, we canapproximate the overall response of the particles plus watersystem by B = µ0H, so that equation (4) becomes:

Fm = Vm!$

µ0(B · !)B. (5)

Furthermore, provided there are no time-varying electric fieldsor currents in the medium, we can apply the Maxwell equation! $ B = 0 to the following mathematical identity:!(B · B) = 2B $ (! $ B) + 2(B · !)B = 2(B · !)B, (6)to obtain a more intuitive form of equation (5):

Fm = Vm!$%!

B2

2µ0

"or

Fm = Vm!$%# 1

2 B · H$,

(7)

in which the magnetic force is related to the differential of themagnetostatic field energy density, 1

2 B · H. Thus, if !$ > 0the magnetic force acts in the direction of steepest ascent of theenergy density scalar field. This explains why, for example,when iron filings are brought near the pole of a permanentbar magnet, they are attracted towards that pole. It is also thebasis for the biomedical applications of magnetic separationand drug delivery, as will be discussed in sections 3 and 4.

R169

(b)

Figure 1: Case 1(a): The measurement time τm is much smaller than therelaxation time. A well defined state can be observed (blocked state). Case1(b): The measurement time τm is much larger than the relaxation time.Due to the fluctuating state of the magnetization, a time-averaged net mo-ment of zero will be observed (superparamagnetic state). Source: [1]

• τm ≪ τ : The average time between flips is much larger than the mea-surement time. This puts the particles in a well defined state and isusually referred to as the blocked state of the system (see figure 1(a)).

• τm ≫ τ : Alternatively, the average time between flips can be muchsmaller than the measurement time. This implies that the measure-ment actually observes a fluctuating state with different unresolvedmagnetization spin directions. As long as there is no external field ap-plied, a time-averaged net moment of zero is measured. This situationis called the superparamagnetic state of a system (see figure 1(b)).

Equation 1 gives us a connection between the time τ and the temper-ature T . A blocking temperature TB can be defined as the temperaturebetween the blocked and the superparamagnetic state (this implies that atthe blocking temperature TB: τm = τ .)

TB = ∆E

kB ln ( τmτ0 ). (2)

Consequentially, the two states can be distinguished as follows:

• The blocked state: τm ≪ τ or T < TB.

• The superparamagnetic state: τm ≫ τ or T > TB.

5

Since measurement times influence the observed state heavily, it wouldbe nice to know some typical measurement times [1]:

• DC magnetization: 100 s.

• AC susceptibility: 10−1 to 10−5 s.

• Mossbauer spectroscopy: 10−7 to 10−9 s.

What are the implications of such superparamagnetic states? Withoutexternal magnetic field, the net moment is zero. As soon as an externalfield is applied, the nanoparticles react similar to a paramagnet (hence the“paramagnetism” in the name) with the one exception that their magneticsusceptibility is much larger (hence the “super” in the name).

A word of clarification: Normally, any ferromagnetic or ferrimagnetic ma-terial can behave paramagnetically. This is from a certain temperature onand upwards, the so called Curie temperature TC . However, superparamag-netic behaviour is observed below the Cure temperature and thus has to beexplained differently.

2.2 Bulk to Nano

Spins can retain their collinearity only over a certain length. This dependson the material, but is usually around 100 nm and smaller. For sphericalparticles, this size limit R can be approximated by [2]:

R = 6√AK

µ0M2s

. (3)

with

• A: Called exchange stiffness and is a measure for the critical temper-ature for magnetic ordering of this specific material.

• K: Is the magnetic anisotropy of the particle.

• µ0: Is the permeability of free space.

• Ms: Is the saturation magnetization. This quantity is relevant sincesingle domain particles are necessarily magnetically saturated, since allmagnetizations are aligned anyway (without or with external magneticfield).

This determines the size of a domain, within which all spins are alignedalong the same direction (single-domain).

Bulk particles: If the material is bigger than these 100 nm, we speak of a

6

440 G.C. Papaefthymiou

Figure 1 Experimental relation between coercivity and diam-eter for particles deriving their coercive force principally fromcrystal anisotropy energy [Reproduced by permission from F.E.Lubrosky, J. Appl. Phys. 32 (1961) S171, Ref. [31]].

The superparamagnetic properties of magnetic nanoparti-cles determine many of their bio-medical applications.

Spin reversal in uniaxial magneticnanoparticles

Since the pioneering work of Néel [32], Brown [33] andAharoni [34] on uniaxial magnetic nanoparticles, super-paramagnetic relaxation processes have been extensivelystudied. Generally, a particle with uniaxial anisotropy ismodeled by an ellipsoid of revolution, or prolate spheroid,with the easy axis of magnetization along the major axis, asshown in Fig. 2(a). The magnetic anisotropy energy:

Eani(˛) = !KV cos2˛ (4)

where ˛ is the angle between the direction of magnetiza-tion "M and the easy axis, V is the volume of the particleand K is the uniaxial magnetic anisotropy constant. Fig. 2(b)gives a graphical representation of the magnetic anisotropyenergy as a function of the angle, ˛. The potential energylandscape has two minima of equal depth, for ˛ = 0 and !,separated by an energy barrier U = KV. In the absence of anexternal field the particle moment has equal probability tolie along either direction of the easy axis. Moment rever-

sals between the two minima can be achieved by thermalexcitations over the energy barrier, when kT > KV, where kis Boltzmann’s constant and T is the temperature. Accordingto the Néel—Brown theory [32,33] the spin relaxation time,"s, follows the Arrhenius Eq. (5):

"s = "0 exp!

KV

kT

"(5)

where "0 is a characteristic attempt time for spin reversal,a constant characteristic of the material and of the order of10!9 to 10!12 [35]. The application of an external magneticfield at a random angle # relative to the anisotropy axis intro-duces competition for moment alignment along "H and awayfrom the easy axis. Fig. 2(b) depicts how the energy land-scape is modified for the case where "H is applied along theanisotropy axis, by lifting the energy degeneracy of the wellsand decreasing the energy barrier. According to the Stonerand Wohlfarth theory [26], in the absence of temperatureassisted spin reversals, uniformly magnetized single-domainparticles with uniaxial anisotropy undergoing coherent spinrotation would exhibit a maximum coercivity Hc = 2K/Ms atzero absolute temperature. Non-temperature induced spinreversals have also been observed to occur through macro-scopic quantum-mechanical tunneling of the magnetizationvector between the two wells [36—38].

Intrinsic spin structure and dynamic spinrelaxation

In real systems the dynamics of spin reversals are sensi-tive to the internal spin structure of the particles. Mountingexperimental evidence in studies of well characterized,monodispersed magnetic nanoparticles point to an intrin-sic spin structure of greater complexity compared to thesimple collinear model of Stoner—Wohlfarth [26]. The com-plexity arises from the abrupt interruption of the crystal-and spin-lattice structure at the particle’s surface. It is gen-erally recognized that novel properties at the nanoscalearise from the large number of atoms that lie on the sur-face, along grain boundaries or particle/support interfaces.Lattice distortions at the surface trap atoms in thermody-namically non-equilibrium states, which are not generallyencountered in the bulk, as depicted in Fig. 3 [39]. Thus, the

Figure 2 (a) Schematic of a prolate spheroid depicting a nanoparticle with uniaxial magnetic anisotropy in the presence ofan external magnetic field "H at an angle # relative to the direction of the anisotropy axis. Angles ˛, $ give the orientation themagnetization of the particle, "M, relative to the anisotropy axis and the magnetic field, respectively. (b) Magnetic orientationalpotential energy as a function of angle ˛ in the absence of an applied field, solid line (—), and in the presence of an applied fieldalong the anisotropy axis, broken line (— — —). The minima occur at ˛ = 0 and !.

Figure 2: A prolate spheroid representing a nanoparticle with uniaxialanisotropy in an external magnetic field H. θ is the angle between thedirection of the external field and the easy axis. α and ϕ give the mag-netization direction relative to the easy axes, respectively relative to theexternal field. Source: [2].

bulk and have to expect that several domains with domains-walls in betweenare formed (multi-domain). These domains have a collinear spin within onedomain, but not necessarily compared to other domains.

Nanoparticles: Magnetic nanoparticles are small than these 100 nm andare necessarily single-domain particles.

Bulk particles and nanoparticles show different behaviour in an externalmagnetic field. Uniaxial nanoparticles show spin rotation, while bulk parti-cles react to an external field by movement of their domain-walls.

2.3 The Energy Barrier ∆E

So far, it was not discussed how the energy barrier ∆E affects the spin re-versals and the corresponding relaxation time. The energy barrier occurs inparticles with anisotropies. Since those particles’s spin shows a preferencefor certain directions, their energy landscapes contain minima in the pre-ferred directions and maxima in the least preferred directions (see figure 3).

A particle with uniaxial anisotropy can be graphically represented as a pro-late spheroid as shown in figure 2. Its preferred axis is commonly referred toeasy axis and there are two minima: One for each direction along the easyaxis.

Without external magnetic field, the energy barrier takes the form:

∆E =KV (4)

with K an anisotropy constant and V the particle’s volume. But as soon asan external field is applied, one of the minima gets preferred. The situation

7


Figure 1 Experimental relation between coercivity and diam-eter for particles deriving their coercive force principally fromcrystal anisotropy energy [Reproduced by permission from F.E.Lubrosky, J. Appl. Phys. 32 (1961) S171, Ref. [31]].

The superparamagnetic properties of magnetic nanoparti-cles determine many of their bio-medical applications.

Spin reversal in uniaxial magneticnanoparticles

Since the pioneering work of Néel [32], Brown [33] andAharoni [34] on uniaxial magnetic nanoparticles, super-paramagnetic relaxation processes have been extensivelystudied. Generally, a particle with uniaxial anisotropy ismodeled by an ellipsoid of revolution, or prolate spheroid,with the easy axis of magnetization along the major axis, asshown in Fig. 2(a). The magnetic anisotropy energy:

Eani(˛) = !KV cos2˛ (4)

where ˛ is the angle between the direction of magnetiza-tion "M and the easy axis, V is the volume of the particleand K is the uniaxial magnetic anisotropy constant. Fig. 2(b)gives a graphical representation of the magnetic anisotropyenergy as a function of the angle, ˛. The potential energylandscape has two minima of equal depth, for ˛ = 0 and !,separated by an energy barrier U = KV. In the absence of anexternal field the particle moment has equal probability tolie along either direction of the easy axis. Moment rever-

sals between the two minima can be achieved by thermalexcitations over the energy barrier, when kT > KV, where kis Boltzmann’s constant and T is the temperature. Accordingto the Néel—Brown theory [32,33] the spin relaxation time,"s, follows the Arrhenius Eq. (5):

"s = "0 exp!

KV

kT

"(5)

where "0 is a characteristic attempt time for spin reversal,a constant characteristic of the material and of the order of10!9 to 10!12 [35]. The application of an external magneticfield at a random angle # relative to the anisotropy axis intro-duces competition for moment alignment along "H and awayfrom the easy axis. Fig. 2(b) depicts how the energy land-scape is modified for the case where "H is applied along theanisotropy axis, by lifting the energy degeneracy of the wellsand decreasing the energy barrier. According to the Stonerand Wohlfarth theory [26], in the absence of temperatureassisted spin reversals, uniformly magnetized single-domainparticles with uniaxial anisotropy undergoing coherent spinrotation would exhibit a maximum coercivity Hc = 2K/Ms atzero absolute temperature. Non-temperature induced spinreversals have also been observed to occur through macro-scopic quantum-mechanical tunneling of the magnetizationvector between the two wells [36—38].

Intrinsic spin structure and dynamic spinrelaxation

In real systems the dynamics of spin reversals are sensi-tive to the internal spin structure of the particles. Mountingexperimental evidence in studies of well characterized,monodispersed magnetic nanoparticles point to an intrin-sic spin structure of greater complexity compared to thesimple collinear model of Stoner—Wohlfarth [26]. The com-plexity arises from the abrupt interruption of the crystal-and spin-lattice structure at the particle’s surface. It is gen-erally recognized that novel properties at the nanoscalearise from the large number of atoms that lie on the sur-face, along grain boundaries or particle/support interfaces.Lattice distortions at the surface trap atoms in thermody-namically non-equilibrium states, which are not generallyencountered in the bulk, as depicted in Fig. 3 [39]. Thus, the

Figure 2 (a) Schematic of a prolate spheroid depicting a nanoparticle with uniaxial magnetic anisotropy in the presence ofan external magnetic field "H at an angle # relative to the direction of the anisotropy axis. Angles ˛, $ give the orientation themagnetization of the particle, "M, relative to the anisotropy axis and the magnetic field, respectively. (b) Magnetic orientationalpotential energy as a function of angle ˛ in the absence of an applied field, solid line (—), and in the presence of an applied fieldalong the anisotropy axis, broken line (— — —). The minima occur at ˛ = 0 and !.

Figure 3: The situation of the minima in an uniaxial anisotropic particlewithout (solid line) and with (dashed line) external magnetic field. Source:[2]

is shown in figure 3.

Remembering equation 1 for the relaxation time, one can see that thevolume V of the particle is in the exponential. This explains easily whyas soon as the nanoparticles become too large, the behaviour of momentreversal ceases to be an interesting aspect and becomes negligible.

2.4 M-H Curves

As a brief repetition: Considering particles of all kinds and sizes, a catego-rization with respect to their volumetric susceptibility χ makes sense:

• Large χ: Ferromagnetic, ferrimagnetic or antiferromagnetic materials(FM). These materials can have, even without the influence of anexternal magnetic field, a strong order with respect to the alignmentof the magnetic moments (see figure 4).

• Small χ:

– χ > 0: Paramagnetic materials (PM). The magnetic momentsare only aligned under the influence of an external field in thedirection of the magnetic field.

– χ < 0: Diamagnetic materials (DM). The magnetic moments areonly aligned under the influence of an external field in the oppositedirection of the magnetic field.

Many materials show paramagnetic as well as diamagnetic properties. Itis the intrinsic structure of the material, which decides which componentcauses the stronger effects.

These different types of magnetisms show different behaviour of the magne-tization M when varying the external magnetic field H. A comparison ofthe differently magnetic materials is shown in figure 5.

8

(a) (b)

Figure 4: This figure shows the difference between the ordering in ferrimag-netic materials (figure 4(a)) compared to antiferromagntic materials (figure4(b)). Source: [5] & [6].

To go a bit more into detail: What happens, if an external magneticfield H is applied to the superparamagnetic nanoparticles? As with param-agnetic materials, their magnetic moments start to align along the appliedfield. This results in a net magnetization which is in contrast to the zero netmagnetization in a superparamagnetic state without external field. Depend-ing on the temperature and with all particles alike, the net magnetization ofa sample of nanoparticles is given by the following two equations, dependingon the situation [3]:

• For TB < T < KV /(10kB): All easy axes should be oriented parallelto the external field.

M(H) = nm tanh(µ0HmkBT

) , (5)

• For KV /(kB) < T : The orientation of the easy axes does not play arole anymore.

M(H) = nmL(µ0HmkBT

) (6)

with

• n: Density of nanoparticles in the sample.

• m: Magnetic moment of the nanoparticle.

• µ0: Magnetic permeability in vacuum.

• L(x): The Langevin function in dependence of x.

The forms of the two functions are shown in figure 6 and the correspondentsusceptibilities are given by [3]:

• For TB < T <KV /(10kB):

χ = nµ0m2

kBT, (7)

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Topical Review

especially with regard to the challenges faced in bringingcurrent laboratory-tested technologies into mainstream use.

2. Basic concepts

2.1. M–H curves

Figure 1 shows a schematic diagram of a blood vessel intowhich some magnetic nanoparticles have been injected. Themagnetic properties of both the injected particles and theambient biomolecules in the blood stream are illustrated bytheir different magnetic field response curves. To understandthese curves better, we need to be aware of some of thefundamental concepts of magnetism, which will be recalledbriefly here. Further details can be found in one of the manyexcellent textbooks on magnetism (e.g. [1, 2]).

If a magnetic material is placed in a magnetic field ofstrength H, the individual atomic moments in the materialcontribute to its overall response, the magnetic induction:

B = µ0(H + M), (1)

where µ0 is the permeability of free space, and themagnetization M = m/V is the magnetic moment per unit

H

M

DM(x1000)

H

M

PM(x100)

H

M

FM

H

M

SPM

Figure 1. Magnetic responses associated with different classes ofmagnetic material, illustrated for a hypothetical situation in whichferromagnetic particles of a range of sizes from nanometre up tomicron scale are injected into a blood vessel. M–H curves areshown for diamagnetic (DM) and paramagnetic (PM) biomaterialsin the blood vessel, and for the ferromagnetic (FM) injectedparticles, where the response can be either multi-domain (- - - - inFM diagram), single-domain (—— in FM diagram) orsuperparamagnetic (SPM), depending on the size of the particle.

volume, where m is the magnetic moment on a volume V

of the material. All materials are magnetic to some extent,with their response depending on their atomic structure andtemperature. They may be conveniently classified in terms oftheir volumetric magnetic susceptibility, ! , where

M = !H, (2)

describes the magnetization induced in a material by H.In SI units ! is dimensionless and both M and H areexpressed in A m!1. Most materials display little magnetism,and even then only in the presence of an applied field;these are classified either as paramagnets, for which !

falls in the range 10!6–10!1, or diamagnets, with ! in therange !10!6 to !10!3. However, some materials exhibitordered magnetic states and are magnetic even without a fieldapplied; these are classified as ferromagnets, ferrimagnetsand antiferromagnets, where the prefix refers to the natureof the coupling interaction between the electrons within thematerial [2]. This coupling can give rise to large spontaneousmagnetizations; in ferromagnets M is typically 104 times largerthan would appear otherwise.

The susceptibility in ordered materials depends not juston temperature, but also on H, which gives rise to thecharacteristic sigmoidal shape of the M–H curve, withM approaching a saturation value at large values of H.Furthermore, in ferromagnetic and ferrimagnetic materialsone often sees hysteresis, which is an irreversibility in themagnetization process that is related to the pinning of magneticdomain walls at impurities or grain boundaries within thematerial, as well as to intrinsic effects such as the magneticanisotropy of the crystalline lattice. This gives rise to openM–H curves, called hysteresis loops. The shape of theseloops are determined in part by particle size: in large particles(of the order micron size or more) there is a multi-domainground state which leads to a narrow hysteresis loop since ittakes relatively little field energy to make the domain wallsmove; while in smaller particles there is a single domainground state which leads to a broad hysteresis loop. At evensmaller sizes (of the order of tens of nanometres or less) onecan see superparamagnetism, where the magnetic momentof the particle as a whole is free to fluctuate in response tothermal energy, while the individual atomic moments maintaintheir ordered state relative to each other. This leads to theanhysteretic, but still sigmoidal, M–H curve shown in figure 1.

The underlying physics of superparamagnetism is foundedon an activation law for the relaxation time " of the netmagnetization of the particle [3, 4]:

" = "0 exp!

#E

kBT

", (3)

where #E is the energy barrier to moment reversal, andkBT is the thermal energy. For non-interacting particlesthe pre-exponential factor "0 is of the order 10!10–10!12 sand only weakly dependent on temperature [4]. The energybarrier has several origins, including both intrinsic andextrinsic effects such as the magnetocrystalline and shapeanisotropies, respectively; but in the simplest of cases ithas a uniaxial form and is given by #E = KV , whereK is the anisotropy energy density and V is the particle

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(a)

Topical Review


2. Basic concepts

2.1. M–H curves



B = µ0(H + M), (1)


H

M

DM(x1000)

H

M

PM(x100)

H

M

FM

H

M

SPM




M = !H, (2)





" = "0 exp!

#E

kBT

", (3)


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(b)

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2. Basic concepts

2.1. M–H curves



B = µ0(H + M), (1)


H

M

DM(x1000)

H

M

PM(x100)

H

M

FM

H

M

SPM




M = !H, (2)





" = "0 exp!

#E

kBT

", (3)


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(c)

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2. Basic concepts

2.1. M–H curves



B = µ0(H + M), (1)


H

M

DM(x1000)

H

M

PM(x100)

H

M

FM

H

M

SPM




M = !H, (2)





" = "0 exp!

#E

kBT

", (3)


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(d)

Figure 5: This figure shows the schematic behaviour of diamagnetic, param-agnetic, ferromagnetic or superparamagnetic materials in an external mag-netic field. Figure 5(a) (diamagnetic material): The higher the externalmagnetic field H, the lower the magnetization M . Figure 5(b) (paramag-netic material): The higher the external magnetic field H, the higher themagnetization M . Figure 5(c) (ferromagnetic material): A hysteresis loopcan be seen. For multi-domain particles, the loop is narrower (dashed line),while for a single-domain particle, the loop is quite broad (fully drawn line).Figure 5(d) (superparamagnetic material): Similar to ferromagnetic mate-rial is the form of sigmoidal shape, but without any loop. The differencebetween the ferromagnetic behaviour and the superparamagnetic behaviouris primarily determined by the size of the particle. As soon as it gets smallenough, the latter effect takes over. Source: [1].

10

Figure 6: A comparison between the functions tanh(x) (blue) and L(x)(red), which describe the behaviour of the magnetization M in dependenceof H in different situations. Source: [3].

• For KV /(kB) < T :

χ = nµ0m2

3kBT. (8)

2.5 Forces on Magnetic Nanoparticles

Since many applications in biomedicine require to manipulate the path ofthe nanoparticles, it is vital to understand the force required to do so. Whilea static magnetic field may give rise to a torque, it cannot be used for a trans-lational movement. In order to do the latter, we require a magnetic fieldgradient.

The magnetic force on a point-like magnetic dipole moment m is given by[1]

Fm = (m ⋅ ∇)B . (9)

Since many applications using nanoparticles take place in some fluid (e.g.body fluid), it is reasonable to use this setting for the following calculations.With some manipulations and simplifications, such as

• m = V M ,

• M = ∆χH with ∆χ = χ−χw (effective susceptibility relative to water),

• dilute suspension of nanoparticles allows approximation: B = µ0H,

• vector-identities & ∇∧ B = 0,

one finally arrives at the following forms of the previous equation:

Fm = V∆χ∇( B2

2µ0) (10)

11

Fm = V∆χ∇(1

2B ⋅ H) . (11)

The factor 12B ⋅ H can be understood as the magnetostatic field energy den-

sity. As a result, for a positive ∆χ (cf. paramagnetic materials in section2.4), there will be a force acting into the direction of the steepest ascent ofthe energy density scalar field.

3 Application of Magnetic Nanoparticles in Biomedicine

This section discusses the paper “Applications of magnetic nanoparticles inbiomedicine”. According to the authors, nanoparticles bring along severalqualities, which make them a good candidate for techniques in biomedicine:

• Their size is comparable to the targeted entities (see section 2.1).

• Nanoparticles can be magnetic. An external magnetic field gradientcan be applied to influence their movement. This way, they can eitherdeliver certain drugs or tag certain entities.

• Nanoparticles may also be resonantly excited. This allows heat trans-fer to the surrounding tissue.

In the following, a few applications are presented, which make use of thementioned qualities of the nanoparticles.

3.1 Magnetic Separation

3.1.1 Cell Labelling & Magnetic Separation

Magnetic separation is in essence separating specific biological entities fromtheir native environment and studying or manipulating them in a bettercontrolled environment. This process is usually done in two steps:

1. First, the entities to separate have to be labelled or tagged with themagnetic particles.

2. In a second step, the entities now attached to the magnetic particlescan be extracted or moved by exerting a force on the latter.

How is the tagging achieved? In brief, the hull of the nanoparticles can beprepared, i.e. coated with some material that interacts only with the entitiesin question.

How is the magnetic separation achieved? The magnetically tagged ma-terial should be in a fluid. The fluid can then be brought into a region witha steep magnetic field gradient. The magnetic force needs to overcome twocompeting forces:

12

• The hydrodynamic drag force of the fluid: Fd = 6πηRm∆v with

– η: The viscosity of the fluid.

– Rm: The radius of the magnetic particle.

– ∆v = vm − vw: The difference in velocities of the entity and thewater.

• The buoyancy force: While this is a competing force, it can generallybe neglected, due to its small effects in this situation.

As a side note: It can be observed that the radius of the magnetic particleRm plays a role in the equation. Even though a larger radius implies a largerdrag force, it can be more reasonable to resort to larger particles, so calledmicrospheres. The reason being is that the microspheres can show moreresponse to manipulations of their velocity compared to nanoparticles.

3.1.2 Separator Design

There are several designs, from quite simple to rather complex ones, toseparate the magnetically tagged material from its surrounding [1]:

• A rather simple method lets the magnetically tagged particles pass bya permanent magnet. All the tagged particles get stuck, while the restof the fluid passes. In a second step, the magnet can be removed andthe tagged particles can be flushed out:

Topical Review

3. Magnetic separation

3.1. Cell labelling and magnetic separation

In biomedicine it is often advantageous to separate outspecific biological entities from their native environmentin order that concentrated samples may be prepared forsubsequent analysis or other use. Magnetic separation usingbiocompatible nanoparticles is one way to achieve this. Itis a two-step process, involving (i) the tagging or labellingof the desired biological entity with magnetic material, and(ii) the separating out of these tagged entities via a fluid-basedmagnetic separation device.

Tagging is made possible through chemical modificationof the surface of the magnetic nanoparticles, usually by coatingwith biocompatible molecules such as dextran, polyvinylalcohol (PVA) and phosopholipids—all of which have beenused on iron oxide nanoparticles [8–10]. As well as providinga link between the particle and the target site on a cell ormolecule, coating has the advantage of increasing the colloidalstability of the magnetic fluid. Specific binding sites on thesurface of cells are targeted by antibodies or other biologicalmacromolecules such as hormones or folic acid [11–13]. Asantibodies specifically bind to their matching antigen thisprovides a highly accurate way to label cells. For example,magnetic particles coated with immunospecific agents havebeen successfully bound to red blood cells [8, 14], lung cancercells [15], bacteria [16], urological cancer cells [17] and Golgivesicles [18]. For larger entities such as the cells, bothmagnetic nanoparticles and larger particles can be used: forexample, some applications use magnetic ‘microspheres’—micron sized agglomerations of sub-micron sized magneticparticles incorporated in a polymeric binder [19].

The magnetically labelled material is separated from itsnative solution by passing the fluid mixture through a region inwhich there is a magnetic field gradient which can immobilizethe tagged material via the magnetic force of equation (7). Thisforce needs to overcome the hydrodynamic drag force actingon the magnetic particle in the flowing solution,

Fd = 6!"Rm#v, (8)

where " is the viscosity of the medium surrounding the cell(e.g. water), Rm is the radius of the magnetic particle, and#v = vm !vw is the difference in velocities of the cell and thewater [6]. There is also buoyancy force that affects the motion,but this is dependent on the difference between the density ofthe cell and the water, and for most cases of interest in biologyand medicine can be neglected. Equating the hydrodynamicdrag and magnetic forces, and writing Vm = 4

3!R3m, gives the

velocity of the particle relative to the carrier fluid as:

#v = R2m#$

9µ0""(B2) or #v = %

µ0"(B2), (9)

where % is the ‘magnetophoretic mobility’ of the particle—aparameter that describes how manipulable a magnetic particleis. For example, the magnetophoretic mobility of magneticmicrospheres can be much greater than that of nanoparticles,due to their larger size. This can be an advantage, for example,in cell separations, where the experimental timeframe for theseparations is correspondingly shorter. On the other hand,

smaller magnetic particle sizes can also be advantageous, forexample, in reducing the likelihood that the magnetic materialwill interfere with further tests on the separated cells [20].

3.2. Separator design

Magnetic separator design can be as simple as the applicationand removal of a permanent magnet to the wall of a test tubeto cause aggregation, followed by removal of the supernatant(figure 3(a)). However, this method can be limited by slowaccumulation rates [21]. It is often preferable to increase theseparator efficiency by producing regions of high magneticfield gradient to capture the magnetic nanoparticles as theyfloat or flow by in their carrier medium. A typical wayto achieve this is to loosely pack a flow column with amagnetizable matrix of wire (e.g. steel wool) or beads [22]and to pump the magnetically tagged fluid through the columnwhile a field is applied (figure 3(b)). This method is fasterthan in the first case, although problems can arise due to thesettling and adsorption of magnetically tagged material on thematrix. An alternative, rapid throughput method which doesnot involve any obstructions being placed in the column is theuse of specifically designed field gradient systems, such asthe quadrupolar arrangement shown in figure 4 which createsa magnetic gradient radially outwards from the centre of theflow column [23].

As well as separating out the magnetically tagged material,the spatially varying magnitude of the field gradient canbe used to achieve ‘fluid flow fractionation’ [24]. Thisis a process in which the fluid is split at the outlet intofractions containing tagged cells or proteins with differing

(a)

(b)

Figure 3. The standard methods of magnetic separation: in (a) amagnet is attached to the container wall of a solution of magneticallytagged (•) and unwanted (#) biomaterials. The tagged particles aregathered by the magnet, and the unwanted supernatant solution isremoved. In (b) a solution containing tagged and unwantedbiomaterials flows continuously through a region of strong magneticfield gradient, often provided by packing the column with steel wool,which captures the tagged particles. Thereafter the tagged particlesare recovered by removing the field and flushing through with water.

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Disadvantage: This method takes quite some time before collecting aseizable amount of tagged particles.

• A more advanced technique lets the fluid pass through some materiallike steel wool, while applying a magnetic field gradient. The mag-netically tagged particles get stuck in the steel wool and then, as inthe method before, can be flushed out as soon as the magnetic field isturned off:

13

Topical Review

3. Magnetic separation

3.1. Cell labelling and magnetic separation

In biomedicine it is often advantageous to separate outspecific biological entities from their native environmentin order that concentrated samples may be prepared forsubsequent analysis or other use. Magnetic separation usingbiocompatible nanoparticles is one way to achieve this. Itis a two-step process, involving (i) the tagging or labellingof the desired biological entity with magnetic material, and(ii) the separating out of these tagged entities via a fluid-basedmagnetic separation device.

Tagging is made possible through chemical modificationof the surface of the magnetic nanoparticles, usually by coatingwith biocompatible molecules such as dextran, polyvinylalcohol (PVA) and phosopholipids—all of which have beenused on iron oxide nanoparticles [8–10]. As well as providinga link between the particle and the target site on a cell ormolecule, coating has the advantage of increasing the colloidalstability of the magnetic fluid. Specific binding sites on thesurface of cells are targeted by antibodies or other biologicalmacromolecules such as hormones or folic acid [11–13]. Asantibodies specifically bind to their matching antigen thisprovides a highly accurate way to label cells. For example,magnetic particles coated with immunospecific agents havebeen successfully bound to red blood cells [8, 14], lung cancercells [15], bacteria [16], urological cancer cells [17] and Golgivesicles [18]. For larger entities such as the cells, bothmagnetic nanoparticles and larger particles can be used: forexample, some applications use magnetic ‘microspheres’—micron sized agglomerations of sub-micron sized magneticparticles incorporated in a polymeric binder [19].

The magnetically labelled material is separated from itsnative solution by passing the fluid mixture through a region inwhich there is a magnetic field gradient which can immobilizethe tagged material via the magnetic force of equation (7). Thisforce needs to overcome the hydrodynamic drag force actingon the magnetic particle in the flowing solution,

Fd = 6!"Rm#v, (8)

where " is the viscosity of the medium surrounding the cell(e.g. water), Rm is the radius of the magnetic particle, and#v = vm !vw is the difference in velocities of the cell and thewater [6]. There is also buoyancy force that affects the motion,but this is dependent on the difference between the density ofthe cell and the water, and for most cases of interest in biologyand medicine can be neglected. Equating the hydrodynamicdrag and magnetic forces, and writing Vm = 4

3!R3m, gives the

velocity of the particle relative to the carrier fluid as:

#v = R2m#$

9µ0""(B2) or #v = %

µ0"(B2), (9)

where % is the ‘magnetophoretic mobility’ of the particle—aparameter that describes how manipulable a magnetic particleis. For example, the magnetophoretic mobility of magneticmicrospheres can be much greater than that of nanoparticles,due to their larger size. This can be an advantage, for example,in cell separations, where the experimental timeframe for theseparations is correspondingly shorter. On the other hand,

smaller magnetic particle sizes can also be advantageous, forexample, in reducing the likelihood that the magnetic materialwill interfere with further tests on the separated cells [20].

3.2. Separator design

Magnetic separator design can be as simple as the applicationand removal of a permanent magnet to the wall of a test tubeto cause aggregation, followed by removal of the supernatant(figure 3(a)). However, this method can be limited by slowaccumulation rates [21]. It is often preferable to increase theseparator efficiency by producing regions of high magneticfield gradient to capture the magnetic nanoparticles as theyfloat or flow by in their carrier medium. A typical wayto achieve this is to loosely pack a flow column with amagnetizable matrix of wire (e.g. steel wool) or beads [22]and to pump the magnetically tagged fluid through the columnwhile a field is applied (figure 3(b)). This method is fasterthan in the first case, although problems can arise due to thesettling and adsorption of magnetically tagged material on thematrix. An alternative, rapid throughput method which doesnot involve any obstructions being placed in the column is theuse of specifically designed field gradient systems, such asthe quadrupolar arrangement shown in figure 4 which createsa magnetic gradient radially outwards from the centre of theflow column [23].

As well as separating out the magnetically tagged material,the spatially varying magnitude of the field gradient canbe used to achieve ‘fluid flow fractionation’ [24]. Thisis a process in which the fluid is split at the outlet intofractions containing tagged cells or proteins with differing

(a)

(b)

Figure 3. The standard methods of magnetic separation: in (a) amagnet is attached to the container wall of a solution of magneticallytagged (•) and unwanted (#) biomaterials. The tagged particles aregathered by the magnet, and the unwanted supernatant solution isremoved. In (b) a solution containing tagged and unwantedbiomaterials flows continuously through a region of strong magneticfield gradient, often provided by packing the column with steel wool,which captures the tagged particles. Thereafter the tagged particlesare recovered by removing the field and flushing through with water.

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• Another method uses a magnet in a quadrature setup. View from top(first figure) and from the side (second figure): Topical Review

(a) (b)

Figure 4. A rapid throughput method of magnetic separation, inwhich an annular column containing a flowing solution ofmagnetically tagged (•) and unwanted (!) biomaterials is placedwithin a set of magnets arranged in quadrature: (a) longitudinalcross-section of the annular column; (b) transverse cross-section ofthe four magnets with the resulting magnetic field lines. Under theaction of the magnetic field gradient the tagged particles move to thecolumn walls, where they are held until the field is removed andthey are recovered by flushing through with water. The central coreof the column is made of non-magnetic material to avoidcomplications due to the near-zero field gradients there.

magnetophoretic mobilities. In a variant of this, the fluid isstatic while an applied magnetic field is moved up the container[25]. The particles move up the container in the resultingfield gradient at a velocity dependent on their magnetophoreticmobility. At the top of the container they enter a removablesection and are held here by a permanent magnet. The bottomsection of the container moves to the next section, a magneticfield with different strength to the first is applied and the processrepeats. The result is a fractionation of the sample into aliquotsof differing magnetophoretic mobility.

3.3. Applications

Magnetic separation has been successfully applied to manyaspects of biomedical and biological research. It has provento be a highly sensitive technique for the selection of raretumour cells from blood, and is especially well suited to theseparation of low numbers of target cells [26]. This has, forexample, led to the enhanced detection of malarial parasitesin blood samples either by utilizing the magnetic properties ofthe parasite [27] or through labelling the red blood cells withan immunospecific magnetic fluid [28]. It has been used asa pre-processing technology for polymerase chain reactions,through which the DNA of a sample is amplified and identified[29]. Cell counting techniques have also been developed. Onemethod estimates the location and number of cells tagged bymeasuring the magnetic moment of the microsphere tags [30],while another uses a giant magnetoresistive sensor to measurethe location of microspheres attached to a surface layered witha bound analyte [31].

In another application, magnetic separation has been usedin combination with optical sensing to perform ‘magneticenzyme linked immunosorbent assays’ [32, 33]. These assaysuse fluorescent enzymes to optically determine the numberof cells labelled by the assay enzymes. Typically the targetmaterial must first be bound to a solid matrix. In a modificationof this procedure the magnetic microspheres act as the surfacefor initial immobilization of the target material and magnetic

separation is used to increase the concentration of the material.The mobility of the magnetic nanoparticles allows a shorterreaction time and a greater volume of reagent to be used thanin standard immunoassays where the antibody is bound to aplate. In a variation of this procedure, magnetic separationhas been used to localize labelled cells at known locationsfor cell detection and counting via optical scanning [14]. Thecells are labelled both magnetically and fluorescently and movethrough a magnetic field gradient towards a plate on which linesof ferromagnetic material have been lithographically etched.The cells align along these lines and the fluorescent tag is usedfor optical detection of the cells.

4. Drug delivery

4.1. Motivation and physical principles

The major disadvantage of most chemotherapies is thatthey are relatively non-specific. The therapeutic drugsare administered intravenously leading to general systemicdistribution, resulting in deleterious side-effects as the drugattacks normal, healthy cells in addition to the target tumourcells. For example, the side effects of anti-inflammatorydrugs on patients who have chronic arthritis can lead to thediscontinuation of their use. However, if such treatments couldbe localized, e.g. to the site of a joint, then the continued use ofthese very potent and effective agents could be made possible.

Recognition of this led researchers in the late 1970sto propose the use of magnetic carriers to target specificsites (generally cancerous tumours) within the body [34–36].The objectives are two-fold: (i) to reduce the amount ofsystemic distribution of the cytotoxic drug, thus reducingthe associated side-effects; and (ii) to reduce the dosagerequired by more efficient, localized targeting of thedrug. In magnetically targeted therapy, a cytotoxic drug isattached to a biocompatible magnetic nanoparticle carrier.These drug/carrier complexes—usually in the form of abiocompatible ferrofluid—are injected into the patient viathe circulatory system. When the particles have entered thebloodstream, external, high-gradient magnetic fields are usedto concentrate the complex at a specific target site within thebody (figure 5). Once the drug/carrier is concentrated at thetarget, the drug can be released either via enzymatic activity orchanges in physiological conditions such as pH, osmolality,or temperature [37], and be taken up by the tumour cells.This system, in theory, has major advantages over the normal,non-targeted methods of cytotoxic drug therapy.

The physical principles underlying magnetic targetingtherapy are similar to those used in magnetic separation,and are derived from the magnetic force exerted on a SPMnanoparticle by a magnetic field gradient, as in equation (7).The effectiveness of the therapy is dependent on severalphysical parameters, including the field strength, gradientand volumetric and magnetic properties of the particles.As the carriers (ferrofluids) are normally administeredintravenously or intra-arterially, hydrodynamic parameterssuch as blood flow rate, ferrofluid concentration, infusionroute and circulation time also will play a major role—as willphysiological parameters such as tissue depth to the target site(i.e. distance from the magnetic field source), reversibility andstrength of the drug/carrier binding, and tumour volume [38].

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Topical Review

(a) (b)

Figure 4. A rapid throughput method of magnetic separation, inwhich an annular column containing a flowing solution ofmagnetically tagged (•) and unwanted (!) biomaterials is placedwithin a set of magnets arranged in quadrature: (a) longitudinalcross-section of the annular column; (b) transverse cross-section ofthe four magnets with the resulting magnetic field lines. Under theaction of the magnetic field gradient the tagged particles move to thecolumn walls, where they are held until the field is removed andthey are recovered by flushing through with water. The central coreof the column is made of non-magnetic material to avoidcomplications due to the near-zero field gradients there.

magnetophoretic mobilities. In a variant of this, the fluid isstatic while an applied magnetic field is moved up the container[25]. The particles move up the container in the resultingfield gradient at a velocity dependent on their magnetophoreticmobility. At the top of the container they enter a removablesection and are held here by a permanent magnet. The bottomsection of the container moves to the next section, a magneticfield with different strength to the first is applied and the processrepeats. The result is a fractionation of the sample into aliquotsof differing magnetophoretic mobility.

3.3. Applications

Magnetic separation has been successfully applied to manyaspects of biomedical and biological research. It has provento be a highly sensitive technique for the selection of raretumour cells from blood, and is especially well suited to theseparation of low numbers of target cells [26]. This has, forexample, led to the enhanced detection of malarial parasitesin blood samples either by utilizing the magnetic properties ofthe parasite [27] or through labelling the red blood cells withan immunospecific magnetic fluid [28]. It has been used asa pre-processing technology for polymerase chain reactions,through which the DNA of a sample is amplified and identified[29]. Cell counting techniques have also been developed. Onemethod estimates the location and number of cells tagged bymeasuring the magnetic moment of the microsphere tags [30],while another uses a giant magnetoresistive sensor to measurethe location of microspheres attached to a surface layered witha bound analyte [31].

In another application, magnetic separation has been usedin combination with optical sensing to perform ‘magneticenzyme linked immunosorbent assays’ [32, 33]. These assaysuse fluorescent enzymes to optically determine the numberof cells labelled by the assay enzymes. Typically the targetmaterial must first be bound to a solid matrix. In a modificationof this procedure the magnetic microspheres act as the surfacefor initial immobilization of the target material and magnetic

separation is used to increase the concentration of the material.The mobility of the magnetic nanoparticles allows a shorterreaction time and a greater volume of reagent to be used thanin standard immunoassays where the antibody is bound to aplate. In a variation of this procedure, magnetic separationhas been used to localize labelled cells at known locationsfor cell detection and counting via optical scanning [14]. Thecells are labelled both magnetically and fluorescently and movethrough a magnetic field gradient towards a plate on which linesof ferromagnetic material have been lithographically etched.The cells align along these lines and the fluorescent tag is usedfor optical detection of the cells.

4. Drug delivery

4.1. Motivation and physical principles

The major disadvantage of most chemotherapies is thatthey are relatively non-specific. The therapeutic drugsare administered intravenously leading to general systemicdistribution, resulting in deleterious side-effects as the drugattacks normal, healthy cells in addition to the target tumourcells. For example, the side effects of anti-inflammatorydrugs on patients who have chronic arthritis can lead to thediscontinuation of their use. However, if such treatments couldbe localized, e.g. to the site of a joint, then the continued use ofthese very potent and effective agents could be made possible.

Recognition of this led researchers in the late 1970sto propose the use of magnetic carriers to target specificsites (generally cancerous tumours) within the body [34–36].The objectives are two-fold: (i) to reduce the amount ofsystemic distribution of the cytotoxic drug, thus reducingthe associated side-effects; and (ii) to reduce the dosagerequired by more efficient, localized targeting of thedrug. In magnetically targeted therapy, a cytotoxic drug isattached to a biocompatible magnetic nanoparticle carrier.These drug/carrier complexes—usually in the form of abiocompatible ferrofluid—are injected into the patient viathe circulatory system. When the particles have entered thebloodstream, external, high-gradient magnetic fields are usedto concentrate the complex at a specific target site within thebody (figure 5). Once the drug/carrier is concentrated at thetarget, the drug can be released either via enzymatic activity orchanges in physiological conditions such as pH, osmolality,or temperature [37], and be taken up by the tumour cells.This system, in theory, has major advantages over the normal,non-targeted methods of cytotoxic drug therapy.

The physical principles underlying magnetic targetingtherapy are similar to those used in magnetic separation,and are derived from the magnetic force exerted on a SPMnanoparticle by a magnetic field gradient, as in equation (7).The effectiveness of the therapy is dependent on severalphysical parameters, including the field strength, gradientand volumetric and magnetic properties of the particles.As the carriers (ferrofluids) are normally administeredintravenously or intra-arterially, hydrodynamic parameterssuch as blood flow rate, ferrofluid concentration, infusionroute and circulation time also will play a major role—as willphysiological parameters such as tissue depth to the target site(i.e. distance from the magnetic field source), reversibility andstrength of the drug/carrier binding, and tumour volume [38].

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The particles are pulled towards the wall, from where they can beflushed out as soon as the magnets are turned off.

• Alternatively, the particles can be static and the magnets itself moves.The particles are collected in a container at the end of the pipe bythe means of a permanent magnet. This allows an easy removal of thecontainer with the captured particles.

3.1.3 Applications of Magnetic Separation

Magnetic separation can be used in several applications, especially exceedingwhen the targeted entities only appear on small numbers:

• As a highly sensitive technique to select and remove rare tumour cells.

• Enhanced detection and separation of malarial parasites in blood sam-ples (using the parasites magnetic properties).

• Cell counting techniques.

• Combined with optical sensing to perform tests regarding the presenceor concentration of certain substances. The magnetic separation tech-nique guarantees an efficient tagging and a high enough concentrationof the substance, while the optical sensing can then use a fluorescenttag to detect the substance.

14

3.2 Drug Delivery

3.2.1 Basic Understanding & Motivation

Drug delivery through magnetic nanoparticles works in a similar fashion tomagnetic separation: The drug can be attached to the magnetic particle andthen a magnetic force can change the path of the tagged particles. Once atthe correct place, the drug can be released from its carrier either via enzy-matic activity or physiological changes (pH, osmolality, temperature).

As before, not only nanoparticles, but also microspheres should be con-sidered due to their high likeliness to be influenced in their path. They aremore successful at withstanding the general flow in the body’s circulatorysystem.

In general, drug delivery seems to be more successful in regions with a slowflow and when the magnet can come into close proximity.

3.2.2 Magnetic Carriers

How should these magnetic particles be built to fulfil their tasks most effi-ciently? As for the tagging process, coating is required. These coatings canbe of organic or inorganic origin. During their journey the coating protectsthe magnetic nanoparticles or microspheres and once at their target, it canserve as an attachment point to the targeted entity. In general, there aretwo types of structural configurations [1]:

• Magnetic core with a biocompatible polymer as coating.

• Porous biocompatible polymer, in which the magnetic nanoparticlescan diffuse through the pores.

3.2.3 Applications of Drug Delivery

The advantages of targeted drug delivery seem numerous: Most drugs arenon-specific, i.e. they get distributed over the whole body as soon as theyget administered intravenously. Targeted delivery can ensure that

• only specific areas get influenced by the (otherwise harmful) drugs and

• as little as possible of the drug needs to be administered.

This method seems especially applicable, when the drug is very damagingto healthy tissue. Fields of application:

• Chemotherapy,

• radionuclide therapy,

15

• arthritis or

• gene therapy.

As a side note: While having proven to be very successful in animal tests,to the date of the publication of this paper (2003) there were not manystudies with humans as test subjects. And while being very promising forthe future, a couple of problems should not be neglected:

• Embolization of blood vessels due to too high concentration of themagnetic carriers.

• Larger distances to cover in humans compared with animals.

• As soon as the drug is released, it cannot be influenced any longer bymagnetic field gradients.

• The magnetic carriers itself may have unwanted side effects.

3.2.4 Radionuclide and Gene Delivery

These two fields of study have only recently become popular among scientificresearchers.

• Radionuclide Delivery: An advantage of radionuclide therapy isthat the radionuclides do not have to decouple from the magnetic car-riers. The magnetic carriers can transport the radionuclides to thetarget area where they can destroy the cancerous tissue. After the de-sired result has been achieved, both the carriers and the radionuclidescan be directed out of the circulatory system.

• Gene Therapy: In gene therapies, the magnetic carriers are coatedwith the therapeutical gene and transported to the target area. Thanksto the possibilitiy of holding the gene and carrier at the target for anextended time, the chances rise that the gene can get transfected. Ap-plications in this field of study are only in their beginning.

3.3 Hyperthermia

3.3.1 Basic Understanding & Motivation

The idea of the treatment is to artificially introduce hyperthermia2 in orderto heat malignant tissue at specific areas while sparing benignant tissue.

2Hyperthermia is usually an unwanted overheating of the body not to be confused withcommon fever. In a hyperthermic state, the body absorbes or produces more heat thanit can dissipate. However, hyperthermia can also be a wanted effect in order to destroytumorous cells and hence is sometimes created artificially.

16

Topical Review

study the group demonstrated that 10–20 nm magnetic particleswere even more effective at targeting these tumours in rats [64].Electron microscopic analysis of brain tissue samples revealedthe presence of magnetic carriers in the interstitial space intumours but in normal brain tissue, they were only found inthe vasculature. Mykhaylyk and others [67] recently had lesssuccess using magnetite–dextran nanoparticles but were ableto target rat glial tumours by disrupting the blood–brain barrierimmediately prior to particle injection.

Studies of magnetic targeting in humans were rare up tonow. A Phase I clinical trial conducted by Lubbe and others[68–70] demonstrated that the infusion of ferrofluids was welltolerated in most of the 14 patients studied. In addition, theauthors reported that the ferrofluid was successfully directedto the advanced sarcomas without associated organ toxicity.More recently, FeRx Inc. was granted fast-track status toproceed with multi-centre Phases I and II clinical trials oftheir magnetic targeting system for hepatocellular carcinomas(a type of liver tumour). This appears to be the most promisingclinical application at present.

As promising as these results have been, there are severalproblems associated with magnetically targeted drug delivery[38, 71]. These limitations include (i) the possibility ofembolization of the blood vessels in the target region due toaccumulation of the magnetic carriers, (ii) difficulties in scalingup from animal models due to the larger distances between thetarget site and the magnet, (iii) once the drug is released, it is nolonger attracted to the magnetic field, and (iv) toxic responsesto the magnetic carriers. Recent pre-clinical and experimentalresults indicate, however, that it is still possible to overcomethese limitations and use magnetic targeting to improve drugretention and also address safety issues [68, 72].

4.4. Radionuclide and gene delivery

One way to overcome the limitation caused by the release of thedrug from the carrier is to use a system in which the therapeuticagent remains coupled to the magnetic carrier throughoutthe duration of the treatment. Based on this idea, thepossibility of targeting radionuclides via magnetic carriershas been investigated. The advantage these complexes haveover cytotoxic drug/magnetic carrier complexes is that theeffectiveness of the radionuclide does not require the tumourcells to actually take up the agent. If the radionuclide is targetedto a region near the tumour site and held there, the radiation willaffect the surrounding tumour tissue while it is still attached tothe magnetic carrier. This type of system was tested in 1995using in vitro and mouse models. In both cases, targeting ofa magnetic carrier coupled to a !-emitter (Y-90) was effectiveat concentrating radiation to the desired site. In the mousetumour model, there was a significant increase in radioactivityat the tumour site compared to using the same complex withouta magnetic field: 73 ± 32% vs 6 ± 4% [73]. Since this study,Hafeli and others [74–76] have demonstrated the effectivenessof this technique in both animal and cell culture studies usingboth yttrium-90 and rhenium-188.

Investigations also have begun with a view towards usingmagnetic carriers for gene therapy. In this case, a viral vectorcarrying the therapeutic gene is coated onto the magneticcarrier’s surface. By holding the carrier at the target site via

external magnetic fields, the virus is in contact with the tissuefor a longer period of time, increasing the efficiency of genetransfection and expression [77, 78]. New magnetic carriersare being developed specifically for these applications [79]and this is an area which shows great promise.

5. Hyperthermia

5.1. Catabolism of tumours by hyperthermia

The possibility of treating cancer by artificially inducedhyperthermia has led to the development of manydifferent devices designed to heat malignant cells whilesparing surrounding healthy tissue [80–82]. Experimentalinvestigations of the application of magnetic materials forhyperthermia date back to 1957 when Gilchrist et al [83]heated various tissue samples with 20–100 nm size particlesof " -Fe2O3 exposed to a 1.2 MHz magnetic field. Sincethen there have been numerous publications describing avariety of schemes using different types of magnetic materials,different field strengths and frequencies and different methodsof encapsulation and delivery of the particles [84–102]. Inbroad terms, the procedure involves dispersing magneticparticles throughout the target tissue, and then applying an ACmagnetic field of sufficient strength and frequency to causethe particles to heat. This heat conducts into the immediatelysurrounding diseased tissue whereby, if the temperature canbe maintained above the therapeutic threshold of 42˚C for30 min or more, the cancer is destroyed. Whereas themajority of hyperthermia devices are restricted in their utilitybecause of unacceptable coincidental heating of healthy tissue,magnetic particle hyperthermia is appealing because it offersa way to ensure only the intended target tissue is heated (seefigure 7).

5.2. Operational constraints

A number of studies have demonstrated the therapeutic efficacyof this form of treatment in animal models (see, e.g. the review

30

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5040

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0 10 20 30 4

Time (minutes)

Tem

pera

ture

(˚ C

)

Figure 7. Animal trial data on hyperthermia treatments in rabbits,showing preferential heating of a tumour using intra-vascularlyinfused ferromagnetic microspheres; ( ) tumour edge, (!) tumourcentre, (") normal liver 1–2 cm from tumour, (!) alternative lobe,and (#) core body temperature.

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Figure 7: This data has been taken from tests with rabbits (liver tumour)and shows the tissue’s temperature in a specific region over time. Legend:(∎) tumour edge, (◆) tumour centre, (▲) normal liver 1-2 cm from tumour,(×) alternate lobe, (◇) core body temperature. The targeting of a specificarea (here the liver) is quite successful: The tumour centre and tumour edgeget heated to the required temperature, while the core body temperaturestays stable. Source: [1].

The magnetic particles first have to be brought to the target area, wherethey can be caused to heat up by an AC magnetic field of sufficient strengthand frequency. The heat should exceed the threshold of 42○ Celsius and lastfor about 30 minutes in order to properly destroy the tumour.

Tests with animals were successful and quite promising (see figure 7), but sofar it could not be applied to humans due to our larger size. A vastly largersize would require vastly larger alternating magnetic fields, which in turnwould be harmful to the organism. Lowering the field on the other hand,would not result in enough heat production.

3.3.2 Heating Mechanism

As already mentioned, an alternating magnetic field is required to produceheat. However, the total heat balance is quite complicated: Additionally tothe magnetic heat production, the cooling of the blood through blood flowand tissue perfusion have to be considered. As a simplification and rule ofthumb, one can expect that 100 mW cm−3 of heat deposition is necessaryto guarantee an effective treatment.

17

As for the amount of magnetic material needed: The adequate amount varieswith the method of how the magnetic nanoparticles are introduced into thetumorous region. Direct injection allows to accumulate larger quantities ofnanoparticles at the target area and thus needs less material injected over-all. Intravascular or antibody targeting needs larger overall quantities ofnanoparticles, since their distribution to the target area is not as successful.Again as a rule of thumb, around 5-10 mg/cm3 of magnetic material shouldbe achieved.

As for the best suited material: Particles from around 10 µm and lowerare considered to be small enough. This implies that they may work asferro- or ferrimagnetic microspheres or, when even smaller, as superparam-agnetic nanoparticles. The heat generation mechanism needs in each case adifferent explanation.

Heating mechanism for FM particles: Ferromagnetic or ferrimagneticparticles show hysteresis, which allows magnetically induced heating. Theamount of heating can be found to be [1]:

PFM = µ0f ∮ HdM (12)

with

• µ0: The magnetic permeability of free space.

• f : Frequency of the alternating magnetic field.

• The loop integral is over the hysteresis loop.

This formula deliberately ignores other possible mechanism for heating (suchas eddy current heating or ferromagnetic resonance heating), since they arenegligible for these types of particles. However, it is difficult to achieveconfigurations in vivo, which can use the full capacity of this heating. Ingeneral, it should be assumed that about 25% of that heat production canactually contribute the heating of the tissue.

Heating mechanism for SPM particles: Superparamagnetic particlescan be suspended in water or a similar fluid in order to yield a magneticfluid or ferrofluid. Consequentially, a change in M slightly lags behind achange in H. The susceptibility has to be composed of a real and a complexpart: χ = χ′+χ′′. The latter, χ′′, is the out of phase component which yieldsthe heat generation [1]:

PSPM = µ0πfχ′′H2 . (13)

18

Heat absorption from the tissue is usually given in the units of W g−1.If compared, techniques using ferro- or ferrimagnetic microspheres yield amaximum possible 75 W g−1 (before the frequency becomes unsafe for theorganism), while techniques using superparamagnetic nanoparticles yield upto 209 W g−1.

3.4 MRI Contrast Enhancement

3.4.1 Basic Understanding

In short, a magnetic resonance imaging scanner, or MRI scanner, systemat-ically alters the alignment of the magnetization of particles in a body. Thisresults in rotating magnetic fields due to the nuclei. This in turn can bedetected and put together to an image of the body. A more detailed analysis[1]:

1. First, an external magnetic field B0 is applied:

Topical Review

nanoparticles suspended in water or a hydrocarbon fluid tomake a ‘magnetic fluid’ or ‘ferrofluid’ [98, 111, 112]. When aferrofluid is removed from a magnetic field its magnetizationrelaxes back to zero due to the ambient thermal energy ofits environment. This relaxation can correspond either tothe physical rotation of the particles themselves within thefluid, or rotation of the atomic magnetic moments within eachparticle. Rotation of the particles is referred to as ‘Brownianrotation’ while rotation of the moment within each particleis known as ‘Neel relaxation’. Each of these processesis characterized by a relaxation time: !B for the Brownianprocess depends on the hydrodynamic properties of the fluid;while !N for the Neel process is determined by the magneticanisotropy energy of the SPM particles relative to the thermalenergy. Both Brownian and Neel processes may be present ina ferrofluid, whereas only !N is relevant in fixed SPM particleswhere no physical rotation of the particle is possible. Therelaxation times !B and !N depend differently on particle size;losses due to Brownian rotation are generally maximized ata lower frequency than are those due to Neel relaxation for agiven size.

The physical basis of the heating of SPM particles by ACmagnetic fields has been reviewed by Rosensweig [113]. It isbased on the Debye model, which was originally developed todescribe the dielectric dispersion in polar fluids [114], and therecognition that the finite rate of change of M in a ferrofluidmeans that it will lag behind H . For small field amplitudes, andassuming minimal interactions between the constituent SPMparticles, the response of the magnetization of a ferrofluid to anAC field can be described in terms of its complex susceptibility" = " ! + i" !!, where both " ! and " !! are frequency dependent.The out-of-phase " !! component results in heat generationgiven by [113]:

PSPM = µ0#f " !!H 2, (11)

which can be interpreted physically as meaning that if Mlags H there is a positive conversion of magnetic energyinto internal energy. This simple theory compares favourablywith experimental results, for example, in predicting a squaredependence of PSPM on H [91], and the dependence of " !! onthe driving frequency [115–117].

Measurements of the heat generation from magneticparticles are usually quoted in terms of the specific absorptionrate (SAR) in units of W g"1. Multiplying the SAR by thedensity of the particle yields PFM and PSPM, so the parameterallows comparison of the efficacies of magnetic particlescovering all the size ranges [88, 111, 118–121]. It is clearfrom such comparisons that most real FM materials requireapplied field strengths of ca 100 kA m"1 or more before theyapproach a fully saturated loop, and therefore only minorhysteresis loops can be utilized given the operational constraintof ca 15 kA m"1, giving rise to low SARs. In contrast, SPMmaterials are capable of generating impressive levels of heatingat lower fields. For example, the best of the ferrofluids reportedby Hergt et al [121] has a SAR of 45 W g"1 at 6.5 kA m"1

and 300 kHz which extrapolates to 209 W g"1 for 14 kA m"1,compared to 75 W g"1 at 14 kA m"1 for the best FM magnetitesample. While all of these samples would be adequate formagnetic particle hyperthermia, importantly, it seems clear thatferrofluids and SPM particles are more likely to offer usefulheating using lower magnetic field strengths.

6. MRI contrast enhancement

6.1. Physical principles

MRI relies on the counterbalance between the exceedinglysmall magnetic moment on a proton, and the exceedinglylarge number of protons present in biological tissue, whichleads to a measurable effect in the presence of large magneticfields [122, 123]. Thus, even though the effect of a steadystate field of B0 = 1 T on a collection of protons, such asthe hydrogen nuclei in a water molecule, is so small that itis equivalent to only three of every million proton momentsm being aligned parallel to B0, there are so many protonsavailable—6.6#1019 in every mm3 of water—that the effectivesignal, 2 # 1014 proton moments per mm3, is observable. Asillustrated in figure 8, this signal can be captured by making useof resonant absorption: applying a time-varying magnetic fieldin a plane perpendicular to B0, tuned to the Larmor precessionfrequency $0 = %B0 of the protons. For 1H protons thegyromagnetic ratio % = 2.67 # 108 rad s"1 T"1, so that in afield of B0 = 1 T the Larmor precession frequency correspondsto a radio frequency field with $0/2# = 42.57 MHz. Inpractice the radio frequency transverse field is applied in apulsed sequence, of duration sufficient to derive a coherentresponse from the net magnetic moment of the protons in theMRI scanner. From the instant that the radio frequency pulse isturned off the relaxation of the coherent response is measuredvia induced currents in pick-up coils in the scanner. Theseresonantly tuned detection coils enhance the signal by a qualityfactor of ca 50–100. As shown in figure 8, for B0 parallel to

B B

m

m

timsig

nal

am

plit

ude

mxy

B0 B0

m

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timesig

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mxy

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sig

nal

am

plit

ud

e

mz

time

sig

nal

am

plit

ud

e

mz

(a) (b)

(c)

(d)

Figure 8. Illustration of magnetic resonance for a large ensemble ofprotons with net magnetic moment m in the presence of a externalmagnetic field B0. In (a) the net moment precesses around B0 at thecharacteristic Larmor frequency, $0. In (b) a second external field isapplied, perpendicular to B0, oscillating at $0. Despite being muchweaker than B0, this has the effect of resonantly exciting themoment precession into the plane perpendicular to B0. In (c) and (d)the oscillating field is removed at time zero, and the in-plane (c) andlongitudinal (d) moment amplitudes relax back to their initial values.

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A net moment then precesses around B0 at a specific Larmor frequencyω0.

2. In a second step, another magnetic field perpendicular to B0 is applied,oscillating with above mentioned precession frequency ω0:

Topical Review



PSPM = µ0#f " !!H 2, (11)







B B

m

m

timsig

nal

am

plit

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mxy

B0 B0

m

m

timesig

nal

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mxy

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sig

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sig

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mz

(a) (b)

(c)

(d)


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Even though the second magnetic field may well be much weaker thanB0, it results in a resonant excitation of the magnetic moment preces-sion into the plane perpendicular to the direction of B0.

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3. Now, the oscillating field is turned off. The following quantities canbe measured and then used to compose an image of the studied body.

The in-plane amplitude relaxes according to

mx, y =m sin(ω0t + φ)e−t/T2 (14)

with

• T2: The transverse relaxation time.

• φ: A phase constant.

This situation is shown in the following figure:

Topical Review



PSPM = µ0#f " !!H 2, (11)







B B

m

m

timsig

nal

am

plit

ude

mxy

B0 B0

m

m

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nal

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(a) (b)

(c)

(d)


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The transverse relaxation is driven by the loss of phase coherence dueto the interactions of the moments with each other. This dephasing isalso helped by local inhomogeneities, which shortens the already shortrelaxation time T2 further.

The longitudinal amplitude relaxes according to

mz =m(1 − e−t/T1) (15)

with

• T1: The longitudinal relaxation time.

The corresponding situation is shown in the following figure:

Topical Review



PSPM = µ0#f " !!H 2, (11)







B B

m

m

timsig

nal

am

plit

ude

mxy

B0 B0

m

m

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sig

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(a) (b)

(c)

(d)


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The longitudinal relaxation is a sign of energy loss of the system to itssurrounding.

20

Topical Review

the z-axis these relaxation signals are of the form:

mz = m(1 ! e!t/T1) (12)

andmx,y = m sin(!0t + ")e!t/T2 , (13)

where T1 and T2 are the longitudinal (or spin–lattice) andtransverse (or spin–spin) relaxation times, respectively, and" is a phase constant. The longitudinal relaxation reflects aloss of energy, as heat, from the system to its surrounding‘lattice’, and is primarily a measure of the dipolar couplingof the proton moments to their surroundings. The relaxationin the xy-plane is relatively rapid, and is driven by theloss of phase coherence in the precessing protons due totheir magnetic interactions with each other and with otherfluctuating moments in the tissue. Dephasing can also beaffected by local inhomogeneities in the applied longitudinalfield, leading to the replacement of T2 in equation (13) by theshorter relaxation time, T "

2 :

1T "

2= 1

T2+ #

$B0

2, (14)

where $B0 is the variation in the field brought about eitherthrough distortions in the homogeneity of the applied fielditself, or by local variations in the magnetic susceptibility ofthe system [124, 125].

6.2. MRI contrast enhancement studies

Both T1 and T "2 can be shortened by the use of a magnetic

contrast agent. The most common contrast agents currentlyused are PM gadolinium ion complexes, although agents basedon SPM nanoparticles are commercially available, such as‘Feridex I. V.’, an iron oxide contrast agent marketed byAdvanced Magnetics Inc. for the organ-specific targetingof liver lesions. The SPM particles used are magneticallysaturated in the normal range of magnetic field strengths usedin MRI scanners, thereby establishing a substantial locallyperturbing dipolar field which leads, via equation (14), to amarked shortening of T "

2 (see figure 9) along with a less markedreduction of T1 [123].

(a) (b)

time

Figure 9. Effect of magnetic particle internalization in cells on T "2

relaxation times: (a) the protons in cells tagged by magnetic particleshave a shorter T "

2 relaxation time than those in (b) untagged cells.

Iron oxide nanoparticles are the most commonly usedSPM contrast agents. Dextran coated iron oxides arebiocompatible and are excreted via the liver after the treatment.They are selectively taken up by the reticuloendothelial system,a network of cells lining blood vessels whose function is toremove foreign substances from the bloodstream; MRI contrastrelies on the differential uptake of different tissues [126]. Thereis also a size effect: nanoparticles with diameters of ca 30 nmor more are rapidly collected by the liver and spleen, whileparticles with sizes of ca 10 nm or less are not so easilyrecognized. The smaller particles therefore have a longerhalf-life in the blood stream and are collected by reticulo-endothelial cells throughout the body, including those in thelymph nodes and bone marrow [127, 128]. Similarly, suchagents have been used to visualize the vascular system [129],and to image the central nervous system [130]. It is also notablethat tumour cells do not have the effective reticuloendothelialsystem of healthy cells, so that their relaxation times are notaltered by the contrast agents. This has been used, for example,to assist the identification of malignant lymph nodes [131],liver tumours [132] and brain tumours [133].

Iron oxide nanoparticles also lend themselves toencapsulation into target-specific agents, such as a liposomethat is known to localize in the bone marrow [134]. Dendrimercoatings comprising a highly branched polymer structure thathas a high rate of non-cell-specific binding and intracellularuptake have also been used to good effect [135], as has the useof lipofection agents, normally used to carry DNA into the cellnucleus, to enable intracellular incorporation of the magneticnanoparticles into stem cells [136]. Magnetic nanoparticleshave also been utilized for the in vivo monitoring of geneexpression, a process in which cells are engineered to over-express a given gene. This process leads to the production ofincreased numbers of certain cell wall receptors, which in turncan be targeted using specially coated nanoparticles, therebyallowing a differentiation between the expressing cells andtheir surroundings [137]. Another aspect of the targeting ofcell receptors has been to selectively study cells that are in theprocess of cell death [138].

7. Discussion and future prospects

In this paper we have reviewed some basic concepts regardingthe interactions between magnetic nanoparticles and a staticor time-varying external magnetic field, and shown howthese pertain to current biomedical applications of magneticnanoparticles. We have focused in particular on magneticseparation, drug delivery, hyperthermia and MRI contrastenhancement, although these are only four of the manybiomedical applications of magnetic nanoparticles that arecurrently being explored. For example, research is beingconducted into magnetic twisting cytometry, a process in whichferromagnetic microspheres are bound to specific receptors ona cell wall. Changing the direction of an applied magnetic fieldtwists the microsphere by a measurable amount, which can thenbe related to the mechanical properties of the cell membraneand cytoskeleton [139–143]. Magnetic nanoparticles arealso being tested for tissue engineering applications, forexample, in the mechanical conditioning of cells growing inculture [144–146]. In such systems magnetic particles are

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(a)

Topical Review

the z-axis these relaxation signals are of the form:

mz = m(1 ! e!t/T1) (12)

andmx,y = m sin(!0t + ")e!t/T2 , (13)

where T1 and T2 are the longitudinal (or spin–lattice) andtransverse (or spin–spin) relaxation times, respectively, and" is a phase constant. The longitudinal relaxation reflects aloss of energy, as heat, from the system to its surrounding‘lattice’, and is primarily a measure of the dipolar couplingof the proton moments to their surroundings. The relaxationin the xy-plane is relatively rapid, and is driven by theloss of phase coherence in the precessing protons due totheir magnetic interactions with each other and with otherfluctuating moments in the tissue. Dephasing can also beaffected by local inhomogeneities in the applied longitudinalfield, leading to the replacement of T2 in equation (13) by theshorter relaxation time, T "

2 :

1T "

2= 1

T2+ #

$B0

2, (14)

where $B0 is the variation in the field brought about eitherthrough distortions in the homogeneity of the applied fielditself, or by local variations in the magnetic susceptibility ofthe system [124, 125].

6.2. MRI contrast enhancement studies

Both T1 and T "2 can be shortened by the use of a magnetic

contrast agent. The most common contrast agents currentlyused are PM gadolinium ion complexes, although agents basedon SPM nanoparticles are commercially available, such as‘Feridex I. V.’, an iron oxide contrast agent marketed byAdvanced Magnetics Inc. for the organ-specific targetingof liver lesions. The SPM particles used are magneticallysaturated in the normal range of magnetic field strengths usedin MRI scanners, thereby establishing a substantial locallyperturbing dipolar field which leads, via equation (14), to amarked shortening of T "

2 (see figure 9) along with a less markedreduction of T1 [123].

(a) (b)

time

Figure 9. Effect of magnetic particle internalization in cells on T "2

relaxation times: (a) the protons in cells tagged by magnetic particleshave a shorter T "

2 relaxation time than those in (b) untagged cells.

Iron oxide nanoparticles are the most commonly usedSPM contrast agents. Dextran coated iron oxides arebiocompatible and are excreted via the liver after the treatment.They are selectively taken up by the reticuloendothelial system,a network of cells lining blood vessels whose function is toremove foreign substances from the bloodstream; MRI contrastrelies on the differential uptake of different tissues [126]. Thereis also a size effect: nanoparticles with diameters of ca 30 nmor more are rapidly collected by the liver and spleen, whileparticles with sizes of ca 10 nm or less are not so easilyrecognized. The smaller particles therefore have a longerhalf-life in the blood stream and are collected by reticulo-endothelial cells throughout the body, including those in thelymph nodes and bone marrow [127, 128]. Similarly, suchagents have been used to visualize the vascular system [129],and to image the central nervous system [130]. It is also notablethat tumour cells do not have the effective reticuloendothelialsystem of healthy cells, so that their relaxation times are notaltered by the contrast agents. This has been used, for example,to assist the identification of malignant lymph nodes [131],liver tumours [132] and brain tumours [133].

Iron oxide nanoparticles also lend themselves toencapsulation into target-specific agents, such as a liposomethat is known to localize in the bone marrow [134]. Dendrimercoatings comprising a highly branched polymer structure thathas a high rate of non-cell-specific binding and intracellularuptake have also been used to good effect [135], as has the useof lipofection agents, normally used to carry DNA into the cellnucleus, to enable intracellular incorporation of the magneticnanoparticles into stem cells [136]. Magnetic nanoparticleshave also been utilized for the in vivo monitoring of geneexpression, a process in which cells are engineered to over-express a given gene. This process leads to the production ofincreased numbers of certain cell wall receptors, which in turncan be targeted using specially coated nanoparticles, therebyallowing a differentiation between the expressing cells andtheir surroundings [137]. Another aspect of the targeting ofcell receptors has been to selectively study cells that are in theprocess of cell death [138].

7. Discussion and future prospects

In this paper we have reviewed some basic concepts regardingthe interactions between magnetic nanoparticles and a staticor time-varying external magnetic field, and shown howthese pertain to current biomedical applications of magneticnanoparticles. We have focused in particular on magneticseparation, drug delivery, hyperthermia and MRI contrastenhancement, although these are only four of the manybiomedical applications of magnetic nanoparticles that arecurrently being explored. For example, research is beingconducted into magnetic twisting cytometry, a process in whichferromagnetic microspheres are bound to specific receptors ona cell wall. Changing the direction of an applied magnetic fieldtwists the microsphere by a measurable amount, which can thenbe related to the mechanical properties of the cell membraneand cytoskeleton [139–143]. Magnetic nanoparticles arealso being tested for tissue engineering applications, forexample, in the mechanical conditioning of cells growing inculture [144–146]. In such systems magnetic particles are

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(b)

Figure 8: A qualitative graph of the changed relaxation time. Figure 8(a):Cells tagged with magnetic nanoparticles and a short relaxation time. Figure8(b): Cells without any enhancement and thus the original relaxation time.Source: [1].

3.4.2 Contrast Enhancement trough SPM Particles

How do magnetic nanoparticles come into play? In short, nanoparticles at-tached to a cell or cell compound can shorten both the transverse relaxationtime T1 and the longitudinal relaxation time T2. Figures 8(a) & 8(b) showthe qualitative effect of superparamagnetic nanoparticles on the relaxationtime T2.

Due to the fact that different tissues take up the nanoparticles differently,an enhancement between the different tissues is achieved and the contrastbetween them is higher. Also, it has been shown that some tumour cells donot have their relaxation time altered and hence can be identified throughthis characteristics.

3.5 Summary

As of 2003, the status of the discussed techniques is as follows:

• Magnetic separation via protein and cell tagging is available.

• MRI contrast enhancement techniques are available as well.

• Drug delivery was successfully tested with animals, but so far not withhumans.

• Hyperthermia treatments are not yet available for humans.

21

These fields of study are prove that there is a long way between successfulin vitro results and successful in vivo results.

4 Nanoparticle Magnetism

This section presents the paper “Nanoparticle magnetism”. The author ar-gues that with the high interest in nanoparticle technology and applications,it seems reasonable to be able to understand the underlying mechanics andtheories as well as possible. With magnetism of nanoparticles as a prominentdirection in nanotechnology, they present their findings in that field. Pub-lished around six years later than the previous paper, this paper presentsnew material on the following topics [2]:

• Dynamic spin fluctuations and spin reversal of uniaxial nanoparticles.

• The intrinsic spin structure of nanoparticles as influenced by surfaceand finite-size effects.

• Core versus surface contributions to the total magnetic behaviour ofthe nanoparticles.

Quite a substantial part of the paper’s results have already been presented inthe previous sections in order to explain the mechanisms of superparamag-netism. The rest of the results shall be presented in the upcoming sections.

4.1 Intrinsic Spin Structure and Dynamic Spin Relaxation

Experimental evidence suggests that the simple model used so far doesnot cover the true extent of complexity of the spin structure in magneticnanoparticles. The unexplained properties are partly believed to arise fromthe comparatively large fraction of atoms on the nanoparticle’s surface. Atthe surface, the crystal structure gets abruptly interrupted. Consequentially,this effect weights much more for particles with a large surface to volumeratio.

One property that is very sensitive to the surface structure is the particle’smagnetic anisotropy. The anisotropy constant influences the energy barrier∆E = KV , which in turn changes the relaxation time. While in bulk ma-terial, magnetocrystalline anisotropy is the deciding factor, in nanoparticlessurface effects come into play and change the overall anisotropy constant Kby up to two orders of magnitude. K shall thus be adapted to incorporatethe diameter D of a particle:

K =Kc +6Ks

D(16)

with

22

Nanoparticle magnetism 441

Figure 3 Schematic depiction of disorder encountered at thesurfaces of grains and grain boundaries of nanostructured mate-rials [Reprinted by permission, H. Gleiter, Acta. Mater. 48 (2000)1, Ref. [39]].

unusually large surface to volume ratio in nanosized materi-als provides for the stabilization of artificial structures withnovel physical properties. With diminishing particle size thesurface to volume ratio increases, rendering strongly size-dependent behavior.

One property that shows extreme sensitivity to surfacestructure is the particle’s magnetic anisotropy, which gov-erns spin relaxation time and coercivity values. In the bulk,crystal field splitting induced magnetocrystalline anisotropyis the primary source of anisotropy. In small particles,additional contributions due to surface effects and surfacestrain become dominant. In magnetic nanoparticles valuesof magnetic anisotropy have been observed up to two ordersof magnitude larger compared to the magnetocrystallineanisotropy of the bulk [40,41]. For spherical particles ofdiameter D the empirical formula of Eq. (6) [40,42—45] hassatisfactorily interpreted many experimental results:

K = Kc + 6Ks

D(6)

Here Kc is the magnetocrystalline anisotropy of the coreof the particle characteristic of the material, and Ks

is the surface anisotropy characteristic of the particle,both anisotropies treated as uniaxial. The above equationassumes a simple additive effect of the surface ignoring anycross-linking terms and predicts effective total anisotropiesthat scale as 1/D, as reported in Fig. 4 [43] for small metaliron particles in the range of 2—7 nm diameter.

Magnetic particles are, thus, modeled as two-phase sys-tems composed of a highly crystalline core surrounded by adisordered surface layer. Vacancies, broken bonds and lat-tice strain at the surface produce not only atomic disorderbut also spin frustration which destabilizes the collinearspin arrangement of the Stoner—Wohlfarth model at the sur-face, producing various canted spin structures (Fig. 5). Thiscomplex intrinsic spin structure is supported by both theo-retical and experimental studies in small particle systems,as discussed below. Consequences are reduced Ms, lack of

Figure 4 Total effective anisotropy energy constant formetallic iron particles as a function of reciprocal particle diam-eter [Reprinted by permission from F. Bødker, S. Mørup and S.Lideroth, Phys. Rev. Lett. 72 (1994) 282, Ref. [43]].

magnetic saturation even in large magnetic fields [46—49],and hysteresis loop shifts in antiferromagnetic nanoparti-cles due to exchange-bias between the core and surfacemagnetization [50].

Mössbauer spectroscopic studies have provided extensiveexperimental data on various nanoparticle systems pertain-ing to their magnetic anisotropies and intrinsic spin structure[2]. The Mössbauer effect detects the nuclear Zeeman split-ting caused by the internal magnetic field at the site of theiron nucleus. An example to demonstrate the methodologyis shown in Fig. 6(a) for the biomineral core of ferritin, theiron storage protein where antiferromagnetic ferrihydritenaturally sequesters within the interior cavity of a proteinnanotemplate of 7 nm interior and 12 nm exterior diameters[51,52]. The thick protein coat insures magnetic isolationof the particles. At 4.2 K two magnetic sites are resolvedassociated with core and surface atoms, respectively, withdifferent internal magnetic hyperfine fields of Hc ! 495 kOeand Hs ! 450 kOe, as measured by the overall splitting ofthe external lines of each magnetic subspectrum (Fig. 6(a)).

Figure 5 (a) Schematic representation of a spherical particlewith uniform magnetization according to the Stoner and Wohl-farth model: all spins are collinear and rotate in unison. (b)Schematic representation of two-phased particle with differentcore and surface magnetization. Surface spins are canted rela-tive to the core’s magnetization and are subject to low energyexcitations (see text).

(a)

Nanoparticle magnetism 441

Figure 3 Schematic depiction of disorder encountered at thesurfaces of grains and grain boundaries of nanostructured mate-rials [Reprinted by permission, H. Gleiter, Acta. Mater. 48 (2000)1, Ref. [39]].

unusually large surface to volume ratio in nanosized materi-als provides for the stabilization of artificial structures withnovel physical properties. With diminishing particle size thesurface to volume ratio increases, rendering strongly size-dependent behavior.

One property that shows extreme sensitivity to surfacestructure is the particle’s magnetic anisotropy, which gov-erns spin relaxation time and coercivity values. In the bulk,crystal field splitting induced magnetocrystalline anisotropyis the primary source of anisotropy. In small particles,additional contributions due to surface effects and surfacestrain become dominant. In magnetic nanoparticles valuesof magnetic anisotropy have been observed up to two ordersof magnitude larger compared to the magnetocrystallineanisotropy of the bulk [40,41]. For spherical particles ofdiameter D the empirical formula of Eq. (6) [40,42—45] hassatisfactorily interpreted many experimental results:

K = Kc + 6Ks

D(6)

Here Kc is the magnetocrystalline anisotropy of the coreof the particle characteristic of the material, and Ks

is the surface anisotropy characteristic of the particle,both anisotropies treated as uniaxial. The above equationassumes a simple additive effect of the surface ignoring anycross-linking terms and predicts effective total anisotropiesthat scale as 1/D, as reported in Fig. 4 [43] for small metaliron particles in the range of 2—7 nm diameter.

Magnetic particles are, thus, modeled as two-phase sys-tems composed of a highly crystalline core surrounded by adisordered surface layer. Vacancies, broken bonds and lat-tice strain at the surface produce not only atomic disorderbut also spin frustration which destabilizes the collinearspin arrangement of the Stoner—Wohlfarth model at the sur-face, producing various canted spin structures (Fig. 5). Thiscomplex intrinsic spin structure is supported by both theo-retical and experimental studies in small particle systems,as discussed below. Consequences are reduced Ms, lack of

Figure 4 Total effective anisotropy energy constant formetallic iron particles as a function of reciprocal particle diam-eter [Reprinted by permission from F. Bødker, S. Mørup and S.Lideroth, Phys. Rev. Lett. 72 (1994) 282, Ref. [43]].

magnetic saturation even in large magnetic fields [46—49],and hysteresis loop shifts in antiferromagnetic nanoparti-cles due to exchange-bias between the core and surfacemagnetization [50].

Mössbauer spectroscopic studies have provided extensiveexperimental data on various nanoparticle systems pertain-ing to their magnetic anisotropies and intrinsic spin structure[2]. The Mössbauer effect detects the nuclear Zeeman split-ting caused by the internal magnetic field at the site of theiron nucleus. An example to demonstrate the methodologyis shown in Fig. 6(a) for the biomineral core of ferritin, theiron storage protein where antiferromagnetic ferrihydritenaturally sequesters within the interior cavity of a proteinnanotemplate of 7 nm interior and 12 nm exterior diameters[51,52]. The thick protein coat insures magnetic isolationof the particles. At 4.2 K two magnetic sites are resolvedassociated with core and surface atoms, respectively, withdifferent internal magnetic hyperfine fields of Hc ! 495 kOeand Hs ! 450 kOe, as measured by the overall splitting ofthe external lines of each magnetic subspectrum (Fig. 6(a)).

Figure 5 (a) Schematic representation of a spherical particlewith uniform magnetization according to the Stoner and Wohl-farth model: all spins are collinear and rotate in unison. (b)Schematic representation of two-phased particle with differentcore and surface magnetization. Surface spins are canted rela-tive to the core’s magnetization and are subject to low energyexcitations (see text).

(b)

Figure 9: Figure 9(a) shows a particle with uniform magnetization, a modelwhich served us up to now quite well. Figure 9(b) shows a particle withdifferent core and surface magnetization. Source [2].

• Kc: The magnetocrystalline anisotropy constant of the core.

• Ks: The surface anisotropy constant.

The larger a particle, the less important the second factor Ks. Althoughthis ignores interferences between the anisotropies, it yields quite acceptableresults.

Consequentially, it makes sense to regard the magnetic particles as hav-ing a crystalline core surrounded by a disordered surface (see figure 9). Theconsequences of this model are (among others) [2]:

• Reduced magnetization saturation Ms.

• Lack of magnetic saturation even in large magnetic fields.

• Hysteresis loop shifts in antiferromagnetic nanoparticles.

Mossbauer spectroscopy was successful at proving this newly introducedmodel. It uses the Zeeman splitting caused by the internal magnetic field.Figure 10 shows the results for a measurement of “iron ferrihydrite nanopar-ticles grown within horse spleen apo-ferritin nanotemplates measured at 4.2K” [2]. Strong indications for two phase magnetic particles can be seen.

As a side note: This temperature is well below the blocking temperatureTB. In other words, this particle is not in a superparamagnetic state at themoment, but rather in a blocked state.

Figure 11 shows the temperature dependence of the spectral lines. Thehigher the temperature, the more important become the spin reversals,

23


Figure 6 (a) Mössbauer spectra of iron ferrihydrite nanopar-ticles grown within horse spleen apo-ferritin nanotemplatesmeasured at 4.2 K. Two magnetic subsites are resolved associ-ated with core and surface iron atoms. (b) Core/surface modelof the iron biomineral core of ferritin [Reprinted by permis-sion from R.A. Brooks, J. Vymazal, R.B. Goldfarb, J.W. Bulte, P.Aisen, Magn. Res. Med. 40 (1998) 227, Ref. [53]].

The iron site with larger magnetic field exhibits sharperabsorption lines indicating a highly crystalline core, whilethe smaller hyperfine field site exhibits broadened absorp-tion lines indicating a more disordered or amorphous stateat the surface. A two-phase model of the ferritin biomineralcore depicted in Fig. 6(b) was originally proposed by Brookset al. [53] on the basis of relaxometry measurements.

Fig. 7 shows the full spectral profile of reconstitutedhorse spleen ferritin in the temperature range from 4.2to 80 K [54]. As temperature increases above 4.2 K, thespectra broaden due to the onset of dynamic spin relax-ation processes prior to full magnetization reversals atthermal energies above the superparamagnetic energy bar-rier KV (Fig. 2). Simultaneously, the magnitudes of theobserved hyperfine fields decrease, prior to their collapsedue to superparamagnetism at high temperatures and theappearance of a quadrupole doublet. The reduction in themagnitude of the magnetic hyperfine field is due to theprecession of the particle’s magnetization vector aboutits anisotropy axis, at temperatures insufficient to inducespin reversals, as proposed by Mørup and Topsøe in theircollective magnetic excitation (CME) model [55], whichsuccessfully describes spin dynamics below the blockingtemperature, where the magnetization vector is trappedor blocked within a single potential well. The tempera-ture dependence of the reduced hyperfine magnetic fields,

H/H0, is shown in Fig. 8. Here, H = Hhf(T) and H0 = Hhf(4.2 K),assumed to be the saturation hyperfine field as T ! 0. Forthe interior iron sites of the core of the particle, the temper-ature dependence of the reduced hyperfine magnetic fieldsis consistent with the CME model of Mørup and Topsøe [55],described by Eq. (7):

H

H0= 1 " kT

2KV(7)

A maximum of 15% diminution in hyperfine field is expectedthrough this process, before the spectrum collapses to aparamagnetic doublet due to superparamagnetism. The pre-cipitous collapse of the reduced hyperfine field at surfacesites observed in Fig. 8 indicates the presence of additionalsurface spin excitation modes, consistent with theories ofmulti-spin nano-magnet systems, where surface anisotropiesintroduce spin canting and a greater complexity in thepotential energy landscape at the surface [56].

The temperature at which the spectra change fromprimarily magnetic (six-line absorption spectra) to paramag-netic (two-line absorption spectra) determines the blockingtemperature, TB, of the ensemble of particles in the sam-ple. For the sample of Fig. 7, TB is estimated to be about40 K, where the absorption area of the spectrum is com-

Figure 7 Mössbauer spectra of lyophilized, in vitro reconsti-tuted horse spleen ferritin at various temperatures. Solid lines(black) through the experimental points are least square fits,to a superposition of iron subsites: purple, interior core sites;green, surface sites; red, superparamagnetic sites [from Ref.[54]].

(a)






H

H0= 1 " kT

2KV(7)




(b)

Figure 10: Figure 10(a): “The Mossbauer spectra of iron ferrihydritenanoparticles grown within horse spleen apo-ferritin nanotemplates mea-sured at 4.2 K” [2]. The highly crystalline core with a larger magnetic fieldshows sharper and deeper absorption lines. The amorphous surface showsbroadened and less deep absorption lines. Figure 10(b): A model accordingto the spectra: A large protein shell to protect the magnetic interior. Themagnetic part consists not only of an ordered core, but also of an amorphoussurface. Source: [2]

which are so characteristic for superparamagnetism. An additional effectwhich reduces the strength of the hyperfine magnetic field, happens wellbefore the field collapses due to superparamagentic behaviour. It is the ef-fect that the magnetization vector starts to precess around the easy axisdue to rising thermal energy. The change from primarily magnetic spectra(six absorption lines) to superparamagnetic spectra (two absorption lines)is characterized by the already introduced blocking temperature TB (for thesample in figure 11 it is around 40 k).

Different measurement techniques can be used to determine the blockingtemperature TB of a specific material. This in turn leads to the material’sanisotropy constant K. A general approach is described in the next fewsteps:

1. A sample is cooled without any magnetic field. Since the two min-ima (with orientations in opposite directions) are equally likely to bepopulated, the overall magnetization should be zero.

2. A small magnetic field is applied, so that it is not sufficient for themagnetic moments to fully align with the field.

3. Increasing the temperature allows the magnetic moments to have morethermal energy and hence get aligned along the external magnetic field.

24






H

H0= 1 " kT

2KV(7)




Figure 11: This figure shows the Mossbauer spectra of “lyophilized, in vitroreconstituted horse spleen ferritin at various temperatures” [2]. Green linesrefer to surface spectral lines, purple to core spectral lines and red to super-paramagnetic site spectral lines. The black line is a superposition of all thesites. Source: [2].

25

4. There is a maximal magnetization before the heat introduces randomorientation. This maximum determines the blocking temperature TB.

5. Since this technique was performed within a certain measurement timeτm, another technique with a different τm has to be used in order todetermine the anisotropy constant K and the parameter τ0.

A quick side note on results obtained from Monte Carlo simulations: MonteCarlo simulations for γ-Fe2O3 particles have suggested that surface contri-butions to the magnetization of particles with 8.3 nm diameter lie around43%, while the ones for particles with 2.5 nm diameter lie around almost95%. They also found that different hysteresis loops have to be expected forthe surface compared to the core of the nanoparticle. The differences can bepartly explained through the presence of spin disorder and spin frustrationsat the surface, which makes it easier to reverse a surface spin.

4.2 Applications: Current Trends and Future Directions

On the contrary to the first paper, this paper also includes applicationsoutside of biomedicine and delves into possible future fields of study:

• Advanced magnetic recording media: They need a well ordered twodimensional nanoparticle array. One of the difficulties of such mediais to keep them well ordered. As soon as the thermal energy gets toohigh, spin reversal becomes an (unwanted) factor, which diminishesthe storage capabilities of the media.

• Magneto-resistive sensors & spin electronics: Spin up-up particlesshow a different resistance compared to (for example) spin up-downparticles. Sending currents through these resistances can be used todetect the spin direction of particles. If the spins can be controlledwell enough, they could be incorporated into existing semiconductortechnology. This would enhance and create new functionalities, notachievable by today’s electronics.

• Biomedical applications: This field is equally mentioned, but alreadywell discussed in the previous section dealing with the first paper.

• Very dense spin systems under special conditions may form spin-glasslike phases with very complex energy landscapes. This effect arisesdue to ferromagnetic and antiferromagnetic interactions, also knownas spin frustrations. There is a so called spin-glass-freezing tempera-ture, below which the particles show mentioned characteristics. Addi-tionally, they change their behaviour, the longer they stay below thefreezing temperature (so called aging). This field promises interestingfindings, but needs further study.

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References

[1] Q. A. Pankhurst, J. Connolly, S. K. Jones and J- Dobson, Applicationsof magnetic nanoparticles in biomedicine, J. Phys. D: Appl. Phys. 36(2003) R167-R181 (18th of June 2003).

[2] Georgia C. Papaefthymiou, Nanoparticle magnetism, Nano Today(2009) 4, 438-447 (11th of September 2009).

[3] Wikipedia.org, English Magnetic Anisotropy [Online], 8th of December2012,

http://en.wikipedia.org/wiki/Superparamagnetism

[4] Wikipedia.org, English Magnetic Anisotropy [Online], 8th of December2012,

http://en.wikipedia.org/wiki/Magnetic_anisotropy

[5] Wikipedia.org, English Ferrimagnetism [Online], 8th of December2012,

http://en.wikipedia.org/wiki/Ferrimagnetism

[6] Wikipedia.org, English Antiferromagnetism [Online], 8th of December2012,

http://en.wikipedia.org/wiki/Antiferromagnetism

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Documents

Superparamagnetism : Theory and Applications · Superparamagnetism : Theory and Applications-Discussion of Two Papers on Magnetic Nanoparticles Manuel Benz December 14, 2012