Oddelek za fiziko

Seminar Ib - 1. letnik II. stopnja

Ferromagnetic liquid crystals

Author: Luka Pirker

Mentor: Doc. Dr. Alenka Mertelj

Ljubljana, October 2014

Abstract

In this seminar I will present ferromagnetic liquid crystals and their properties. Ferromag-netic liquid crystals have the characteristics of ferromagnets as of liquid crystals. Their existencewas predicted over 40 years ago and, until recently, researchers were unable to experimentallyobserve them.

Contents

1 Introduction 1

2 Liquid crystals 1

3 Ferrofluids and ferromagnetism in liquids 2

4 Magnetic platelets in a nematic liquid crystal 3

5 Response to magnetic field 4

6 Free energy density 9

7 Conclusions 10

1 Introduction

Liquid crystals have properties between those of conventional liquid and those of a solid crystal.A liquid crystal may flow like an ordinary liquid, but its molecules may arrange themselves as ifthey were in a crystal. In 1888, Friedrich Reinitzer, an Austrian botanical physiologist observedthat cholesteryl benzoate did not melt in the same way as other compounds he was studying. Heobserved that it has two melting points, one at 145.5◦C where it melts in a cloudy liquid, and thesecond at 178.5◦C, where it melts again and the cloudy liquid becomes clear [1]. He also foundthat the new material has the ability to rotate the polarization of light. He wrote to physicist OttoLehmann for help. Lehmann examined the cloudy fluid and reported seeing crystallites. He namedthe new material liquid crystals and continued studying them. The term liquid crystals describes theliquid properties of the material and their crystal-like optical properties. However, liquid crystalswere not popular among scientists at the time. It took almost 80 years before scientists restartedstudying them. They quickly became a topic of research in many laboratories around the world. Inthe years that followed many different properties of liquid crystals were discovered that theoreticalmodels predicted.In 1970 Francoise Brochard-Wyart and Pierre-Gilles de Gennes proposed that a colloidal suspensionof ferromagnetic particles in nematic liquid crystals could form macroscopic ferromagnetic phasesat room temperatures. Many researchers have tried to make such liquid crystals, but failed untilrecently.

2 Liquid crystals

Liquid crystals are materials made of anisotropic molecules. There are many different types ofliquid crystals. In this seminar I will write only about nematic liquid crystals that are usuallycomposed of rod-like molecules. These molecules have an orientational order that is described by aunit vector called the director n, that represents the average molecular orientation in the nematicphase. Because there is no physical polarity along the director axis, vectors n and −n are equiva-lent, n ≡ −n. The orientation of the molecules can be controlled by external electric or magneticfields or by preparing the confining surfaces so that the director at the surface has a predefined

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direction. Nematic liquid crystals have two liquid phases. In the isotropic phase molecules do nothave a defined direction, but cooling a nematic liquid crystal under a certain temperature Tiso→nem,molecules orient themselves along the director, Figure 1.

(a) (b)

Figure 1: (a) A representation of the isotropic phase of a liquid crystal. [2] A representation of anematic phase in a liquid crystal with rod-like molecules. [2]

Introducing anisotropic particles in a nematic liquid crystal causes a distortion of the director,Figure 2. The deformation of the director field depends on the surface anchoring and on the shapeof the particle. An elongated rod-like particle with surface anchoring parallel to the particle’ssurface and to the particle’s long axis will orient itself in the nematic phase with its long axisparallel to n0, where n0 is the average director orientation, Figure 2 a. If the nematic directorat the particle surface is perpendicular to the surface, then the particle orients with its long axisperpendicular to the director n0, Figure 2 b. A disk with perpendicular anchoring orients with itsaxis along n, Figure 2 c.

(a) (b) (c)

Figure 2: A schematic presentation of the distortion of the director around a anisotropic particle ina nematic liquid crystal. A rod-like particle with the surface anchoring: (a) parallel with its surfaceand long axis, (b) perpendicular to the surface. (c) A disk with perpendicular surface anchoring.[3]

3 Ferrofluids and ferromagnetism in liquids

Ferromagnetic ordering was already experimentally observed in two liquids. In 1978 ferromag-netism was observed in superfluid 3He, and in 1997 ferromagnetism and ferromagnetic domains

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were observed in undercooled alloys at temperatures above 1,000 K [2].Ferromagnetism is a phenomenon where under a certain temperature, known as the Curie tem-perature Tc, the material exhibits spontaneous magnetization M in the absence of an externalmagnetic field. Magnetization curves, that is, magnetization as a function of an external field B,show hysteresis.

Figure 3: (a) Monodomain nanoparticles are randomly oriented in a ferrofluid in absence of anexternal magnetic field B. [2] (b) Particles orient along B. [2]

Ferrofluids are not ferromagnetic, they are composed of ferromagnetic monodomain nanoparti-cles that act as nanomagnets. Ferrofluids are superparamagnetic liquids which become stronglymagnetized in the presence of a magnetic field. In the absence of an external magnetic field, theaverage magnetic interaction between two nanoparticles is smaller than thermal energy, and themagnetic moments of the particles are randomly oriented within the fluid, Figure 3. So ferrofluidsdo not have macroscopic spontaneous magnetization in the absence of an external magnetic fieldand thus are not ferromagnetic. When we apply an external magnetic field, magnetic momentsof the nanoparticles orient along the external magnetic field. The magnetic interaction betweenthe particles becomes larger than kBT. Because the nanomagnets attract each other, if they areoriented in the same way, chaining of the particles occurs, which leads to an increase of viscosityof ferrofluids [4].Ferromagnetic nanoparticles in the isotropic phase of a liquid crystal behave as any other ferrofluid.In the nematic phase, as explained before, anisotropic particles adopt a certain orientation. If theyhave magnetic moments pinned to their shape, the nematic phase will also orient magnetic mo-ments. Because nematic phase is non-polar (n ≡ −n), this is not enough to induce ferromagneticordering of the moments, Figure 4b. For that, strong enough magnetic interaction between theparticles is needed.

4 Magnetic platelets in a nematic liquid crystal

It has been shown that nanometre-sized ferromagnetic platelets with perpendicular surface anchor-ing can be used to make a stable ferromagnetic phase in nematic liquid crystal [2]. A stable nematicsuspension is the result of the balance between nematic-mediated force and the magnetic interac-tion between particles. When particles are put in a liquid crystal, the direction of the directoraround them is changed, as seen on Figure 5. Other particles are affected by the distortion of thedirector and the interaction between them can be repulsive or attractive. The symmetry of thedeformation determines if the nematic force is dipolar or quadrupolar. In this case the nematicforce is quadrupolar, and gives the strongest attraction when the line joining two particles makes

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(a) (b)

Figure 4: (a) Ferrofluid on a glass surface in a magnetic field that is produced by a magnet. [5] (b)Platelet nanoparticles in a nematic liquid crystal. If the magnetic interaction is not strong enough,magnetic moments (red arrows) will be randomly oriented. [2]

an angle of about 50◦ with respect to n0.A stable ferromagnetic phase in nematic liquid crystal can not be made with rod-shaped particles.The deformation of the nematic field, using rod-shaped particles, is small and the nematic interac-tion is too weak to prevent aggregation.Because the vectors n and −n are equivalent, the ferromagnetic phase will not appear unless themagnetic interaction between magnetic dipoles is strong enough and such that magnetic momentsof the particles orient ferromagnetically, that is, in the same direction. In Figure 5 b there is aschematic representation of the magnetic field and the distortion of the director. It turns out,that the nematic quadrupolar interaction combined with sufficient magnetic interaction gives aferromagnetic phase. Spontaneous magnetization is along n0 which can be seen with polarizedmicroscopy imaging in an external magnetic field.A suspension of magnetic platelets in a liquid crystal in the isotropic phase was used to fill planarglass cells. The cells were prepared so that the director was parallel with the interior surface of thecell, Figure 6. To achieve an optimal sample, the cell must be quenched into the nematic phase.Quenched samples remain stable and no additional aggregation occurs even after several monthsor when exposed to external magnetic fields. If the cell is cooled slowly, aggregates form. Themagnetization in the cell is also parallel with the glass surface.

5 Response to magnetic field

Samples were examined using polarizing microscopy. The sample is put between a polarizer andan analyser, Figure 6 b. The polarizer and analyser are optical filters that pass light of a specificpolarization. When they are crossed at an angle of 90◦, no light can go through and a dark pictureis obtained. When the sample is put between the filters and the external magnetic field B is 0,once again a dark image is obtained. This means that no light goes through the analyser. Thisis because the director is aligned within the sample, and it can not change the polarization of thetransmitted light. When a magnetic field parallel to the director is applied, dark and bright domains

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(a) (b)

Figure 5: (a) TEM image of magnetic platelets. [2], (b) A schematic representation of the ferro-magnetic liquid crystal. Blue lines represent the distortion of the director, orange the magneticfield, red horizontal lines represent magnetic platelets and red arrows the direction of magneticmoments. [2]

(a) (b)

Figure 6: (a) A schematic representation of the cell filled with a suspension of magnetic platelets ina liquid crystal. [6], (b) A schematic representation of the experiment using polarizing microscopy.[2]

are observed, Figure 7 b,c. This is because the sample is made out of domains that have oppositemagnetization. The domains in which the magnetization points in the same direction as the externalmagnetic field, will appear dark. The magnetic platelets will point in the same direction as beforeand thus the director around them will not change. The domains, in which the magnetization

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points in the opposite direction as the external magnetic field, will appear bright. This is becausethe magnetic platelets within the sample will rotate because their magnetic moments want to alignwith the external magnetic field, Figure 8. At the cell surface the director will not change becausethe surface anchoring is too strong. This will cause the director to twist which will cause a changein the polarization of the transmitted light. Some of that light will go through the analyser and wewill observe it as a bright area. If the field is reversed, bright domains become dark and vice versa,Figure 7 c. If a field perpendicular to the director is applied, domain walls become visible, Figure7 d. The alteration of light properties with a magnetic field is called a magneto-optic effect. Thisexperiment shows that spontaneous magnetization is present along the director and that the twotypes of domains have opposite magnetization.

Figure 7: Polarizing microscopy images of a polydomain sample in an external magnetic field. Ashows the direction of the analyser and P the direction of the polarizer. The scale bar in thefirst image is 40 µm. When an external magnetic field parallel with n is applied, dark and brightdomains are observed. Dark domains become bright when the field is reversed and previously darkdomains become bright. When the external field is perpendicular to n, the domain walls are visible.[2]

Figure 8: A scheme showing two domains with opposite magnetization. When there is no externalmagnetic field, no light is transmitted. When an external magnetic field parallel with n is applied,the director in one of the domains twists. This causes a change in the polarization of transmittedlight, and is visible as a bright area. [2]

Monodomain samples can also be created by quenching from the isotropic to the nematic phase inan external magnetic field parallel to the director. Magnetization curves of a monodomain sampleare obtained using a vibrating sample magnetometer, Figure 9.

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(a) (b)

Figure 9: (a) A scheme of a vibrating sample magnetometer. [7] (b) LakeShore 7400 Seriesvibrating-sample magnetometer used to measure the magnetization curve. [8]

The sample is placed in a uniform magnetic field and then physically vibrated in a sinusoidal patternusing a piezoelectric material. Stationary pickup coils are mounted on the poles of the electromag-net. The change in magnetic flux originating from the vertical movement of the magnetized sampleinduces a voltage Uind in the coils. The induced voltage can be written as

Uind = −∂φ∂t, (1)

Where φ is the magnetic flux. For the pickup coils with a flat surface A and n windings, one canwrite

Uind = −nA∂B

∂t, (2)

Where B is the magnetic field density. For a sample with magnetization M in a homogeneousmagnetic field H0, the magnetic field density can be written as

B = µ0H0 + µ0M. (3)

The magnetization M is defined as the density of magnetic dipole moments in the sample. In aconstant magnetic field H0 we have

∂B

∂t= µ0

∂M

∂t. (4)

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From this we can see that the induced voltage is proportional to the magnetic moment of thesample. By measuring it as a function of the external magnetic field, a magnetization curve can beobtained.The magnetization curve of a monodomain sample was measured. When the external field is ap-plied in the same direction as the magnetization of the sample, the magnetization does not changebecause the magnetic moments of all particles are already oriented in this direction. When thefield is applied in the opposite direction, magnetization along the director starts to decrease. Atthe coercive external magnetic field, the magnetization changes direction and at larger magneticfields it saturates. The absolute value of saturated magnetization is the same as at the beginning.This means that all platelets have rotated for 180◦. When the field is again reversed the samplemagnetization returns at its initial value and a magnetic hysteresis is observed. At low concen-trations of the particles, the hysteresis is asymmetric because the director at the cell surface ispinned, and so magnetization cannot completely switch in the external magnetic field. For largerconcentrations, the magnetization and director reverse also at the surface and a hysteresis curveis observed. The magnetization and director reversal at the surface happens by motion of surfacedomain walls. The surface domain walls are seen by polarizing microscopy as white lines, Figure 11.

Figure 10: The magnetization curve at different concentrations c of ferromagnetic platelets. [2]

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Figure 11: Sequence of images showing the complete switching of a monodomain sample. Thereare two white lines, one for each surface of the sample. [2]

6 Free energy density

Nematic liquid crystals, e.g. 5CB, have a very small magnetic anisotropy χa=1.6 10−6, where χa isthe difference of magnetic susceptibility, parallel and perpendicular to n. This means that magneticcoupling of the liquid crystal with the external magnetic field is very weak. In a ferromagnetic liquidcrystal, the orientation of n is coupled to the orientation of platelets, i.e. magnetic moments. Sowhen an external magnetic field is applied, it reorients the platelets and consequently also theorientation of n is affected. In the Landau-de Gennes description, the free energy density f offerromagnetic liquid crystals can be written as:

f = fnem +α

2M2 +

β

4M4 − µ0M · H − 1

2γµ0(n · M)2 − 1

2χaµ0(n · H)2, (5)

where fnem is the free energy density of nematic phase [4]. The following three terms, α2M

2 +β4M

4 − µ0M ·H, give the magnetic free energy density, with µ0 being vacuum permeability, α andβ the Landau expansion coefficients describing the ferromagnetic transition, and H the externalmagnetic field. The term 1

2γµ0(n · M)2 describes the coupling of the nematic director with themagnetization M , where γ is a constant. The last term in the equation, 1

2χaµ0(n · H)2, describesthe coupling of the nematic director with the external magnetic field. The coupling constant γ isaround 100 and is 8 orders of magnitude larger than magnetic anisotropy χa [2]. Consequently,ferromagnetic liquid crystals are very sensitive to small magnetic fields. Constant γ is obtained bymeasuring the threshold field Bc at which the reversal of M begins. The threshold field is writtenas

Bc = γπµ0KMs

Kπ2 + γµ0M2s d

2, (6)

where Ms is spontaneous magnetization, K elastic constant and d the thickness of the sample.Measured Bc is around 1mT which gives an estimate for γ of 100 [2].

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7 Conclusions

Over 40 years, researchers have struggled to experimentally realize ferromagnetic liquid crystals.Ferromagnetic liquid crystals have the properties of ferromagnets as well as the properties of nematicliquid crystals. Monodomain and polydomain samples can be obtained. Both respond to an externalmagnetic field as expected for a ferromagnet. The new material switches at very small magneticfields which may lead to new magneto-optic devices. Mixing ferromagnetic platelets in a chiral orsmectic liquid crystal could give new magnetic phenomena in complex fluids.

References

[1] http://en.wikipedia.org/wiki/Liquid crystal (18.10.2014)

[2] A. Mertelj, D. Lisjak, M. Drofenik, M. Copic: Ferromagnetism in suspension of magneticplatelets in liquid crystal, Nature, Vol. 504, (2013)

[3] B. Senyuk, D. Glugla, I. I. Smalyukh: Rotational and translational diffusion of anisotropicgold nanoparticles in liquid crystals controlled by varying surface anchoring, Physical Review,E 88, (2013)

[4] S. Odenbach: Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids,p. 270-275, Springer, Germany, (2009)

[5] http://en.wikipedia.org/wiki/Ferrofluid (24.5.2014)

[6] A. Mertelj, N. Osterman, D. Lisjak, M. Copic: Magneto-optic and converse magnetoelectriceffects in a ferromagnetic liquid crystal, Soft Matter, (2014)

[7] http://en.wikipedia.org/wiki/Vibrating sample magnetometer (24.5.2014)

[8] http://www.lakeshore.com/products/Vibrating-Sample-Magnetometer/7400-Series-VSM/Pages/Overview.aspx (24.5.2014)

[9] A. Boczkowska: Advanced Elastomers - Technology, Properties and Applications, p. 150-160,InTech, USA, (2012)

[10] http://phelafel.technion.ac.il/∼hilag/tutorial/LCPhases.html (24.5.2014)

[11] F. Brochard, P.G. de Gennes: Theory of magnetic suspensions in liquid crystals, Le Journalde Physique, Vol. 7, (1970)

[12] W. Burgei, M.J. Pechan, H. Jager: A simple vibrating sample magnetometer for use in amaterials physics course, American Journal of Physics, Vol. 71, (2003)

[13] S. Ovtar, D. Lisjak, M. Drofenik: Barium hexaferrite suspension for electrophoretic deposition,Journal of Colloid and Interface Science, Vol. 337, (2009)

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