Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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University of Alabama, Tuscaloosa, Alabama, USA

Magnetic Recording Systems: Spin

Electronics

Hitherto, conventional electronics has ignored the

spin of the electron. The charge carriers in ordinary

electronic devices can not only have charges of dif-

ferent sign, they also possess spin which may be ‘‘up’’

or ‘‘down’’ with respect to a local quantization axis.

However no use is made of this property.

Spin electronics is the new science and technology

of electronic devices that recognizes the spin of the

electron as a distinguishing label. Just as a conven-

tional semiconductor transistor distinguishes families

of electrons and holes by their opposite charge, a spin

transistor divides the electrical carriers into differen-

tially manipulated families (spin channels) which are

either spin up or spin down.

Spin electronic devices function by transferring

magnetic information from one part of the device

to another by using nanoscale magnetic elements

(mesomagnets) to encode it onto (and subsequently

read it off) the spin channels. This coding may be

changed by remagnetizing the mesomagnets thus

enabling the creation of electronic components whose

characteristics may be engineered to respond to

applied magnetic ﬁelds.

The ﬁrst (and simplest) spin electronic components

were passive two-terminal devices—the giant magne-

toresistance (GMR) trilayers that have already been

adopted as the next generation read head technology

in the hard-disk industry. Then followed the all-metal

spin transistor, a passive three-terminal device. Its

successor, the hot spin transistor, represents a very

significant advance in that it is the ﬁrst attempt to

integrate silicon and ferromagnetic metals to make a

hybrid spin-dependent electronic component.

Hybrid spin electronics (HSE) (which combine

semiconductor and spin asymmetric technologies to

make devices such as the hot spin transistor) is at-

tractive because, in principle, it can offer nonvolatile

memory function and sensitivity to magnetic ﬁelds in

combination with the other functions generally avail-

able from semiconductors such as power gain, high

input impedance, etc. Moreover, transport phenom-

ena found only in semiconductors (such as depletion

layers, diffusion currents, and the ability of junctions

to screen out electric ﬁelds from adjacent material)

offer a versatility of device design that is unthinkable

in systems containing metals alone.

Two- and three-terminal spin-tunnel devices rep-

resent a parallel development, which has also gener-

ated two- and three-terminal memory and transistor

devices with unusual characteristics. Spin tunneling

would seem to have a number of advantages in terms

of ease of fabrication, ﬂexibility in design parameters,

and size of output signal. Spin-tunnel devices seem set

to dominate the magnetic memory market for the

foreseeable future.

A development of the single electron transistor

involving ferromagnetic electrodes has not been

realized experimentally, but has wide potential appli-

cation in information processing and electronic

miniaturization.

Likewise the spin FET proposed by Datta and Das

(1990) has received much attention but a working

example has not yet been demonstrated.

1. Technical Basis of Spin Electronics: the Two

Spin Channel Model

The basis of spin electronics was established in the

1930s with the observation that features of electrical

transport in ferromagnets distinguished them from

other metals. Mott (1936) explained this by postu-

lating that the transport was effected by two inde-

pendent families of carriers whose members are

distinguished by their being either up-spin or down-

spin. Spin ﬂip processes are rare on the timescale of

the other scattering processes that control the trans-

port, hence these two spin channels may be regarded

as being pseudo-independent.

1.1 Spin Asymmetry

The two-spin channel model is further qualiﬁed by

the fact that the spin-up and spin-down electrons

have different properties and this spin asymmetry

610

Magnetic Reco rding Systems: Spin Electronics

arises from the bandstructure splitting caused by the

ferromagnetic exchange interaction. The splitting

causes different densities of states at the Fermi en-

ergy and this in turn has two consequences: (i) the

number of available carriers of a particular spin type

or (in a tunneling process) the number of available

ﬁnal states for such carriers is different for each spin

type; and (ii) owing to the different densities of ﬁnal

states for each spin type, they are differently affected

by momentum-changing scattering processes and

hence their mobilities are in general different. Most

spin electronic phenomena are based on either or

both of these asymmetries that have a common origin

in the bandstructure splitting (Barthelemy and Fert

1991).

1.2 The Half-metallic Ferromagnet

In the extreme limit of spin asymmetry lies the half-

metallic ferromagnet (HMF) (de Groot et al. 1984),

in which the bandstructure splitting is such that only

one spin band is available at the Fermi surface and

hence all current must be carried by these so-called

majority spins. Practical examples include chromium

dioxide, lanthanum strontium manganite, magnetite,

and some Heusler alloys. In reality, obtaining half-

metallic spin electronic behavior is fraught with

problems mainly to do with the interfaces.

1.3 Density of States Asymmetry Versus Mobility

Asymmetry

The density of states asymmetry (which leads in the

extreme case to half-metallic ferromagnets) and the

mobility asymmetry compete with one another in

spin electronics. The mobility asymmetry arises where

the bandstructure at the Fermi surface contains com-

ponents which have s and d character respectively.

The s-like effective masses are small compared to the

d-like masses and so the current is primarily mediated

by s-electrons. However, the d-electrons are signiﬁ-

cantly split by the exchange interaction and present

very different densities of states into which the

s-electrons may be scattered. As a result, the s chan-

nel whose spin corresponds to the spin of the major-

ity d-electrons suffers the most scattering and hence

has lower mobility than the other s channel; the latter

consequently carries most of the current. Thus, in a

system with s- and d-like character at the Fermi sur-

face, the tendency is for the current to be carried by

the minority carriers (those with the lower density of

states at the Fermi energy) whereas in a HMF clearly

the current may only be carried by majority carriers.

This conﬂict between the two types of asymmetry

is one reason why spin tunnel devices have an ad-

vantage over their competitors since they exploit only

the density of states asymmetry and the mobility

asymmetry has no chance to compete and reduce the

overall device performance.

2. Spin Injectio n Across an Interface

Clearly if one carrier spin type is dominant in the

electrical transport of a ferromagnet, then when a

current is passed from such a ferromagnet to a par-

amagnetic metal such as silver or aluminum, the

electrical current brings with it a net injection of spin

angular momentum and hence also magnetization

(Johnson and Silsbee 1985).

2.1 Spin Accumulation and Spin Diffusion Length

This magnetization that builds up in the new material

is known as a spin accumulation. Its size in the para-

magnetic metal is determined by a balance between

the spin injection rate at the interface and the spin-

ﬂipping rate in the body of the paramagnet. The in-

jected magnetization diffuses away from the interface

and decays exponentially on a length scale called the

spin diffusion length test l

given by

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

l=3

where v

is Fermi velocity, t

is the spin ﬂip time,

and l is the mean free path. The actual size of the

spin accumulation in terms of the spin density n at

distance x from the interface is given as

n ¼ n

exp ðx=l

where n

, the density at the interface, is given by

¼ 3ajl

=ev

where a is polarization of the ferromagnet and j is

current density at the interface. Substituting typical

numbers of j ¼1000 Acm

2

, a ¼1, v

¼10

1

l ¼5 nm, l

¼100 nm gives a value of spin density of

3

as opposed to a total electron density of

about 10

3

That such small asymmetries in spin density can

give rise to such huge electrical transport effects as

GMR is yet one more example of the dominance of

the electrons at the metal Fermi surface which is

where these spins are concentrated.

Various practical methods of measuring the spin

diffusion length have been described (Yang et al.

1994). Measuring the spin density or its associated

magnetization is difﬁcult owing to its smallness and

the difﬁculty in distinguishing convincingly the mag-

netic ﬁelds associated with the accumulation itself

from those caused by the current that is generating

the accumulation.

An elegant analysis of the spin accumulation phe-

nomenon (Valet and Fert 1993) proceeds by treating

611

Magnetic Reco rding Systems: Spin Electronics

it as a divergence of the electrochemical potentials for

spin-up and spin-down carriers either side of the in-

terface. This treatment shows clearly the relationship

between the accumulations both sides of the interface

and also how the magnitude of the accumulation de-

pends on the relative conductivities of each metal.

This has implications for spin injection into low con-

ductivity materials such as doped semiconductors.

2.2 The Role of Impurities in Spin Electronics

From the expression above for spin diffusion length it

is clear that introducing impurities into the material

concerned diminishes l

rapidly for two reasons: the

impurities shorten the mean free path and also the

spin ﬂip time via spin-orbit scattering (Fert et al.

1995). The latter may be thought of as a relativistic

effect: under Lorentz transform, electric ﬁelds assume

a magnetic component. To electrons at the Fermi

surface which have weakly relativistic velocities, the

electric ﬁelds generated by impurity atoms appear

weakly magnetic. If the symmetry of the impurity site

is sufﬁciently low, this ﬁeld may Zeeman couple to

the S



operators that induce spin–ﬂip transi-

tions. Hence materials with point defects and low

symmetry structural disorder are likely to exhibit re-

duced spin diffusion lengths (Dubois et al. 1999).

3. Two-terminal Spin Electronics

The simplest spin electronic devices are called GMR

trilayers or spin valves depending on their magnetic

construction, i.e., whether the layers are RKKY-

coupled or exchange pinned. They have two terminals

and consist of sandwiches comprising three metal

ﬁlms: two ferromagnetic metal ﬁlms ﬂanking a ﬁlm of

nonmagnetic metal. If the terminals are contacted to

the two ferromagnetic ﬁlms the conﬁguration of the

device is described as current perpendicular to plane

(CPP). However the terminals may also be attached

to opposite ends of the ﬁlm stack such that the cur-

rent ﬂows through all three ﬁlms to transit the device:

this conﬁguration is known as current in plane (CIP).

The magnetizations of the ferromagnetic layers are

engineered to lie antiparallel in zero magnetic ﬁeld

(by either RKKY coupling or exchange biasing), but

application of an external ﬁeld may align them. When

this happens the electrical resistance between the

device terminals drops, a phenomenon known as

giant magnetoresistance. For a fuller description see

Magnetoresistance, Anisotropic; Giant Magnetoresis-

tance, Magnetoresistance: Magnetic and Nonmagnetic

Intermetallic.

3.1 CPP GMR

CPP GMR may be explained, with recourse to the

Valet/Fert model (Valet and Fert 1993), in terms of

the electrochemical potential splittings at the succes-

sive interfaces. If the interfaces are separated by a

distance less than a spin diffusion length, the succes-

sive spin accumulations interfere and generate addi-

tional electrochemical potential drops associated with

the interfaces. These change with the magnetic con-

ﬁguration of the device and in turn they translate

into changes in the resistance of the overall device

(Lee et al. 1993).

3.2 The Analogy with Polarized Light

A more immediate way to understand the physical

significance of this phenomenon is by analogy with

crossed optical polarizers. In the extreme case in

which the ferromagnets are half metallic, they accept

or dispense only electrons of one spin type, for ex-

ample spin-up (parallel to the magnetization). As-

suming that the intermediate nonmagnetic layer is

thinner than a spin diffusion length, this means that

the spin emitted by one magnetic layer preserves its

polarization until it meets the other layer. Whether it

gains access to this second ferromagnetic layer then

depends on whether the magnetizations of the two

layers are parallel or antiparallel. The analogy with

optical linear polarizers is exact except in that the

extinction angle in the spin electronic case is 1801

rather than 901. As expected from this model, the

GMR varies as the cosine of the angle between mag-

netic layers (Dieny et al. 1991).

3.3 The Resistor Model of GMR

A simple parallel resistor model may thus be used to

describe CPP GMR. The two parallel paths, each

consisting of two series resistors, represent the re-

spective spin channels and the ﬁrst and second resis-

tors in each path are the resistances which they

experience at the ﬁrst and second interfaces respec-

tively.

If we arbitrarily assign resistance values of 1 O and

10 O to the majority and minority interface resist-

ances, it is seen that the magnetization parallel and

antiparallel conﬁgurations have overall resistance of

1.8 O and 5.5 O respectively.

3.4 CIP GMR

This was in fact the ﬁrst GMR to be experimentally

demonstrated, its geometry being easier to realize

than the CPP geometry, which requires sophisticated

nanolithography (Baibich et al. 1988). CIP GMR is

characterized by the same drop in electrical resistance

of the thin ﬁlm sample when a magnetic ﬁeld is ap-

plied. However the explanation is fundamentally dif-

ferent. Symmetry considerations show clearly that no

spin accumulation is set up in this case since current

ﬂow is parallel to the layers. Instead the explanation

612

Magnetic Reco rding Systems: Spin Electronics

invokes the differential mobilities of the spin-up and

spin-down electrons and relies on the nonmagnetic

interlayer being sufﬁciently thin that a high propor-

tion of the current carrying electrons experience suc-

cessive momentum scattering events in different

magnetic layers. This in turn means that if the lay-

ers are antiparallel, either spin type has high mobility

since each experiences heavy scattering in one or

other layer. However if the layers are parallel, one

spin type is heavily scattered in both layers and the

other spin type is relatively unscattered and hence its

high mobility electrically short-circuits the device.

The resistor model above works equally for the CIP

geometry: the two parallel paths are again represent-

ative of the spin channels and the resistors represent

the scattering they experience in the respective layers,

assuming that their trajectories sample both layers.

3.5 Comparative Length Scales of CIP and CPP

GMR

It is evident for this discussion that two quite differ-

ent length scales are relevant to CIP and CPP GMR.

For CPP GMR, the interlayer must be less than the

spin diffusion length whereas for CIP GMR to ap-

pear the interlayer must be less than a mean free path

which is a rather shorter distance. In practice typical

CIP GMR multilayers use nonmagnetic spacers of

the order of 10 A

or less.

3.6 Inverse GMR

In the above discussion it is assumed that the metals

in the two ferromagnetic layers are similar, or at least

that the sign of their polarizations is the same. That is

to say that the majority spin for each ferromagnet is

parallel to the magnetization (positive polarization)

or antiparallel to the magnetization (negative polar-

ization). If a combination of two ferromagnets with

opposite polarizations is used to make a GMR tri-

layer, the GMR is inverted which means that the re-

sistance of the device increases on application of an

external magnetic ﬁeld. This is because when the

ferromagnets have parallel magnetizations they dis-

agree as to which spin direction is the majority type

(Renard et al. 1996).

3.7 Obtaining Differential Magnetization: RKKY

Coupling Versus Exchange Pinning—The Spin Valve

There are two techniques used to engineer GMR

systems such that the two ferromagnetic layers are

differentially switchable in an externally applied ﬁeld.

(a) RKKY coupling

The ﬁrst technique involves making the metallic in-

terlayer of such a thickness (of order 1 nm) that the

RKKY coupling across it between the magnetic lay-

ers is antiferromagnetic and so the layers antialign in

zero applied ﬁeld but are parallel in applied ﬁeld

(Parkin et al. 1990). This technique imposes con-

straints on the device design, which may militate

against obtaining the best GMR signal.

(b) The spin valve

The other technique is to make one layer magneti-

cally hard by exchange pinning it to an antiferro-

magnet on the side opposite to that which abuts the

GMR device. In this case only the unpinned soft layer

moves in small magnetic ﬁelds. The resulting device is

termed a spin valve (Dieny et al. 1991).

3.8 The Artiﬁcial Antiferromagnet (AAF)

The AAF is a clever combination of the two above

ideas. No RKKY coupling is used in the GMR

spacer layer. However, one of the ferromagnetic elec-

trodes is rendered magnetically hard by fabricating it

from two distinct ferromagnetic layers A and B of

almost identical thickness, which are RKKY-coupled

such that in zero applied ﬁeld they are antiparallel

and hence their net moment is small. The switching

ﬁeld of this artiﬁcial antiferromagnet block (A þB) is

thus enhanced by a so-called Q factor which is the

ratio of the total magnetic moment when A and B are

aligned in a high ﬁeld to the net moment when A and

B are antialigned (Tiusan et al. 1999).

3.9 GMR in Nanowires

An interesting practical realization of CPP GMR is

by using electroplating technology to construct me-

tallic nanowires in nanopores of a membrane (Piraux

et al. 1994). With a suitable electrolyte containing a

selection of ions, the material being deposited may be

varied every few nanometers along the wire by

switching the value of the electroplating potential,

thereby creating a magnetic multilayer structure. This

technique has the added convenience that the geo-

metry of the wires is conducive to easy measurement,

unlike thin evaporated ﬁlms, which must be litho-

graphed in order to obtain specimens whose resist-

ance is high enough for practical purposes.

4. Quantum Tunneling

If two conducting layers between which a potential is

applied are separated by a thin insulating ﬁlm, elec-

trical current passes between the metal electrodes by

quantum mechanical tunneling of the current carriers

through the insulating tunnel barrier. The tunneling

rate for carriers of a particular energy is proportional

to the product of the carrier densities of states at that

energy each side of the barrier. Also, the thinner the

613

Magnetic Reco rding Systems: Spin Electronics

barrier and the lower the barrier height, the larger the

current. This phenomenon was extensively studied in

the context of superconducting thin ﬁlms where it

enables accurate determination of the superconduct-

ing energy gap (Giaever and Megerle 1961).

4.1 Spin Tunnel Junctions

Spin tunnel junctions are two-terminal spin electronic

devices whose magnetotransport characteristics close-

ly mirror those of CPP GMR trilayers, except that

their parameters are more readily adaptable to prac-

tical applications. They consist of pairs of ferromag-

netic electrodes separated by electrical insulators and

they exhibit large changes in tunnel resistance de-

pending on the relative alignment of the ferromag-

netic electrode magnetizations. The thickness of the

tunnel barrier must be in the low nanometer regime

to obtain reasonable current densities. The effect may

be understood, at least simplistically, according to a

model of Julliere (1975) which was in turn inspired by

the ideas of Merservey and Tedrow (1971), in which

the tunnel current is proportional to the product of

the densities of spin-states either side of the tunnel

barrier.

In the simple case of HMF electrodes whose mag-

netic moments are anti-aligned, it is clear that the

product of the initial and ﬁnal densities of states is

zero for either spin type and no current ﬂows. How-

ever if the moments are aligned the half band of ma-

jority spins may tunnel and the device will have low

resistance. It may be seen that this device is highly

analogous to the CPP GMR trilayer except that it

relies exclusively on asymmetry in density of states

and does not invoke mobility spin asymmetry. This

makes analysis cleaner and also means that in general

the magnetoresistance (MR) effects are larger. Also,

because tunneling and not ohmic conduction is in-

volved, the resistance of a tunnel junction is higher

than that of an all-metallic GMR system of compa-

rable geometry and this makes spin tunnel junctions

rather more easily adaptable to practical applica-

tions.

4.2 Reﬁnements in the Understanding of Spin

Tunneling

The simple Julliere tunneling theory gives good in-

sight into the physical basis of spin tunneling but is

incapable of explaining the ﬁner experimental detail.

For example, most spin tunnel junctions display a

bias-dependent magnetoresistance whose explanation

needs a more sophisticated treatment (Chui 1997).

Moreover, simple spin tunneling theory suggests that

a particular spin asymmetric material should always

exhibit the same characteristic polarization for tun-

neling processes and that this polarization value

is closely related to and predictable from its bulk

bandstructure. However, experiment reveals that, on

the contrary, the polarization which magnetic elec-

trodes manifest for tunneling purposes is found to be

a function of the magnetic metal/insulator combina-

tion, not just of the magnetic metal itself. The polar-

ization of a particular spin electronic material may

actually change sign depending on which insulator

accompanies it (De Teresa et al. 1999). The explana-

tion is thought to be that the tunneling electrons

come from the ﬁrst few atomic layers of the metal

which are hybridized with the insulator and hence do

not have the bulk bandstructure. Since spin electronic

effects are almost all interface related, it is generally

these interface bandstructures that are more relevant

to practical device performance.

4.3 Spin Tunnel Junction Resistance and Heat

Dissipation

Spin tunnel junctions are characterized by a real con-

ductance per unit area. The associated junction re-

sistance scales roughly exponentially (according to

the very simplest theory) with thickness and barrier

height. However the net dissipation associated with

this tunnel resistance when a tunnel current ﬂows is

not dissipated in the junction itself but rather in the

conducting material on its downstream side. Hot

carriers are injected into this region from the junction

insulator and thermalize rapidly owing to their being

high above the Fermi surface where there is a high

density of empty states into which they may scatter.

4.4 Coherent Spin Tunneling—Resonant Structures

Clearly if two separate tunnel junctions are cascaded

their resistances add according to Ohm’s law. How-

ever, if the junctions are sufﬁciently close that the

wavefunction of the electrons entering the ﬁrst junc-

tion is coherent with those exiting the second junc-

tion, in other words the transport is ballistic in the

layer separating the junctions, the analysis is more

complex. This implies that, since the electrons have at

least partially preserved their phase memory, they

have not been properly thermalized in the interme-

diate layer and the concept of single junction resist-

ance is not valid. The entire multiple tunnel structure

must then be analyzed as an entity in similar fashion

to that in which optical thin ﬁlm interference ﬁlters

are treated. Such resonant tunnel structures are po-

tentially useful for making spin-tunnel devices with a

high back-to- front electrical transmission ratio.

5. Superparamagnetism

There are three main energy terms that govern ferro-

magnetic behavior: the magnetostatic energy stored

in the magnetic ﬁeld surrounding a ferromagnet

with free magnetic poles; the exchange energy, which

614

Magnetic Reco rding Systems: Spin Electronics

varies with the cosine of the angle between adjacent

spins; and the anisotropy energy, which increases if

any individual spin orients itself at an angle to the

easy direction in the material. Reduction of the mag-

netostatic energy is the reason for the existence of

ferromagnetic domains. However, between any two

domains is a domain wall whose width and energy are

determined by a trade-off between the other two en-

ergy terms, the exchange and the anisotropy energies.

The magnetostatic energy of a specimen scales as its

volume V and domain wall energy as cross-sectional

area. This implies that for ferromagnetic systems be-

low a certain dimensional threshold, the energy need-

ed to create a domain wall in the system exceeds the

magnetostatic energy reduction that this would effect.

Such particles are thus single domained and termed

superparamagnetic since they behave as a single giant

spin. This giant spin has lowest free energy when

aligned along its easy axis. If the system has uniaxial

anisotropy with the easy direction on this axis, then

below a certain critical temperature T

(called the

blocking temperature) given by KV ¼k

, single

domain particles are trapped in one or other of

the potential wells in free energy which correspond

to magnetization parallel or antiparallel to the easy

direction. Such a system is said to be blocked and,

unlike a superparamagnet (i.e., itself at higher tem-

perature) has a hysteretic magnetic response (Bean

and Livingstone 1959).

5.1 Granular GMR Materials

When different proportions (say 20%, 80%) of two

immiscible metals are cosputtered and then annealed,

the initial interatomic mixture phase separates into

granules of one metal in a matrix of the other. If the

granules are ferromagnetic and the matrix paramag-

netic, the resulting material exhibits GMR. Such ma-

terials may also be formed by mechanical alloying.

The effect was ﬁrst observed by Gerritson (1959) be-

fore the theory existed to explain the phenomenon.

The GMR arises because in zero ﬁeld the angle be-

tween adjacent magnetic granules is totally random

whereas in high magnetic ﬁeld the moments are vir-

tually all aligned. Simple trigonometry shows that the

GMR, which is again proportional to the cosine of

these inter-grain angles, varies as the square of the

sample magnetization (Barnard et al. 1992, Berkowitz

et al. 1992). In the absence of significant interaction

between the grains this is experimentally veriﬁed.

Owing to the geometry of such granular systems, the

GMR that they exhibit is a mixture of CIP and CPP

and both characteristic length scales for these two

phenomena are in play (see Giant Magnetoresistance).

5.2 Jitterbug Depolarization

Granular GMR systems comprise a spread of mag-

netic particle sizes whose span depends on the mode

of preparation. The larger particles whose diameters

are of the order of the electron mean free path con-

tribute to the GMR. The smaller particles are insuf-

ﬁciently large to cause appreciable scattering but they

nevertheless play a role in determining the magneto-

transport by causing passing spins to precess. This

spin precession causes the spin to turn through an

angle, which is a function of the incident spin orien-

tation, the particle magnetization orientation, and the

particle thickness. The result is a progressive depo-

larization or mixing of the spin channels, which mil-

itates against the GMR. This spin mixing mechanism

is called the jitterbug effect after the swing-dance of

that name which the electron’s successive random

precessions resemble (Gehring et al. 1995).

6. Giant Thermal Magnetoresistance

Electrical current carriers are capable of mediating a

variety of signals. These include not only electric

current and magnetization but also heat. Thermal

and electrical transport in metals generally are closely

related, as witness the Peltier effect (using an electric

current to produce cooling) and the thermoelectric

effect (using a thermal difference to generate a volt-

age). The Wiedemann–Franz Law (see Boltzmann

Equation and Scattering Mechanisms) also tells us

that there is an intimate relationship between the

thermal and electrical conductivities of metals under

most circumstances. This close connection is further

extended in the case of magnetoconductivity. Just as

the electrical conductivity of a giant magnetoresistive

material is a function of applied magnetic ﬁeld, so

also is the thermal conductivity, though the percent-

age effects may be different owing to the different

way in which the thermal information is encoded

onto the electrical carriers that mediate it (Daniel

et al. 1995).

7. The Exchange Length in Spin Electronics: The

Ferromagnetic Domain Wall as a Giant

Magnetoresistor

Exchange length is an ambiguous term in nanomag-

netism, which may be taken as the characteristic

length scale deﬁned by the exchange energy and the

magnetostatic energy, or more practically by the ex-

change energy and the anisotropy energy. In the lat-

ter case it is closely related to the thickness of

ferromagnetic domain walls.

The electrical resistivity associated with ferromag-

netic metal domain walls has been a subject of in-

tensive study for many decades (Berger 1991, Cabrera

and Falicov 1974). A spin electronic interpretation of

this resistance is possible which draws on the analogy

between a ferromagnetic domain wall and a GMR

trilayer (Gregg et al. 1996). When the wall is present

the magnetizations either side are antiparallel and

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Magnetic Reco rding Systems: Spin Electronics

when it is absent they are parallel. In the limit where

the carrier spins traverse the wall with spin directions

unaltered, the analogy with CPP transport in a GMR

trilayer is complete. However, depending on the

strength of the exchange ﬁeld and hence the spin’s

pseudo-Larmor precession frequency, and also the

wall thickness, the spin directions of the transiting

carriers may track the magnetization rotation in the

domain wall more or less adiabatically. Any mis-

tracking gives rise to a quantum mechanical admix-

ture of the opposite spin wavefunction which lays the

spin open to momentum scattering by the normal

processes which cause resistance. This model gives

rise to an expression for the increase in resistivity of

material in a domain wall of:

¼ðl



=l þ l=l



 2Þ/sin

ðy=2ÞS

Unlike other previous models for domain wall re-

sistance, this model predicts a percentage resistance

change for such material which is independent of

impurity content.

Very large magnetotransport effects (of the order

of 600%) have been observed in ferromagnetic nano-

contacts between oppositely magnetized domains of

half-metallic ferromagnet (magnetite) (Versluijs et al.

2001).

8. Three-terminal Spin Electr onics:

The Johnson Transistor

Three-terminal spin electronics is the logical succes-

sion to GMR and TMR devices and is realized in the

simplest case by attaching a third electrode to the

intermediate layer in an all-metallic GMR system

(Johnson 1993).

The result is the Johnson spin transistor. Its func-

tion may be briefly understood as follows. It is

assumed for simplicity that the ferromagnets are

half-metallic. We denote the new connection to the

paramagnetic intermediate layer of the trilayer as the

‘‘base,’’ and the connections to the ferromagnetic

layers as the ‘‘emitter’’ and ‘‘collector,’’ respectively.

The device is biased by pumping an electron current

through from emitter to base, thereby establishing a

spin accumulation in the base, which extends to meet

the base–collector interface. If the collector is left

electrically ﬂoating, i.e., its potential is monitored by

a high impedance voltmeter, which draws from it no

current. Since the collector is capable of accepting

only one spin type, it ﬂoats at a potential which

equalizes its electrochemical potential with that of the

corresponding spin type in the base. Since the base

has a spin accumulation, this implies that its spin-up

and spin-down electrochemical potentials are differ-

ent and hence that the ﬂoating potential of the

collector will alter by this differential if the magnet-

ization of the collector (of the emitter spin injector) is

reversed. Thus, we have the embodiment of a three-

terminal spin electronic device: electrical characteris-

tics of the third electrode determined by the relative

conditions at the other two and in addition the ca-

pability of changing this dependence by applying a

magnetic ﬁeld.

9. Power Gain and Noise Considerations in

All-metallic Spin Electronics

The Johnson transistor is an all-metal device that

obeys Ohm’s law and as such it cannot deliver signal

power gain without further modiﬁcation. This might

take the form of additional terminals or a change

to the internal structure. Moreover, the source im-

pedances of such devices are small, particularly

those with perpendicular structures. Optimizing noise

ﬁgure when matching small source impedances to

conventional electronics is difﬁcult and requires im-

pedance transformation, which is frequently bulky

and impractical.

10. Hybrid Spin Electronics

A potential solution to these technical problems is

found in hybrid spin electronics. This is the combi-

nation of spin-asymmetric materials with convention-

al semiconductors. It releases to the spin electronic

designer a variety of constructional options such as

deployment of reverse biased junctions with minimal

admittance, depletion layers to screen regions of the

device, and diffusive carrier transport.

10.1 The Monsma Transistor

The ﬁrst hybrid spin electronic device was the Mon-

sma transistor produced by the University of Twente

which was fabricated by sandwiching a traditional spin

valve device between two layers of silicon (Monsma

et al. 1995). Three electrical contacts are made to the

spin-valve base layer and the respective silicon layers.

The spin valve is more sophisticated than that dis-

cussed above and comprises multiple magnetic/non-

magnetic bilayers, but the operating principle is the

same. Schottky barriers form at the interfaces between

the silicon and the metal structure and these absorb

the bias voltages applied between pairs of terminals.

The collector Schottky barrier is back biased and the

emitter Schottky is forward biased. This has the effect

of injecting (unpolarized) hot electrons from the semi-

conductor emitter into the metallic base high above its

Fermi energy. The question now is whether the hot

electrons can travel across the thickness of the base

and retain enough energy to surmount the collector

Schottky barrier. If not they remain in the base and get

swept out the base connection.

By varying the magnetic conﬁguration of the base

magnetic multilayer the operator can determine how

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Magnetic Reco rding Systems: Spin Electronics

much energy the hot electrons lose in their passage

across the base. If the magnetic layers are antiferro-

magnetically aligned in the multilayer then both spin

types experience heavy scattering in one or other

magnetic layer orientation, so the average energy of

both spin types decays rapidly as a function of dis-

tance. On the other hand, if the magnetic multilayer is

in an applied ﬁeld and its layers are all aligned, one

spin class gets scattered heavily in every magnetic

layer, whereas the other class is lightly scattered eve-

rywhere and hence retains its ‘‘hot’’ status over a

longer distance. Thus, for parallel magnetic align-

ment, spins with higher average energy impinge on

the collector barrier and the collected current is cor-

respondingly higher. Once again we have a transistor

whose electrical characteristics are magnetically tun-

able. This time, however, the current gain and the

magnetic sensitivity are sufﬁciently large that, with

help from some conventional electronics, this is a

candidate for a practical working device.

Evidently, there is a tradeoff to be made in deter-

mining the optimum base thickness. A thin base al-

lows a large collector current harvest but affords little

magnetic discrimination. A thick base on the other

hand means a large factor between the collector cur-

rents corresponding to the two magnetic states of the

multilayer but an abysmally small current gain. (The

low current gain has always been the Achilles heel of

metal base transistors, and is probably the main rea-

son for their fall from favor as practical devices de-

spite their good high frequency performance owing to

the absence of base charge storage).

An interesting feature of the Monsma transistor is

that the transmission selection at the collector barrier

is done on the basis of energy. Thus, the scattering

processes in the base that determine collected current

are the inelastic ones. Elastic collisions that change

momentum but not energy are of less significance.

This contrasts with the functioning of a spin valve-

type system in which all momentum changing colli-

sion processes have the same status in determining

device performance.

10.2 Spin Transport in Semiconductors

The Monsma transistor represents a very important

step in the evolution of spin electronics. It is the ﬁrst

combination of spin-selective materials with semi-

conductor. However, as yet, the semiconductor is

used only to generate barriers and shield the spin-

dependent part of the device from electric ﬁelds. To

release the full potential of hybrid spin electronics we

need to make devices that exploit spin-dependent

transport in the semiconductor itself.

10.3 The SPICE Transistor

The current gain of a conventional bipolar transistor

is in part due to the screening action of the junctions

either side of the base, which absorb the bias voltages

and leave the base region relatively free of electric

ﬁelds. The current which diffuses across the base is

primarily driven by carrier concentration gradient

and to a rather lesser extent by electric ﬁeld and the

randomness associated with concentration driven

current ﬂow helps to improve the current gain. The

carriers injected by the emitter are forced to wander

towards the base along the top of an extended cliff in

voltage, at the bottom of which lies the collector. For

example, 99% of the carriers stumble over the cliff

and are swept out the collector and the remaining 1%

make it to the base connection; this gives a very sat-

isfactory current gain b ¼I

of 99.

Implementing spin-polarized current transport in a

semiconductor enables a new concept in spin tran-

sistor design—the spin-polarized injection current

emitter device (SPICE) (Gregg et al. 1997) in which

the emitter launches a spin-polarized current into the

electric ﬁeld screened region and a spin-selective

guard-rail along the top of the cliff determines

whether these polarized carriers are allowed to fall

into the collector. Thus, we have a device with a

respectable current gain from which power-gain may

easily be derived, but whose characteristics may again

be switched by manipulating the magnetic guard

rail via an externally applied magnetic ﬁeld. A wide

variety of designs are possible which answer to this

general principle. For example the emitter and col-

lector interfaces may be realized by p–n junctions,

Schottky barriers, or spin tunnel junctions and the

geometry of the device may be adjusted to allow a

greater or lesser degree of electric ﬁeld driving com-

ponent to the diffusion current in the base depending

on the application.

10.4 Measuring Spin Decoherence in Semiconductors

The crucial question which needs to be answered in

order to realize this kind of spin transistor is whether

spin transport is possible at all in semiconductors,

and, if so, whether it is possible over the sort of

physical dimensions on which a typical transistor is

built. In other words, we need an estimate of the spin

diffusion length in a typical semiconductor. A sub-

sidiary question concerns the role of dopants in the

semiconductor and whether they introduce spin-orbit

scattering, which militates against the spin transport

by reducing the spin ﬂip times. Some consideration

has been given to allowed nonequilibrium spin con-

ﬁgurations in a semiconductor (Flatte and Byers

2000).

10.5 Direct Spin Injection from Metals to

Semiconductors

Experiments have been performed (Gregg et al. 1997,

Jia et al. 1996) in which ferromagnetic contacts

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Magnetic Reco rding Systems: Spin Electronics

perform direct spin-injection into a semiconductor

and analyze the polarization of the current that

emerges on the other side. Transport results are ob-

served which are insensitive to magnetic ﬁeld direc-

tion, have even symmetry (thereby eliminating AMR

and Hall effect as a possible cause) and they are

compatible with the observed domain magnetization

processes for the cobalt pads. They appear to corre-

spond to spin transport through the semiconductor.

However the spin transport effects are of the order of

a few percent at best, yet the effect decays only very

slightly with silicon channel length and was still well

observable for 64 mm channels. This suggests that the

spin diffusion length in silicon is many tens of mi-

crons at the least, but that the spin injection process

at the metal/silicon interface is highly inefﬁcient.

Clearly the process is highly preparation sensitive as

witnessed by the null results with evaporated silicon

(Loraine et al. 2000).

This direct injection inefﬁciency is being widely

observed and its cause is still hotly debated. It may

arise from spin depolarization by surface states, or it

may be explainable by the Valet/Fert model (Valet

and Fert 1993) in which spin injection is less efﬁcient

for materials of very different conductivities. The

discussion below in connection with spin tunneling

concerning hybridization at the interface with the

spin selective injector is no doubt relevant in this

context also. It may also be because the spin injection

is not being implemented at the optimum point in the

semiconductor bandstructure. From the latter point

of view, spin tunnel injection into semiconductors is a

more versatile technique, since, for a given injected

tunnel-current density, the necessary bias (and hence

the point in the band-structure where injection oc-

curs) may be tuned by varying the thickness and/or

the tunnel barrier height.

10.6 Optical Polarized Carrier Generation

A direct measurement of semiconductor spin diffu-

sion length has been made by decoupling from the

spin injection problem and generating the spin-po-

larized carriers in the semiconductor itself (Hagele

et al. 1998, Kikkawa and Awschalom 1999). Gallium

arsenide was used as the host that has the property

that, when pumped with circularly polarized light, the

selection rules are such as to populate the conduction

band with predominantly one spin type. These spins

can be made to precess by application of a small

magnetic ﬁeld. The resulting precessing magnetiza-

tion is then detected using optical Faraday rotation

using a probe beam from the same optics as provides

the pump. The magnetization drifts under the appli-

cation of a driving electric ﬁeld and the spatial decay

in precession signal gives a measure of the spin dif-

fusion length. The results are of the order of many

tens of microns, in accordance with the silicon direct

injection experiment discussed above.

Thus, it would seem beyond doubt that the spin

diffusion length in semiconductors is adequate for the

design and realization of SPICE-type transistor struc-

tures—so long as means are provided for efﬁcient

delivery of the initial spin-polarized current.

10.7 Spin Injection from Magnetic Semiconductors

An alternative method of generating spin-polarized

carriers in a semiconductor is by injection from a

magnetic semiconductor (Fiederling et al. 1999, Ohno

et al. 1999). Striking results are obtained by injecting

spin-polarized carriers from a magnetic semiconduc-

tor into a normal semiconductor light emitting diode

structure. The polarization of the injected carriers is

dependent on the magnetization direction of the mag-

netic semiconductor that supplies them. This is re-

ﬂected in the polarization of the light emitted by the

LED—its polarization is related to the spin of the

electrons which cause it via the same selection rules

as discussed above in the Awschalom experiment

(Hagele et al. 1998, Kikkawa and Awschalom 1999).

The polarization of the light emitted correlates well

with the hysteresis loop for the magnetic semiconduc-

tor and decays with temperature exactly as the mag-

netic moment of the magnetic semiconductor, leaving

little doubt that successful spin injection has been

achieved. The percentage injection achieved here is

more favorable than has been possible by direct in-

jection from metals and it may be that magnetic semi-

conductors have an important role to play in future

spin electronics development, notwithstanding the

non-negligible materials problems which they pose.

Spin-tunnel injection into semiconductors is also

a promising technique which offers higher injection

efﬁciency than direct spin-injection (Prins et al. 1996).

11. The Rashba Effect

The Lorentz transformation indicates that to a rel-

ativistic observer traveling with respect to the source

of an electric ﬁeld, it appears to have a magnetic

component whose orientation depends on the geo-

metry of the observer’s travel relative to the ﬁeld axis.

If the electric ﬁeld in question originates from crystal

ﬁeld effects or from the depletion layer in a semicon-

ductor structure, then the magnetic component that

appears to relativistic electrical carriers is capable of

spin-splitting the conduction band if it is diagonal

and of causing spin precession if it is off-diagonal.

This is the Rashba effect.

11.1 The Datta–Das Transistor or Spin FET

The Rashba effect gives rise to a novel spin electronic

device concept proposed by Datta and Das (Datta

and Das 1990), but not realized experimentally. The

device has the construction similar to that of a

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Magnetic Reco rding Systems: Spin Electronics

conventional ﬁeld effect transistor with source and

drain electrodes made in ferromagnetic metals and a

semiconductor channel which is subject to a trans-

verse electric ﬁeld whose magnitude may be tuned by

applying a gate voltage. Spin-polarized carriers leave

the source with their spins parallel to the source

magnetization and precess in transit through the

channel owing to the Rashba effect. If the drain

magnetization is parallel to that of the source and the

carriers perform an integral number of precessions

in transit, then the device conductance is high. How-

ever, slight modiﬁcation to the gate voltage changes

the precession rate and if the spins now execute

N þ1/2 precessions in transit, the device conductance

is minimized. The resulting device thus behaves like a

normal FET with the additional feature that the dif-

ferential magnetization of its electrodes (and hence its

electrical characteristics) are sensitive to externally

applied magnetic ﬁeld.

Although the device has not been realized, much

groundwork on the materials properties and princi-

ples exist in the literature and spin-valve effects have

apparently been observed in experiments involving

two-dimensional electron gases in which spin-polar-

ized carriers are injected from a permalloy contact

into an AlSb/InAs quantum well and analyzed by a

second permalloy contact with a different switching

ﬁeld (Hammar et al. 1999).

However some skepticism has been voiced by other

workers on the spin FET problem (van Wees et al.

2000), and theoretical signposts have been placed to

spin precession-type data which will unambiguously

conﬁrm that Datta–Das-type device function has

been observed (Tang et al. 2000). This is clearly an

exciting topic which will continue to attract attention

and research activity for the foreseeable future.

12. Coulomb Effects: Coulomb Blockade and the

Single Electron Transistor

The electrostatic energy of a charged capacitor is

=C.IfC is sufﬁciently small, this energy can com-

pete with thermal quanta of size k

T, even for Q ¼e,

the electronic charge. Small metallic spheres or pads

with physical dimensions in the nanometer range

have capacitances in the right ballpark for this con-

dition to be obtained. If such a metallic island is

sandwiched between two physically close metallic

electrodes (the source and the drain), a single electron

transistor (SET) is formed (Devoret and Grabert

1992). A third electrode (the gate) which is cap-

acitatively coupled to the metallic island is biased

in order to pass current or to coulomb blockade the

SET.

The physics involved is a competition between

three energy terms; the electrostatic energy, E

, of the

island due to the presence on it of just one electron,

the thermal quantum k

T, and the energy eV

gained

by an electron in falling through the bias voltage V

The ﬁrst electron which arrives on the island from the

source electrode charges it to a potential which is

sufﬁcient to prevent any further electrons hopping to

the island until the ﬁrst electron has left via the drain

electrode. The charges are encouraged to jump from

the island to the drain (and hence make room for

more charges to arrive from the source) by appro-

priate bias on the gate electrode. If the thermal

quantum size is arranged to be small compared with

the electrostatic energies in play, the risk of random

thermal interference with the current control is

negligible.

12.1 The Ferromagnetic Single Electron Transistor

In a spin transistor, there is a fourth energy term

which we can now introduce into the problem,

namely the electrochemical potential difference for

spin-up and spin-down electrons associated with a

spin accumulation. In practice this is achieved by

making the electrodes and/or the island from ferro-

magnetic material. A ferromagnetic source electrode

will in principle produce a spin accumulation on a

nonmagnetic island and, under certain bias condi-

tions, the associated electrochemical potential holds

the balance of power between the main energy terms

and hence has a large degree of control over the cur-

rent ﬂow to the ferromagnetic drain. Other conﬁgu-

rations are possible in which the island also is

magnetic. Fert and Barnas have made extensive cal-

culations for various temperature regimes of the var-

ious possible modes of behavior of such devices

which are called ferromagnetic single electron tran-

sistors (FSETs) or spin SETs (Barnas and Fert 1998).

12.2 Spin Blockade

Another possibility which arises also if the magnetic

island is itself a ferromagnet is that of a spin-block-

aded system in which electrical transport across

the device is switched by magnetizing the island

(Sirisathitkul et al. 2001a). An example is a Schottky

barrier on the edge of which has been placed a series

of magnetic islands which are antiferromagnetically

coupled (and hence blockaded) in zero applied mag-

netic ﬁeld. Applying a ﬁeld orients these superpara-

magnetic particles and the resistance of the structure

decreases owing to a tunnel-hopping current between

adjacent islands. Exposure to light increases the re-

sistance of the structure owing to photon-promotion

of electrons from the islands to the large density of

adjacent surface states. The geometry of this system is

not unlike that of a high electron mobility transistor

(HEMT) in which the performance of the main cur-

rent channel is controlled by localized states in a

physically distinct nearby region of the device.

619

Magnetic Reco rding Systems: Spin Electronics