GIANT

MAGNETORESISTANCE

A SEMINAR REPORT BY

ECE Department

3rd year

APRIL 22, 2014

A report submitted to the Respective Faculty in partial fulfillment

of the Seminar on

GIANT MAGNETORESISTANCE

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ABSTRACT

Giant magnetoresistance (GMR) is a quantum mechanical

magnetoresistance effect observed in thin film structures composed of

alternating ferromagnetic and nonmagnetic layers.

The effect manifests itself as a significant decrease (typically 10-80%)

in electrical resistance in the presence of a magnetic field. In the absence

of an external magnetic field, the direction of magnetization of adjacent

ferromagnetic layers is antiparallel due to a weak anti-ferromagnetic

coupling between layers. The result is high-resistance magnetic scattering

as a result of electron spin.

When an external magnetic field is applied, the magnetization of the

adjacent ferromagnetic layers is parallel. The result is lower magnetic

scattering, and lower resistance(3).

The effect is exploited commercially by manufacturers of hard disk

drives. The 2007 Nobel Prize in physics was awarded to Albert Fert and

Peter Grünberg for the discovery of GMR.

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Contents

1 Introduction 4

2 Background

A. Ferromagnetic Metals………………………………………………..... 7

B. Resistance …………………………..…………………………………… 9

C. Growth of Superlattices……………………………………………….. 10

D. Interlayer Coupling……………………………………………………… 12

3 Giant Magnetoresistance

A. Introduction………………………………………………………………. 14

B. Mathematicl Model…………………………………………………….. 14

C. Carrier transport through a magnetic superlattice………………. 16

D. CIP & CPP Geometry………………………………………………….... 17

E. Experimental Findings…………………………………………………… 18

4 Spintronics

A. What is Spintronics? ……………………………………………………….... 20

B. Logic of Spin…………………………………………………………………. 20

C. Half Metals…………………………………………………………………..… 21

5 Other improvements on GMR

A. Tunneling Magnetoresistance …………………………………………….. 23

B. Colossal Magnetoresistance ………………………………………………. 24

6 Recent Developments & Future works

A. Work so far………………………………………………………………………. 25

A.1. Magnetic switching and microwave generation by spin

Transfer…………………………………………………………………… 25

A.2. Field Effect Spin Transistors……………………………………………. 26

7 Concluding Remarks 28

8 References 29

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1. Introduction

The phenomenon called magnetoresistance (MR) is the change of resistance of a

conductor when it is placed in an external magnetic field. For ferromagnets like iron,

cobalt and nickel this property will also depend on the direction of the external field

relative to the direction of the current through the magnet. Exactly 150 years ago W.

Thomson (1) (Lord Kelvin) measured the behaviour of the resistance of iron and nickel

in the presence of a magnetic field. He wrote “I found that iron, when subjected to a

magnetic force, acquires an increase of resistance to the conduction of electricity

along, and a diminution of resistance to the conduction of electricity across, the lines

of magnetization”. This difference in resistance between the parallel and

perpendicular case is called anisotropic magnetoresistance (AMR) (2). It is now known

that this property originates from the electron spin-orbit coupling. In general

magnetoresistance effects are very small, at most of the order of a few per cent.

The MR effect has been of substantial importance technologically, especially in

connection with read-out heads for magnetic disks and as sensors of magnetic fields.

The most useful material has been an alloy between iron and nickel, Fe20Ni80

(permalloy). In general, however, there was hardly any improvement of the

performance of magnetoresistive materials since the work of Kelvin. The general

consensus in the 1980s was that it was not possible to significantly improve on the

performance of magnetic sensors based on magnetoresistance.

Therefore it was a great surprise when in 1988 two research groups independently

discovered materials showing a very large magnetoresistance, now known as giant

magnetoresistance (GMR). These materials are so called magnetic multilayers, where

layers of ferromagnetic and non-magnetic metals are stacked on each other (figure

1). The widths of the individual layers are of nanometre size – i.e. only a few atomic

layers thick. In the original experiments leading to the discovery of GMR one group, led

by Peter Grünberg (3), used a trilayer system Fe/Cr/Fe, while the other group, led by

Albert Fert (4), used multilayers of the form (Fe/Cr)n where n could be as high as 60.

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Figure 1. Schematic figure of magnetic

multilayers. Nanometre thick layers of iron

(green) are separated by nanometre thick

spacer layers of a second metal (for example

chromium or copper). The top figure illustrates

the trilayer Fe/Cr/Fe used by Grünberg´s group

(3), and the bottom the multilayer (Fe/Cr)n ,

with n as high as 60, used by Fert´s group (4).

In figure 2 the measurements of Grünberg´s group are displayed (left) together with

those of Fert´s group (right). The y-axis and x- axis represent the resistance change and

external magnetic field, respectively. The experiments show a most significant negative

magnetoresistance for the trilayer as well as the multilayers. The systems to the right,

involving large stacks of layers, show a decrease of resistance by almost 50% when

subjected to a magnetic field.

Figure 2. After refs. (3) and (4). Left: Magnetoresistance measurements (3) (room temperature) for the trilayer system Fe/Cr/Fe. To the

far right as well as to the far left the magnetizations of the two iron layers are both parallel to the external

magnetic field. In the intermediate region the magnetizations of the two iron layers are antiparallel. The

experiments also show a hysterisis behaviour (difference 1 and 4) typical for magnetization

measurements. Right: Magnetoresistance measurements (4) (4.2K) for the multilayer system (Fe/Cr)n . To the far right (>HS , where HS is the saturation field) as well as to the far left (< – HS ) the magnetizations of all iron layers are parallel to the external magnetic field. In the low field region every second iron layer is magnetized antiparallel to the external magnetic field. 10 kG = 1 Tesla.

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The effect is much smaller for the system to the left, not only because the system is

merely a trilayer but also because the experiments led by Grünberg were made at

room temperature, while the experiments reported by Fert and co-workers were per-

formed at very low temperature (4.2K).

Grünberg (3) also reported low temperature magnetoresistance measurements for

a system with three iron layers separated by two chromium layers and found a

resistance decrease of 10%.

Not only did Fert and Grünberg measure strongly enhanced magnetoresistivities, but

they also identified these observations as a new phenomenon, where the origin of the

magnetoresistance was of a to-tally new type. The title of the original paper from

Fert´s group already referred to the observed effect as “Giant Magnetoresistance”.

Grünberg also realized at once the new possibilities for technical applications and

patented the discovery. From this very moment the area of thin film magnetism

research completely changed direction into magnetoelectronics.

The discovery of giant magnetoresistance immediately opened the door to a wealth

of new scientific and technological possibilities, including a tremendous influence on

the technique of data storage and magnetic sensors. Thousands of scientists all

around the world are today working on magnetoelectronic phenomena and their

exploration. The story of the GMR effect is a very good demonstration of how a totally

unexpected scientific discovery can give rise to completely new technologies and

commercial products.

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2. Background

A. Ferromagnetic metals Among the d transition metals (Sc…Cu, Y…Ag, Lu…Au, i.e. 3d, 4d, and 5d

transition elements), the 3d metals iron, cobalt and nickel are well-known to be

ferromagnets. Among the lanthanides (the 4f elements, La-Lu) gadolinium is also a

ferromagnet. The origin of magnetism in these metals lies in the behaviour of the 3d

and 4f electrons, respectively. In the following it is mainly the magnetism in the 3d

elements that will be discussed.

In the free atoms, the 3d and 4s atomic energy levels of the 3d transition

elements are hosts for the valence electrons. In the metallic state these 3d and 4s

levels are broadened into energy bands. Since the 4s orbitals are rather extended in

space there will be a considerable overlap between 4s orbitals belonging to

neighbouring atoms, and therefore the corresponding 4s band is spread out over a

wide energy range (15–20 eV). In contrast to this, the 3d orbitals are much less

extended in space. Therefore the energy width of the associated 3d energy band is

comparatively narrow (4–7 eV). In practice one cannot make a clear distinction

between the 3d and 4s orbitals since they will hybridize strongly with each other in the

solid. Nevertheless for simplicity this two band picture will be used here and the 3d

electrons will be considered as metallic – i.e. they are itinerant electrons and can carry

current through the system, although they are still much less mobile than the 4s

electrons. A useful concept in the theory of solids is the electron density of states (DOS),

n(E), which represents the number of electrons in the system having energy within the interval (E, E+dE). According to the exclusion principle for fermions (in this case electrons), only one electron can occupy a particular state. However each state is degenerate with respect to spin and can therefore host both an electron with spin up and an electron with spin down. In the ground state all the lowest energy levels are filled by electrons and the highest occupied energy level is called the Fermi energy,

EF. In figure 3 (left) the density of states is illustrated schematically for a non-magnetic

3d metal, sometimes referred to as a paramagnet, where there are equally many electrons with spin up as with spin down, i.e. there is no net magnetization. The so

called spin polarization, P, [ P = (N↑ – N↓)/(N↑ + N↓), where N↑ ( N↓) = number of electrons

with spin up (down)], is here equal to zero.

For a ferromagnet N↑ is larger than N↓, so that there is a net spin polarization, P >

0. In order to com-pare the energy for the ferromagnetic state with the energy for the paramagnetic state one can start from the paramagnetic state and allow for a small imbalance in the number of spin up and spin down electrons. A transfer of spin down electrons from the spin down band into the spin up band leads to more exchange energy in the system, which means a lowering of the total energy (a gain) On the other hand such a process requires a transfer of electrons from spin down levels below the initial Fermi energy, into spin up levels situated just above the initial Fermi energy.

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Figure 3. To the left a schematic plot is shown for the energy band structure of a d transition metal. The

density of states N(E) is shown separately for the spin up and down electrons and where a simplified

separation has been made between the 4s and 3d band energies. For the non-magnetic state these

are identical for the two spins. All energy levels below the Fermi energy are occupied states (orange

and blue). The coloured area (orange + blue) corresponds to the total number of valence electrons in

the metal. To the right the corresponding picture is illustrated for a ferromagnetic state, with a spin-

polarization chosen to be in the up direction (N↑ > N↓; blue area > orange area). This polarization is

indicated by the thick blue arrow at the bottom figure to the right.

This will necessarily lead to a loss of band energy, “kinetic energy” and thus to an

increase of the total energy (a loss). Thus there is a competition between two opposite

effects. This can be formulated as the so called Stoner criterion (5) for magnetism,

namely that when

I N(EF) > 1,

the system will be a ferromagnet. Here I is called the Stoner exchange parameter and

N(EF) is the density of states at the Fermi energy. The Stoner parameter has a specific

value for the individual element, while N(EF) depends much more on the particular spatial arrangements of the atoms relative to each other (like crystal structure).

Furthermore, and most important, N(EF) tends to be high for systems with narrow

energy bands as is the case for the heavier 3d transition elements (Fe, Co and Ni). This is the explanation for the ferromagnetism among the d transition metals.

The situation for a ferromagnetic spin polarization is illustrated to the right in figure

3 (with a direction chosen to be upwards). The vertical displacement between the spin

up and spin down densities of states exemplifies the exchange energy splitting

between the spin up and spin down energy bands, which is relevant for the metals Fe,

Co and Ni. In particular the density of states at the Fermi energy N(EF) can now be very

different for the two spin bands. This also means that for a ferromagnet the character

of the state at the Fermi energy is quite different for spin up and spin down electrons.

This is an important observation in connection with the GMR effect. This picture of 3d

energy bands (figure 3 to the right) for the ferromagnetic metals is often referred to as

the itinerant model (6), also known as the Stoner-Wohlfarth model (5).

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One important property of ferromagnets is that at high temperature their magnetism is lost. This hap - pens at a well-defined temperature, the so called Curie

temperature, TC. For the present systems (Fe, Co and Ni) these critical temperatures

are far above room temperature and can be neglected.

B. Resistance An electrical current of electrons sent through a metallic system will always

experience a resistance R. (Exceptions are the so called superconductors where

below a certain temperature the current can flow without resistance). There are a

number of reasons for this. In a crystal the atoms will always vibrate (phonons) around

their equilibrium positions, thereby deviating from the perfect lattice positions, and the

conduction electrons may be scattered by these deviations (electron – phonon

interaction). Other important contributions to the resistance of a metal are scattering

of electrons against impurities and defects. The only electrons that participate in the

electrical conduction process are those at (or very close to) the Fermi level. For

paramagnetic metals there is no difference between the spin up and spin down

electrons, and they contribute equally to the resistance.

Figure 4. To the left is the scattering event for spin dependent electrons due to impurities and defects.

The spin is shown on the individual electrons by either up or down. The scattering event is shown by a

star.

To the right is the Mott’s equivalent circuit for the two current model. One part(Green) is due to the spin

up electron and the other(Purple) is due to the spin down electron

Already in 1936 Sir Nevil Mott (7) considered the electrical conductivity of d

transition elements. He suggested that the conductivity was mainly determined by the

4s electrons which are easily mobile due to the wide energy range of the bands

derived from the 4s-states. However in a scattering process the s electrons can scatter

into the many d states which are available at the Fermi level. Therefore they

experience a strong scattering giving rise to a considerable resistance. On the other

hand for Cu, the element following Ni in the Periodic Table, all the 3d states are

situated below the Fermi level and therefore not available for scattering processes.

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This explains the particularly high conductivity of Cu.

In the 1960s and 1970s Fert together with Campbell studied in great detail the

conductivity of 3d ferromagnetic materials (3, 8). They carried out extensive

investigations of resistivity changes which occur when low concentrations of alloying

elements, like Cr and other transition metals, are put as scattering centres into for

example Fe and Ni. From these studies they could confirm that in a ferromagnet like

iron there are two types of carriers, one made up from spin up electrons and one from

spin down electrons. Since the density of states at the Fermi surface is quite different

for the two spin states it follows that there is a significant difference in resistance for the

spin up electrons and the spin down electrons. There could also be contributions to

the resistance from scattering processes where the spins are flipped. This could for

example be due to scattering against spin waves or from the spin orbit coupling.

However these effects are small and will be neglected here. Thus the picture which is

emerging is that the electrical current in a ferromagnet like iron, cobalt and nickel

consists of spin up and spin down carriers, which experience rather different

resistances.

C. Growth of superlattices From the beginning of the 1970s the development in physics, chemistry and

materials science had led to new experimental techniques allowing scientists to

manufacture completely novel materials. Using what was called epitaxial growth one

could start to produce artificial materials building one atomic layer after the next.

Techniques that were introduced at this time involved for example sputtering, laser

ablation, molecular beam epitaxy and chemical vapour deposition. Molecular beam

epitaxy was already being used in the late 1960s to make thin semiconducting

materials and at the end of the 1970s nanometre thick metallic layers could be

produced. This was first applied to non-magnetic metals, but later also to metallic

ferromagnets. At the same time, a number of characterization techniques had been

largely improved, utilizing for example the magneto-optic Kerr effect (MOKE) and light

scattering from spin waves. Using these methods it was possible to grow metallic

multilayers involving for example iron and study their magnetic properties.

In order to produce well-defined materials the choice of substrate on which to

grow the material is of great importance. Commonly used materials are silicon, silicon

dioxide, magnesium oxide and aluminium oxide. To obtain well-behaved metallic

multilayers it is important that the lattice parameters for the different metallic layers

match each other (figure 5) and it is also an advantage if the two metals forming the

multilayer have the same crystal structure. This is the case for chromium and iron, where

both metals adapt the bcc (body-centred cubic) crystal structure and where in

addition they have very similar lattice spacing. This was important for the studies for

which this Nobel Prize is awarded under-taken by the groups of Fert and Grünberg. In

addition it was also extremely important that it was now possible to grow multilayers

where the spatial separation between the magnetic layers is of the order of

nanometres. In order to exhibit the GMR effect the mean free path length for the

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conduction electrons has to greatly exceed the interlayer separations so that the

electrons can travel through magnetic layers and pick up the GMR effect. Without the

new experimental growth techniques this requirement could not have been fulfilled

and the GMR effect would have remained unknown. In this connection it should be

mentioned that, in several publications prior to the work of Fert and Grünberg, there

were reports of observations of substantial (of the order of a few per cent)

magnetoresistance effects (9, 10, 11, 12). In none of them were the observations

recognized as a new effect.

Figure 5: Molecular Beam Epitaxy facility at Forschungszentrum Jülich - Peter Grünberg Institute in

Julich at the University of Germany.

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D. Interlayer coupling It has been known for a long time that disturbances like defects and impurities in

metallic systems become screened by the surrounding conduction electrons. The

disturbance gives rise to decaying oscillations of the electron density as a function of

the distance from the disruption (so called Friedel oscillations). Similarly, a magnetic

impurity atom in a metallic surrounding gives rise to an induced spin polarization of the

electron density. With increasing dis-tance from the magnetic impurity there will be an

oscillation in the sign of the polarization and the disturbance will also decay in

magnitude with distance. As a consequence, the magnetic moment of a second

impurity placed relatively close to the first one, will become aligned parallel or

antiparallel to the magnetic moment of the first moment depending on the sign of the

induced polarization at that particular distance. This coupling (exchange coupling)

between magnetic moments (schematically shown in figure 6) was well-known for the

rare-earth metals where each atom possesses a magnetic moment originating from

the very tightly bound (and localized) 4f electronic configuration positioned deep

inside the atom. In fact the magnetism of the heavier lanthanide metals originate from

this interaction.

As already mentioned gadolinium is a ferromag-

net where the magnetic moments originate from

the localized 4f electrons on each atom having a

4f7 configuration. That is, all the 4f magnetic mom-

ents point in the same direction and surrounding

these moments there are three conduction elec-

trons per atom which mediate the interaction

between the 4f magnetic moments. In 1986

Majkrzak et al. (13) published work on a super-

lattice of Gd/Y/Gd where they reported an anti-

parallel mag-netic moment alignment between

the Gd layers for the case of 10 monolayers of Y.

This could be understood from the way that a

ferromagnetic Gd layer induces an oscillatory spin

polarization of the normally non- magnetic Y metal

and that the second Gd layer happens to be at a

distance where an antiferro-magnetic alignment is

preferred. Practically simultaneously Grünberg et al.

(14) discovered an antiferromagnetic coupling

between the iron layers for the Fe/Cr/Fe tri-layer.

This can be explained in a similar way to the Gd/Y/Gd case. It should be

remarked, however, that in both cases, due to the geometry, there are important

contributions to the interlayer exchange coupling from quantum interference of the

Figure 6. Schematic illustration of the behaviour of the exchange coupling as a function of distance.

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electron waves reflected at the magnetic layers (15). In the present context it is

however sufficient to conclude that the important role of the electrons of the non-

magnetic layer(s) is that they provide the coupling mechanism between the magnetic

layers.

The next step was to investigate the dependence of the coupling on the

thickness of the intermediate non-magnetic layers. Several groups identified a

change of sign with increasing thickness (13, 15, 16, 17,18). A thorough study of the

dependence of the oscillatory behaviour on the thickness of the non-magnetic layer,

its dependence on the material of the non-magnetic layer as well as on the

dependence of the material of the magnetic layer itself was made by Parkin (1). Here

he actually utilized the GMR effect as a tool to study this dependence. In the

preparation of the multilayers Parkin used a magnetron sputter deposition technique.

With this method it was possible to prepare a large number of samples under

comparable conditions. This extensive work was important for the further

development of the GMR effect into a working device (20, 21,22).

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3. Giant Magnetoresistance

A. Introduction

In 1988, the Giant

Magnetoresistance (GMR) effect was

discovered independently by two

groups led by Albert Fert and Peter

Grünberg. In recognition of their

achievement, Albert Fert and Peter

Grünberg and were awarded with the

Nobel Prize in 2007. Both groups found

that the electric conductance of a

layer system consisting of ferromag-

netic and non-magnetic layers would

depend on the relative orientation of

the magnetization in neighbouring

ferromagnetic layers. The resistance

was small when the magnetization was

parallel and vice versa.

B. Mathematical Model

The resistance of a GMR device can be understood from the following

somewhat simplified picture. In figure 7 a plot of the magnetic configuration for the

FM/NM/FM (ferromagnetic/non-magnetic/ferromagnetic) multilayer is made together

with the corresponding electron density of state for the two ferromagnetic sides (FM).

In the absence of a magnetic field (at the top) the two FM layers are separated from

each other in such a way that they have opposite magnetization directions. In the

presence of a magnetic field the magnetizations of the two FM layers will be parallel

(at the bottom). An electrical current is now sent through the system for both

configurations. As already mentioned above the current through the FM layer is

composed of two types – one spin up current and one spin down current – and the

resistance for these two currents will differ. When an electron leaves the first iron layer

and enters the non-magnetic metal there will be additional scattering processes giving

rise to extra resistance. Since the spin up and spin down particles have different density

of states at the Fermi level (or rather, they originate from energy levels having different

character), the resistance not only within the FM layers, but also that originating from

the FM/NM interface will be different for the two spins. Inside the NM layer the up and

down spins will experience the same resistance, but generally this is low compared to

those in the FM layers and FM/NM interfaces and can here be neglected.

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Figure 7. Schematic illustration

of the electronic structure of a

trilayer system with two

ferromagnetic layers (light

green) on both sides separated

by nonmagnetic material

(grey). The top figure is for the

case without external magnetic

field (H=0), i.e. when the two

magnetic layers have opposite

magnetizations (indicated by

the thick blue and orange

arrows at the top of the

topmost figure). The bottom

figure is for the case when an

external magnetic field (H ≠ 0)

has forced the two

magnetizations to be parallel

(two thick blue arrows at the

bottom of the lower figure.).The

magnitude of the four

magnetizations is the same.

When the electrons enter the second iron layer they will again experience spin

dependent scattering at the NM/FM interface. Finally the spin up and spin down

electrons go through the second iron layer with the same resistance as in the first iron

layer, which still of course differs for the two spins. For simplicity the resistance for the

spin up (down) electrons through the FM layer and the scattering at the interface to

the NM layer will be called R↑ (R↓). Thus when the two layers have parallel spin

polarizations (magnetizations), i.e. in the presence of an external magnetic field (H),

the resistance for the spin up channel is 2 R↑ and for the spin down channel it is 2 R↓.

Standard addition of resistances for a parallel current configuration gives the following

total resistance, RH, in the presence of an external magnetic field;

RH = 2R↑R↓/(R↑ + R↓). In the case of no external magnetic field, (H=0), the configuration between the

two magnetic layers is antiparallel (top part of figure 8). In this case the first scatterings

in the left part of the multilayer system are exactly the same as before for the lower

part of the figure. However, when a spin up electron enters into the second FM layer it

finds itself in a totally upside-down situation where the conditions are now exactly the

same as they were for the spin down electron in the initial FM layer. Thus the spin up

particle will now experience a total resistance of R↑ + R↓. The spin down particle will be

affected in the same (but opposite) way and its resistance will be R↓ + R↑. The total

resistance will accordingly be

𝑅0 =𝑅↑+𝑅↓

2

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Figure 8. The same physical system as in figure 6.

The magnetic layers are now represented by

resistances R↑ and R↓. This shows very clearly

that the total resistance for the two cases are

different, i.e. there is a magnetoresistance

effect. In case R↑ >> R↓ it is practically only the

lowest of the four possibilities which will permit a

current. In the lower picture with parallel

magnetizations the resistance for the spin up

(spin down) electrons will be R↑ (R↓) in both

magnetic layers. In the upper picture with

antiparallel magnetizations the spin up (spin

down) electrons will have a resistance R↑ (R↓) in

the first magnetic layer to the left. In the second

magnetic layer the resistance for the spin up

(spin down) electron will be R↓ (R↑), since the

magnetization environment has here become

totally opposite compared to the first magnetic

layer.

Thus the difference in resistance between the two cases (magnetic field or not)

becomes:

R = RH – R0 = - (𝑅↑−𝑅↓)

2

2((𝑅↑+𝑅↓)

Thus the larger the difference between R↑ and R↓ the larger the negative

magnetoresistance. This expression clearly shows that the magnetoresistance effect

arises from the difference between the resistance behaviour of the spin up and down

electrons.

C. Carrier transport through a magnetic superlattice Magnetic ordering differs in superlattices with ferromagnetic and anti-

ferromagnetic interaction between the layers. In the former case, the magnetization

directions are the same in different ferromagnetic layers in the absence of applied

magnetic field, whereas in the latter case, opposite directions alternate in the

multilayer. Electrons traveling through the ferromagnetic superlattice interact with it

much weaker when their spin directions are opposite to the magnetization of the

lattice than when they are parallel to it. Such anisotropy is not observed for the

antiferromagnetic superlattice, as a result, it scatters electrons stronger than the

ferromagnetic superlattice and exhibits a higher electrical resistance.(31)

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Figure 9: Carrier transport through a structured FM/NM/FM layer. To the left we can see that the current

consisting of spin up and spin down electron faces low resistivity when the spins are parallel due to

external applied magnetic field. To the right the current is facing more resistance due to the anti-parallel

alignment of the ferromagnetic layer and gets scattered away.

Applications of the GMR effect require dynamic switching between the parallel

and antiparallel magnetization of the layers in a superlattice. In first approximation, the

energy density of the interaction between two ferromagnetic layers separated by a

non-magnetic layer is proportional to the scalar product of their magnetizations:

𝜔 = −𝒥(𝑀1. 𝑀2)

The coefficient J is an oscillatory function of the thickness of the non-magnetic

layer ds; therefore J can change its magnitude and sign. If the ds value corresponds

to the antiparallel state then an external field can switch the superlattice from the

antiparallel state (high resistance) to the parallel state (low resistance).

D. CIP and CPP geometries

Electric current can be passed through magnetic superlattices in two ways. In

the current in plane (CIP) geometry, the current flows along the layers, and the

electrodes are located on one side of the structure. In the current perpendicular to

plane (CPP) configuration, the current is passed perpendicular to the layers, and the

electrodes are located on different sides of the superlattice.(31) The CPP geometry

results in more than twice higher GMR, but is more difficult to realize in practice than

the CIP configuration

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Figure 10: To the left is shown the current in plane (CIP) geometry where the contact electrode is

connected parallel to Structure

To the right is shown the current perpendicular to the plane (CPP) where the contact electrode is

connected perpendicular to Structure. CPP results in better performance than CIP

Image courtesy Seagate

E. Experimental findings

The trilayer system of Grünberg et al. consisted of a Fe-Cr-Fe sandwich(3) that

was grown epitaxially on a GaAs substrate. The 12 nm thick iron film grow epitaxially.

The thickness of the chromium layer amounted to 1nm. With that particular thickness,

the magnetization in the two iron layer assume an anti-parallel orientation due to

interlayer coupling(52). In a

strong magnetic field parallel

to the direction in the film

plane the magnetizations in

the iron film turn parallel. The

electrical resistance

measured parallel to the layer

is 1.5 smaller in that case.

The reason for smaller

resistance is that conducting

electrons traversing the

chromium layer from one iron

layer into the other carry their

spin orientation along. If the

magnetization of both iron

films point in the same

direction, a spin-up electron

originating in one iron layer

easily finds matching states

concerning its k-vector and

Figure 11: Magnetoresistance in a three layer sandwich from Grunberg et al. In zero field,

the magnetization in the two iron layers are held antiparallel via interlayer coupling

through the antiferromagnetic chromium. On application of external magnetic field the

magnetization are forced to become parallel hence electrical resistance decreases.

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energy in the second to continue its path without being scattered. In case of anti-

parallel orientation, the spin-up states in the second layer are shifted by the exchange

energy. In general there will be no matching states for electronic the second iron layer.

The electron is hence scattered to loose its preferential direction, which increases the

electric resistance.

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4. Spintronics

A. What is Spintronics? To enhance the multifunctionality of devices (for example, carrying out

processing and data storage on the same chip), investigators have been eager to

exploit another property of the electron—a characteristic known as spin. Spin is a

purely quantum phenomenon roughly akin to the spinning of a child’s top or the

directional behavior of a compass needle. The top could spin in the clockwise or

counterclockwise direction; electrons have spin of a sort in which their compass

needles can point either “up” or “down” in relation to a magnetic field.

Spin therefore lends itself elegantly to a new kind of binary logic of ones and zeros. The

movement of spin, like the flow of charge, can also carry information among devices.

One advantage of spin over charge is that spin can be easily manipulated by

externally applied magnetic fields, a property already in use in magnetic storage

technology.

Another more subtle (but potentially significant) property of spin is its long

coherence, or relaxation, time—once created it tends to stay that way for a long time,

unlike charge states, which are easily destroyed by scattering or collision with defects,

impurities or other charges.

B. Logic of spin Spin relaxation (how spins are created and disappear) and spin transport (how

spins move in metals and semiconductors) are fundamentally important not only as

basic physics questions but also because of their demonstrated value as phenomena

in electronic technology.

Researchers and developers of spintronic devices currently take two different

approaches. In the first, they seek to perfect the existing GMR-based technology either

by developing new materials with larger populations of oriented spins (called spin

polarization) or by making improvements in existing devices to provide better spin

filtering. The second effort, which is more radical, focuses on finding novel ways both

to generate and to utilize spin-polarized currents—that is, to actively control spin

dynamics. The intent is to thoroughly investigate spin transport in semiconductors and

search for ways in which semiconductors can function as spin polarizers and spin

valves. This is crucial because, unlike semiconductor transistors, existing metal-based

devices do not amplify signals (although they are successful switches or valves). If

spintronic devices could be made from semiconductors, however, then in principle

they would provide amplification and serve, in general, as multi-functional devices.

Perhaps even more importantly, semiconductor-based devices could much more

easily be integrated with traditional semiconductor technology. Although

semiconductors. In addition to the near-term studies of various spin transistors and spin transport properties

of semiconductors, a long-term and ambitious subfield of spintronics is the application of

electron and nuclear spins to quantum information processing and quantum computation. The

late Richard Feynman and others have pointed out that quantum mechanics may provide

great advantages over classical physics in computation. However, the real boom started after

20

Peter Shor of Bell Labs devised a quantum algorithm that would factor very large numbers into

primes, an immensely difficult task for conventional computers and the basis for modern

encryption. It turns out that spin devices may be well suited to such tasks, since spin is an

intrinsically quantum property.

Figure 12: Spins can arrange themselves in a variety of ways that are important for spintronic devices.

They can be completely random, with their spins pointing in every possible direction and located

throughout a material in no particular order (upper left). Or these randomly located spins can all point

in the same direction, called spin alignment (upper right). In solid state materials, the spins might be

located in an orderly fashion on a crystal lattice (lower left) forming a nonmagnetic material. Or the

spins may be on a lattice and be aligned as in a magnetic material (lower right).

C. Half-metals

Since magnetoresistance deals with electrical conductivity it is obvious that it

is the behaviour of the electrons at the Femi surface (defined by the Fermi energy)

which is of primary interest. The more spin-polarized the density of states (DOS) at the

Fermi energy, i.e., the more N↑ (EF) deviates from N↓ (EF), the more pronounced one

expects the efficiency of the magnetoelectronic effects to be. In this re-spect a very

interesting class of materials consists of what are called half-metals, a concept

introduced by de Groot and co-workers (23). Such a property was then predicted

theoretically for CrO2 by Schwarz in 1986 (24). The name half-metal originates from

the particular feature that the spin down band is metallic while the spin up band is

an insulator. This is shown schematically in figure 13, and it is clear that there is a 100%

spin polarization at the Fermi level. The theoretical prediction for CrO2 was later

confirmed by experiment (25,26).

21

Figure 13. Schematic illustration

of the density of states for non-

magnetic (left) and

ferromagnetic CrO2 (right). As

can be seen immediately for

the ferromagnetic case (right),

the spin down electrons

(orange) are placed in a

metallic band, while the spin up

electrons (blue) show an

electronic structure that is

typical for an insula-tor. The net

spin polarization is shown by a

thick blue arrow.

In figure 14 it is shown the two DOS (spin up and spin down) for the ferromagnetic

state. For a trilayer of two ferromagnetic half-metals with one non- magnetic metallic

layer between them, it becomes very easy to appreciate the mechanism behind the

GMR effect. When the magnetizations of the two half-metals are parallel there will be

a current made up exclusively of spin down electrons. However, for an antiparallel

magnetization, the spin down channel will be totally blocked for conduction of

electricity. Hence a magnetic field which can switch between these two

configurations will give rise to a large change in resistance, i.e. will show a strong

magnetoresistance behaviour. An enhanced magnetoresistance for the half-metal

CrO2 was confirmed experimentally by Hwang and Cheong (27).

Figure 14. Illustration of the

magnetoresistance effect for a half-

metal. Two ferromagnetic half-metallic

layers (light green) separated by a non-

magnetic metal (grey). In the absence of

an external magnetic field (H = 0) the two

ferromagnets have antiparallel spin

polarizations (blue and orange thick

arrows at the top). In the presence of an

external field (H ≠ 0) the two magnets

have parallel spin polarization (two thick

blue arrows at the bottom of the figure).

As can be immediately understood, there

will be no current for the upper case. For

the lower case there will only be a spin

down current.

22

6. Other improvements on GMR

A. Tunnelling magnetoresistance

Another variation of multilayers in the present context is to grow layered materials

with an alternation between metallic and insulating layers. Here the insulating material

should be only a few atomic layers thick so that there is a significant probability that

electrons can quantum mechanically tunnel through the insulating barrier (figure 15).

In this manner a current can be sent through the multilayer. The first publication on such

a system was made by Julliere (28). This work was done for a trilayer junction with the

following structure Fe/amorphous Ge/Co. The experiments were done at low

temperature and an effect of about 14% was reported.

Figure 15. Illustration of

tunneling magnetoresistance

(TMR). Two ferromagnetic

layers separated by an

insulating layer (i = electron

current).

The next work of this type was carried out by Maekawa and Gäfvert (29). They investigated junctions of the type Ni/ NiO /FM, where FM stands for Fe, Co or Ni. The magnetoresistance they found was of the order of a few per cent, again at low temperatures. These two reports remained essentially unnoticed for a long time. In fact it was only after the discovery by Fert and Grünberg that attention focussed on these types of systems again. The breakthrough came in 1995 when two groups reported significant progress. Thus Moodera and his group (30,31) measured tunneling layers on CoFe / Al2O3 /Co (or NiFe) and found resistance changes of 24% at 4.2 K and 12% at room temperature. Similarly, Miyazaki and Tesuka (32) used a Fe /Al2O3/ Fe junction and found resistance changes of 30% and 18% at 4.2 K and room temperature, respectively. Today it is rather common to find changes of the order of 50% at room

23

temperature. This is indeed higher than the resistance changes found in “standard” GMR materials. Recently barriers of Fe/MgO/Fe have been shown to give rise to TMR-values that sometimes exceeded 200% (33,34,35).

Due to the better performance of the magnetic tunnel junctions they are

expected to become the material of choice when it comes to technical

applications. Their use in connection with non-volatile magnetic random access

memories (MRAM) is of particular interest and MRAM systems based on TMR are

already on the market. One expects that TMR based technologies will become

dominant over the GMR sensors. However, the discovery of the GMR effect paved

the way for the TMR technology.

B. Colossal magnetoresistance

The discovery of the GMR effect for magnetic multilayers gave rise to an

increased interest in finding related effects among bulk materials (36). Thus von

Helmolt and his group (37) found even larger magnetoresistance effects than for GMR

in certain manganese perovskites. These materials are some-times referred to as mixed

valence systems. Jin and co-workers (38) also found these effects, where the

resistance change in an applied magnetic field could be several magnitudes higher

than for GMR. Hence the observed effect became known as colossal

magnetoresistance (CMR). These extraordinary systems exhibit a very rich variety of

exceptional properties, where electron correlations play a very central role. However

it is unlikely that they will become of technological interest, mainly because the

required magnetic fields are very high.

24

7. More recent developments & Future work

A. Work so Far Here I just mention a few of the vast number of different research areas which

represent more recent trends regarding spin materials and their applications. One such

area is for example magnetic semiconductors, where the Ohno’s group demonstrated

the potential of such materials (39,40) using the semiconductor (Ga, Mn)As.

Another area concerns spin injection. Here the early work by Johnson on metallic

systems should be mentioned (41,42). Injection of spin from a metallic ferromagnet into

a semiconductor was successfully accomplished by Zhu et al. (43) and Hanbicki et al.

(44), using Fe and GaAs.

Injection of spins from a magnetic semiconductor to a non-magnetic

semiconductor was shown by Ohno et al. (45) and by Fiederling et al. (46). The question

of how far spin-polarized electrons can travel in a material while maintaining their spin

polarization is of great importance and promising work has been reported by

Awshalom and his colleagues (47,48,49).

Very intense work is now being directed towards magnetic switching induced

by spin-currents. This interest started from two theoretical papers where it was shown

that a spin-current through a magnetic multilayer can lead to a magnetization

reversal (50,51). This prediction was soon verified experimentally (52,53,54). The

realization of current induced domain wall motions (55,56,57) forms the basis for the

idea of a magnetic “Race-Track Memory” (58).

A.1 Magnetic Switching And Microwave Generation By Spin Transfer

The study of the spin transfer phenomena is one of the most promising new

directions in spintronics today and also an important research topic in our CNRS/Thales

laboratory. In spin transfer experiments, one manipulates the magnetic moment of a

ferromagnetic body without applying any magnetic field but only by transfer of spin

angular momentum from a spin-polarized current. The concept, which has been

introduced by John Slonczewski and appears also in papers of Berger, is illustrated in

Fig. 16. As described in the caption of the figure, the transfer of a transverse spin current

to the “free” magnetic layer F2 can be described by a torque acting on its magnetic

moment. This torque can induce an irreversible switching of this magnetic moment or,

in a second regime, generally in the presence of an applied field, it generates

precessions of the moment in the microwave frequency range. The first evidence that

spin transfer can work was indicated by experiments of spin injection through point

contacts by Tsoi et al.(23) but a clear understanding came later from measurements

performed on pillar-shaped metallic trilayers (Fig. 11a). In Fig.11b-c, I present examples

of the experimental results in the low field regime of irreversible switching, for a metallic

pillar and for a tunnel junctions with electrodes of the dilute ferromagnetic

25

semiconductor Ga1-xMnxAs. For metallic pillars or tunnel junctions with electrodes

made of a ferromagnetic transition metal like Co or Fe, the current density needed for

switching is around 106-107 Amp/cm2, which is still slightly too high for applications,

and an important challenge is the reduction of this current density. The switching time

has been measured in other groups and can be as short as 100 ps, which is very

attractive for the switching of MRAM

The spin transfer phenomena will have certainly important applications.

Switching by spin transfer will be used in the next generation of MRAM and will bring

great advantages in terms of precise addressing and low energy consumption. The

generation of oscillations in the microwave frequency range will lead to the design of

Spin Transfer Oscillators (STOs). One of the main interests of the STOs is their agility that

is the possibility of changing rapidly their frequency by tuning a DC current. They can

also have a high quality factor.

Figure 16. Illustration of the spin transfer concept introduced by John Slonczewski45 in 1996. A spin-

polarized current is prepared by a first magnetic layer F with an obliquely oriented spin-polarization with

respect to the magnetization axis of a second layer F2. When this current goes through F2, the exchange

interaction aligns its spin-polarization along the magnetization axis. As the exchange interaction is spin

conserving, the transverse spin polarization lost by the current has been transferred to the total spin of

F2, which can also be described by a spin-transfer torque acting on F2.This can lead to a magnetic

switching of the F2 layer or, depending on the experimental conditions, to magnetic oscillations in the

microwave frequency range

A.2 Field effect Spin Transistor

The first scheme for a spintronic device based on the metal-oxide-

semiconductor technology familiar to microelectronics designers was the field effect

spin transistor proposed in 1989 by Supriyo Datta and Biswajit Das of Purdue University.

In a conventional field effect transistor, electric charge is introduced via a source

electrode and collected at a drain electrode. A third electrode, the gate, generates

an electric field that changes the size of the channel through which the source-drain

current can flow, akin to stepping on a garden hose. This results in a very small electric

field being able to control large currents. In the Datta-Das device (60), a structure

made from indium-aluminum-arsenide and indium-gallium-arsenide provides a

26

channel for two-dimensional electron transport between two ferromagnetic

electrodes. One electrode acts as an emitter, the other a collector (similar, in effect,

to the source and drain, respectively, in a field effect transistor). The emitter emits

electrons with their spins oriented along the direction of the electrode’s magnetization,

while the collector (with the same electrode magnetization) acts as a spin filter and

accepts electrons with the same spin only. In the absence of any changes to the spins

during transport, every emitted electron enters the collector. In this device, the gate

electrode produces a field that forces the electron spins to precess, just like the

precession of a spinning top under the force of gravity. The electron current is

modulated by the degree of precession in electron spin introduced by the gate field:

An electron passes through the collector if its spin is parallel, and does not if it is

antiparallel, to the magnetization. The Datta-Das effect should be most visible for

narrow band-gap semiconductors such as InGaAs, which have relatively large spin-

orbit interactions (that is, a magnetic field introduced by the gate current has a

relatively large effect on electron spin).

Another interesting concept is the all-metal spin transistor developed by Mark

Johnson at the Naval Research Laboratory. Its trilayer structure consists of a

nonmagnetic metallic layer sandwiched between two ferromagnets. The all-metal

transistor has the same design philosophy as do giant magnetoresistive devices: The

current flowing through the structure is modified by the relative orientation of the

magnetic layers, which in turn can be controlled by an applied magnetic field. In this

scheme, a battery is connected to the control circuit (emitterbase), while the direction

of the current in the working circuit (base-collector) is effectively switched by changing

the magnetization of the collector. The current is drained from the base in order to

allow for the working current to flow under the “reverse” base-collector bias

(antiparallel magnetizations). Neither current nor voltage is amplified, but the device

acts as a switch or spin valve to sense changes in an external magnetic field.

Figure 17: In the spin transistor invented by Mark Johnson, two ferromagnetic electrodes - the emitter

and collector—sandwich a nonmagnetic layer—the base. When the ferromagnets are aligned, current

flows from emitter to collector (left). But when the ferromagnets have different directions of

magnetization, the current flows out of the base to emitter and collector (right). Although it can act as

a spin valve, this structure shares the disadvantage of allmetal spintronic devices in that it cannot be an

amplifier.

27

8. Concluding remarks

The discovery by Albert Fert and Peter Grünberg of giant magnetoresistance

(GMR) was very rapidly recognized by the scientific community. Research in

magnetism became fashionable with a rich variety of new scientific and technological

possibilities. GMR is a good example of how an unexpected fundamental scientific

discovery can quickly give rise to new technologies and commercial products. The

discovery of GMR opened the door to a new field of science, magnetoelectronics (or

spintronics), where two fundamental properties of the electron, namely its charge and

its spin, are manipulated simultaneously. Emerging nanotechnology was an original

prerequisite for the discovery of GMR, now magnetoelectronics is in its turn a driving

force for new applications of nanotechnology. In this field, demanding and exciting

scientific and technological challenges become intertwined, strongly reinforcing

progress.

The field of spintronics already has promising future for future electronics with the

most important being the Quantum computing. Although much remains to be

understood about the behaviour of electron spins in materials for technological

applications, but much has been accomplished. A number of novel spin-based

microelectronic devices have been proposed, and the giant magnetoresistive

sandwich structure is a proven commercial success, being a part of every computer

coming off the production line. In addition, spintronic-based non-volatile memory

elements may very well become available in the near future. But before we can move

forward into broad application of spin-based multifunctional and novel technologies,

we face the fundamental challenges of creating and measuring spin, understanding

better the transport of spin at interfaces, particularly at ferromagnetic/semiconductor

interfaces, and clarifying the types of errors in spin-based computational systems.

Tackling these will require that we develop new experimental tools and broaden

considerably our theoretical understanding of quantum spin, learning in the process

how to actively control and manipulate spins in ultra-small structures.

28

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