Spin-Polarized Tunneling at Interfaces Between Oxides and 

Metals or Semiconductors 

by Douglas J. Strand 

ARL-TR-3925 September 2006 

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Army Research Laboratory 

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ARL-TR-3925 September 2006 

Spin-Polarized Tunneling at Interfaces Between Oxides and 

Metals or Semiconductors 

Douglas J. Strand 

Weapons and Materials Research Directorate 

Materials Division 

Materials Applications Branch 

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14. ABSTRACT 

Spin-polarized tunneling is a way to create a new type of electric current whose two driving forces are spin momenta rather than opposite 

charges. Much research has been done with this idea and that research has been reviewed and developed to propose an experimental program 

to use this new type of current to devise such electronic devices as the Datta-Das spin field-effect transistor (SFET), the magnetic bipolar 

transistor, the hot-electron spin transistor, and the spin-valve photo-diode. This report includes a short history of spin-polarized transport and 

then outlines the developed theory. The experimental methods and materials of the field are also discussed. This research proposes to use 

electron paramagnetic resonance (EPR) and Barkhausen Noise Analysis (BNA) with other standard methods of materials science and 

engineering to examine the feasibility and develop an experimental plan to make spin-polarized transport effective for the manufacture of the 

above named devices. Some materials will be effective for spin-polarized transport devices and some will not. The quest for the effective 

materials is a major part of this research. Half-Heusler and full-Heusler alloys are studied as possible candidates for the devices. The term 

spintronics, an acronym for spin electronics, is used almost synonymously with spin polarization transport devices. 

15. SUBJECT TERMS

 Spintronics, spin polarization, spin injection, paramagnetic resonance, 

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19a. NAME OF RESPONSIBLE PERSON

Douglas J. Strand 

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(410) 306-0827 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18
Contents 

List of Figures iv

1. Introduction 1

2. Problem Areas 4

3. Research Objectives 7

4. Recent Breakthroughs 8

5. Theory 8

6. Proposed Research Plan 13

7. Anticipated Results and Conclusions 25

References 33

Acronyms 36

Bibliography 38

Distribution List 39

iii 
List of Figures 

Figure 1. Full Heusler alloy with L21 structure............................................................................... 5 

Figure 2. Half-Heusler alloy with C1b structure. ............................................................................ 6 

Figure 3. The basic principle of MBE showing coevaporation of atoms or molecules from 

two different sources onto a heated substrate. ........................................................................ 16 

Figure 4. Heterojunction , with dangling bonds at the interface, of a lattice mismatched 3-D 

crystal...................................................................................................................................... 16 

Figure 5. Spin-valve photo-diode (48).......................................................................................... 29 

iv 
1. Introduction 

It was shown in the 1970s that the spin conservation in electron tunneling gives rise to the 

possibility of spin sensitive tunneling between two ferromagnetic films. One example is the 

study of the interface of iron (Fe) and nitrogen (Ni) with aluminum oxide (Al2O3) in 

Fe / Al2O3 / Ni. This is an example of a FM/I/FM junction, where FM stands for ferromagnetic 

and I stands for insulator. The current technique of forming Al2O3 barriers is by oxidizing a thin 

aluminum (Al) layer deposited on the ferromagnet. 

X-ray Photoelectron Spectroscopy (XPS) can be used to characterize the compositional, 

chemical, and electronic properties of this system. These properties can then be correlated to 

other properties of the interface, such as magnetoresistance (MR). MR is the increase in the 

electrical resistance of a metal or semiconductor when placed in a magnetic field. The analysis of 

the experimental results on MR bears directly on the shape and connectivity of the Fermi surface. 

Transverse MR is of greatest interest. Using an (x,y,z) Cartesian coordinate system, x is the 

direction of transport and of the applied electric field; z is the direction of the applied magnetic 

field; and y is called the transverse direction and is the direction of the Hall field. 

The most interesting experiments are those carried out at low temperatures on very pure 

specimens in strong magnetic fields, since under these conditions the product c τω of the 

cyclotron frequency and the relaxation time may be 1. Also under these conditions, the 

details of the collision processes are suppressed and the details of the Fermi surface enhanced. 

The effect of a weak magnetic field 

ff

( τω pp1) c is to increase the resistance by an additive term 

proportional to H2. 

In very strong fields, when c τω ff1, the transverse MR of a crystal may generally do one of 

three things: saturate, continue to increase, or saturate in some crystal directions but not in 

others. Crystals are known in all three categories. The first category consists of crystals with 

closed Fermi surfaces, such as indium (In), Al, sodium (Na), and lithium (Li). The second 

category consists of crystals with equal numbers of electrons and holes, such as bismuth (Bi), 

antimony (Sb), tungsten (W), and molybdenum (Mo). The third category consists of crystals with 

Fermi surfaces having open orbits for some directions of the magnetic field, such as copper (Cu), 

silver (Ag), gold (Au), magnesium (Mg), zinc (Zn), cadmium (Cd), gallium (Ga), thallium (Tl), 

tin (Sn), lead (Pb), and platinum (Pt). The value of MR tells us whether the Fermi surface is 

closed or contains open orbits, and in which directions the open orbits lie. The transverse MR 

does not saturate if there are equal numbers of holes and electrons. 

It is remarkable that in some crystals the MR saturates except for certain special crystal 

orientations. This can be explained in terms of open orbits, which occur in strong magnetic 

fields. An orbit is open if it carries current essentially only in a single direction in the plane 

normal to the magnetic field. Therefore, the open orbit cannot be saturated by the field. It has 

been shown that the MR saturates except when the open orbit carries current almost precisely 

parallel to the y direction, i.e., the direction of the Hall electric field. This explains the 

extraordinary anisotropy of the transverse MR observed in single crystals. (1) 

1 
Quantized energy levels or the interaction of quantized spins create quantum functionality. 

Contemporary materials engineering techniques now enable the fabrication of a wide variety of 

compositionally modulated materials, which are commonly called “heterostructures.” These 

heterostructures have excellent control of explicitly quantum mechanical phenomena such as 

quantum confinement and quantum tunneling. They have had a lasting impact on quantum 

device technologies as well as on fundamental discoveries in condensed matter physics. For 

example, semiconductor heterostructures play an important role in contemporary 

opto-electronics and microwave frequency devices, while also providing a rich arena for 

examining correlated electron physics in low dimensions. 

At the same time, advances in the fabrication of metallic magnetic heterostructures now allow us 

to read memory of unprecedented density with the giant magnetoresistance (GMR) effect and 

also form the basis for a nonvolatile memory know as “magnetic random access memory” 

(MRAM). MRAM uses magnetic hysteresis to store data and MR to read data. In addition to the 

nonvolatility of MRAM, other advantages include much faster write times, no wearout with 

write cycling, lower energy for writing, and access times that are about 1/10,000 of those of hard 

disk drives. 

Galvanic isolators are another application of spin electronics (spintronics) (2). These advances 

have led to the integration of the fields of semiconductor heterostructures and magnetic materials 

to create the new field of “semiconductor spintronics” that ties these usually disparate areas of 

science and technology (3). 

Nanostructures are another class of materials that are important to spintronics. Transport 

experiments have been performed on ferromagnetic (Ga,Mn)As* nanoconstrictions that can be 

used to trap and investigate domain walls, which can, in turn, be used to study spin injection. (4) 

The effect of spintronics on technology can only be speculated. Moore’s Law may give us an 

idea of the magnitude of its impact. It states that microprocessors will double in power every 

18 months as electronic devices shrink and more logic is packed into every chip (5). 

The Chambers or kinetic formulation of the transport equation is more revealing for the MR 

problem with a general Fermi surface than is the common iterative Boltzmann method, where 

magnetic effects appear only in second order. The most useable transport equation for MR is the 

general nonlinearized result of Chambers, which for the distribution function is 

( ) ( ) ( ) ( ) ( ) ( ) ∫ ∞− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = Δ− − t

t sk

ds tf tk

dt f ' 0 exp' ' '

τ

εε

τ ∫

t

, (1) 

where is the energy gain from the force F between times t’ and t in the 

absence of collisions;

( ) ∫ ⋅=Δ t

t tvFdt ' ε ''''

τ is the relaxation time; and is the equilibrium distribution function. 

This leads to the fact that there is always a longitudinal MR that always saturates. For

0 f

Tk ω f Bc

andωcτ ff 1, an oscillatory behavior is observed in the conductivity components. The quantum 

 

*Ga = gallium, Mn = manganese, and As = arsenic. 

2
oscillations in transport properties have the same origin as the susceptibility oscillations in the de 

Haas-van Alphen effect (1). 

There are two types of MR, anisotropic magnetoresistance (AMR) and GMR. AMR measures 

the change in resistance seen when the current flowing through a sample changes from being 

parallel to the internal magnetization to being perpendicular to it. AMR is applicable to singlecrystal magnetic metal whiskers, but the discovery of GMR brought a new class of 

magnetoresistive systems into being. GMR is a term coined to describe the behavior of materials 

consisting of alternating layers of ferromagnetic and nonmagnetic metals deposited on an 

insulating substrate. The GMR effect is the phenomenon that the resistance, measured by current 

flowing parallel to the layers (of constant thickness) in multilayered metallic film structures, is 

greatest when the magnetic moments in the alternating layers are oppositely aligned and smallest 

when they are all parallel. This change was found to be 100% in the original experiments 

reporting GMR, while the most recent record is 220% at low temperatures. The largest effects 

are seen with Fe-chromium (Cr) or cobalt (Co)-Cu alternating layers up to approximately 100 

repeats at layer thicknesses of a few nanometers. (6) 

These developments led to the field of spintronics. The goal of spintronics is to understand the 

interaction between a particle’s spin and its solid-state environments, and to make useful devices 

using the acquired knowledge. The common goal in many spintronic devices is to maximize the 

spin detection sensitivity to the point that it detects not the spin itself, but changes in the spin 

states (7). The use of electron spin offers the potential advantages of nonvolatility, lower power 

consumption, increased data processing speed, and increased integration densities compared with 

conventional semiconductor devices (2). 

To compare spin current to charge current, we start by calling density spin polarization a and 

current spin polarization b. Then, b is the ratio of spin current js, which is the difference between 

the charge currents formed by the spin-up and spin-down electrons and the total charge j: 

 j

j b s = . (2) 

The current spin polarization is much less intuitive than the density spin polarization. There are 

several reasons for this. First, b involves not only the carrier and spin densities, but also the drift 

or diffusion velocities, which can be spin dependent. Second, unlike a, the magnitude of b is not 

restricted to a small interval. The magnitude of b is not even bounded. Therefore, the spin current 

can be finite even if there is no charge current, making b infinite. In addition, the signs of b and a

can be different. Third, unlike the charge current, the spin current need not be uniform. Because 

of spin relaxation, js (and also b) is not conserved. For these reasons, unless the relation between 

a and b is obvious or is explicitly derived, b is not indicative of the spin injection efficiency. (8) 

In addition to XPS, electron paramagnetic resonance (EPR) spectroscopy can be used to 

characterize the properties. Electronic paramagnetism exists when the atoms or molecules in a 

substance possess a net electronic magnetic moment. There are four types of substances that 

exhibit paramagnetism (9): 

1. All atoms and molecules that have an odd number of electrons 

2. All free atoms and ions with unfilled inner electron shells and many of these ions when in 

solids or in solution 

3
3. Several miscellaneous compounds, including molecular oxygen and organic biradicals 

4. Metals 

When a variable magnetic field is applied to such a material, resonance occurs when the 

frequency of this applied field is equal to the frequency of the magnetic field created by the 

atoms’ (molecules) electronic magnetic moment. An EPR spectrometer works off this principle 

and provides a spectrum that can be interpreted to characterize the substance. The results of the 

two methods, XPS and EPR, will be compared and contrasted to obtain a further understanding 

of the properties of the interface, because each method complements the other by giving a 

different perspective of the material. 

2. Problem Areas 

An ideal spintronic material would be one that enables the transport of only one spin carrier 

across the interface between it and an unpolarized material, without any spin-flip scattering. This 

project will attempt to find such an ideal spintronic material. Epitaxial (having a semiconductor 

layer grown from a substrate layer) Heusler alloys are considered to be prime candidates, 

because they show great potential for spin-injection contacts to compound and elemental 

semiconductors. The Heusler structures consist of four interpenetrating face-centered-cubic (fcc) 

sublattices with atoms at X1(0,0,0), X2(1⁄2,1⁄2,1⁄2), Y(1⁄4,1⁄4,1⁄4), and Z(3⁄4,3⁄4,3⁄4), some of which may or 

may not be filled. In the full Heusler alloy, X2YZ with the L21 crystal structure, all of the 

sublattices are filled. A drawing of this is shown in figure 1. 

4
Figure 1. Full Heusler alloy with L21 structure. 

NOTE: From the Center for Computational Materials Science (CCMS) Naval Research Laboratory Web site, 

http://cst-www.nrl.navy.mil. 

5
For the half Heusler alloy, XYZ with the C1b crystal structure, the X1 is empty. A drawing is 

shown in figure 2. 

Figure 2. Half-Heusler alloy with C1b structure. 

NOTE: From the CCMS Naval Research Laboratory Web site, http://cst-www.nrl.navy.mil. 

Major challenges remain in controlling composition, atomic ordering, and defects, both in the 

film itself and at the interface, in order to minimize spin-randomizing scattering. Whether or not 

truly half-metallic Heusler alloys can be realized depends critically on controlling defects at the 

appropriate level. Fortunately, the band structures are compatible for highly polarized injection, 

even if the Heusler alloy is half-metallic. 

6 
Gardelis et al. (2) have attempted to produce the ternary half-Heusler alloy NiMnSb as a bulk 

material with very good properties for spintronics using arc welding. This material has been used 

as a target to grow highly crystalline NiMnSb thin films on semiconductor substrates at low 

temperatures of approximately 200 °C by pulsed laser deposition (PLD). NiMnSb crystallizes in 

the C1b structure. This structure consists of four interpenetrating fcc superlattices equally spaced 

along the (1,1,1) direction. Ni occupies the lattice site at (0,0,0). Mn occupies the site at 

(1⁄4, 1⁄4, 1⁄4). The site at (1⁄2, 1⁄2, 1⁄2) is unoccupied and, lastly, Sb occupies the site at (3⁄4, 3⁄4, 3⁄4). The 

magnetic properties are due to magnetic moments localized at the Mn atoms, which interact by 

itinerant electrons. It has been shown that 9 out of 22 valence electrons are located in spin-down 

bands; therefore, the total spin magnetic moment of NiMnSb becomes 4.0 μb, i.e., an integral 

number as expected for half-metallic ferromagnets. All the properties of NiMnSb that were 

investigated by Gardelis et al. (2) indicated that at a temperature of approximately 150 K there is 

a crossover from half-metallic to normal ferromagnetic behavior. They also demonstrated that 

PLD could be used for low-temperature deposition of highly crystalline thin films of this 

material (2). In addition, spin-injection polarization measurements for transport from a Heusler 

alloy into a semiconductor are anticipated in the near future, utilizing spin-light emitting diode 

(LED) structures (10). 

Magnetic tunnel junctions with a stacking structure of Cr/Co-Mn-Al/Al-O/Co-Fe/Ir-Mn2 were 

fabricated using an ultra-high vacuum (UHV) magnetron-sputtering machine. The Co-Mn-Al 

films showed a B2 structure, which involves partial disorder between Mn and Al sites. Tunnel 

magnetoresistance (TMR) ratios at room temperature were 27% and 40% before and after 

annealing at 250 °C, respectively. Those values are much higher than the ones obtained in 

previous experiments using half Heusler alloys. Optimization of sputtering and oxidation 

conditions can further enhance the TMR ratios. Furthermore, a high spin polarization material 

can engender a large TMR. Since Co2MnAl was found to have such a high spin polarization, this 

alloy is very promising for future applications. (11) 

3. Research Objectives 

The objective of this research will be to develop arrays of individual magnetic memory cells in 

which the data is stored as the direction of magnetization of very small ferromagnetic elements. 

A multiplexed current pulse technique to reverse selected magnetic elements will be used for the 

writing process, while a tunneling MR technique will be used for the read process (12). 

 

2O = oxygen and Ir = iridium. 

7
4. Recent Breakthroughs 

The potential impact of this research is that information can be stored in a new and more 

efficient way in communications and computer systems. The energy within the spins of electrons 

can be directed to produce faster and more controlled systems. The carriers of current in a 

ferromagnetic metal, such as Fe, Co, or Ni, are themselves magnetically polarized. The magnetic 

moments of these carriers reflect an imbalance between up and down spins. A normal metal, 

such as Cu, has equal numbers of electrons with up and down spins, and hence have no net 

moment. These electrons, which are at the top of the filled states (Fermi level), are unpolarized. 

However, a ferromagnetic metal, to avoid the high energy of having a high density of states at 

the Fermi level, has a splitting between the up and down spin states, called “exchange splitting,” 

which lowers the total energy of the system. Here, there is a spin imbalance with the up-spin (or 

majority) d-electron states all filled and the d-electron states at the Fermi level containing 

entirely down-spin (minority) electrons. The moment of the atom is simply proportional to the 

difference between the number of spins in the two spin bands. At the Fermi level, the carriers can 

be s, p, or d shell electrons. The d electrons are more highly polarized than the s or p electrons 

and produce a current that is partially spin polarized (6, p. 58). This concept of spin polarization 

will be studied and applied to data storage in this project. 

5. Theory 

The theoretical models of junction magnetoresistance (JMR) will be examined for their 

correctness and applicability using modern technology. Julliere’s formula will be studied for its 

applicability, along with Slonczewski’s model. One critical issue will be determining which 

theoretical model provides the truest picture of spin-polarized tunneling as applied to 

ferromagnetic junctions (13). 

The early theories of JMR were based on a number of simplifying assumptions. Specifically, 

they usually employ simple parabolic bands and/or momentum and energy independent 

tunneling matrix elements. The classical theory of tunneling assumes that the left and right 

electrodes are two completely independent systems and the insulating barrier is a perturbation 

permitting quantum tunneling between them. In a tunnel junction, the relative change in the 

resistance of the junction is given by 

RL

RL

TMR PP

PP R

+ =1

2 , (3) 

where PL and PR are the spin polarizations of the left and right electrodes, respectively. This is 

Julliere’s formula. 

Slonczewski’s model treats the ferromagnetic/barrier interface more realistically than Julliere’s 

classical theory of tunneling. He considered the electrodes and the barrier to be a single quantum 

mechanical system; however, each electrode has an evanescent wave function of electrons that 

8
penetrate into the tunnel barrier. Slonczewski recognized that these wave functions need to be 

matched across the junction. His principal result was that the polarization P of tunneling 

electrons depends on the height of the barrier, Vb, through an imaginary wave vector, iκ , in the 

barrier defined by 

 [ ( )] 2/1 hκ 2 −= EVm Fb , (4) 

 which is 

+ ↑ ↓

↓↑−

↑ + ↓

↓−↑ = kkkk

kk

kk P 2

2

κ

κ , (5) 

where are the Fermi wave vectors in the up- and down-spin bands. (In a 

three-dimensional (3-D) crystal, modes may propagate in any direction and the wavenumber k

becomes a vector

, kk ↓↑

κ . It is limited to a Brillouin zone. For each wavenumber, there are three 

acoustical modes.) 

For a high barrier, the polarization P reduces to Julliere’s formula, but P can even change sign 

when the barrier is low (13). A problem that was encountered with the Slonczewski model was 

that the method of matching the wave functions is not easily generalizeable beyond a simple 

parabolic band. For this reason, most recent theories of JMR are based on the versatile and 

rigorous Kubo/Landauer formula for conductance. In this formula, the total conductance Gσ in a 

spin channel σ can be expressed in terms of the one-electron Green’s functions 

. Here L and R represent the left and right neighboring planes of the 

junction and is the electron momentum parallel to the junction. The formula is 

( )( 11 11 FL FR ,,, kEgkEg σ σ )

11 k

= ∑ ( ) [ ] ( ) ⋅[ ] ( ) 11

11 11

2

,Im ,Im 4

k

FL

t

FR kEgTkEgTTr h

e G σ

σ

σ

σ

σ , (6) 

where , and represent matrices in the orbital space, and the imaginary part of the 

Green’s function represents the density of states for the system. 

11 RL ,, kgg σσ Tσ

The summation is over the two-dimensional (2-D) Brillouin zone and the trace is over the orbital 

indices corresponding to (s,p,d) orbitals, which are required in a tight-binding parameterization 

of the electrodes and the barrier. The matrix, , is given by Tσ

( ) ( ) ( ) ( )( ) [ ] , (7) 1

11 11 11 1111 , , −

−= FL ktkEgktkEgIktT t

FR

σ σ

σ

where I is a unit matrix in the orbital space and ( ) 11 kt is the matrix of tight-binding hopping 

integrals connecting atomic orbitals in the left and right planes between which the tunneling 

current is calculated. 

The Kubo/Landauer formula can be used to describe coherent tunneling, i.e., conservation of the 

momentum parallel to the junction, or noncoherent tunneling. There are two categories of 

noncoherent tunneling: either disorder is simplified and band structure is realistic, or it is the 

other way around and band structure is simplified and disorder is realistic. The simplest 

treatment of disorder in the barrier is provided by the classical theory of tunneling, i.e., Julliere’s 

formula, which assumes that tunneling from any occupied state of the left electrode to any 

9
unoccupied state in the right electrode is equally probable. This model has two problems. First, it 

leads to an incorrect sign of the tunneling current, and second, it fails to describe JMR in 

junctions with a nonmagnetic metallic interlayer. Julliere’s formula can be corrected by 

examining the approximations that must be made to derive it from the Kubo/Landauer formula. 

The generalization of Julliere’s formula incorporating all of the corrections resulting from the 

approximations takes the form 

= [ ] ∑ () ( ) × [∑ ( ) ( )] ' '

11

'

11

11

2

' 11 11

,Im0 ,Im0 4

k FL

t

k FR kEgtkEgtTr hN

e Gσ σ σ , (8) 

where the prime indicates that all the quantum well states are excluded and the trace is again 

over all the orbital indices. Quantum well states are bound states that are formed in junctions 

with a nonmagnetic metallic interlayer and do not contribute to transport of charge. This 

generalized Julliere’s formula is the simplest physically plausible description of tunneling in the 

presence of disorder. Disorder is the degree to which the tunneling is not coherent, i.e., the 

degree to which the momentum, , parallel to the junction, is not conserved. 11 k

Two additional effects are the Coulomb blockade effect and the enhancement of the JMR in the 

Coulomb blockade regime, which apply when a small grain of a ferromagnetic material is 

separated by insulating barriers from ferromagnetic leads. In this case, tunneling to the grain may 

be strongly influenced by the charging energy in the grain. For a very small grain, the 

electrostatic energy increases by 

C

e

2

2

 (9) 

when an electron tunnels into the grain (e is the electron charge and C is the capacitance of the 

grain). Tunneling is, therefore, blocked unless the charging energy is overcome by bias voltage 

or thermal energy. This effect is the Coulomb blockade effect. 

The second effect is an enhancement of the JMR in the Coulomb blockade regime for a double 

junction explained by the fact that there is an absence of Coulomb blocking in small grains 

resulting in sequential tunneling (two independent tunneling effects) at high temperatures and cotunneling (a coherent tunneling through both junctions via a virtual intermediate state) at low 

temperatures. For sequential tunneling, the effective resistance of a double junction is 

proportional to the sum of the resistances of the two junctions, whereas, for co-tunneling, the 

total resistance is proportional to the product of the junction resistances. 

The conductance G(Hs) of a tunnel junction with two ferromagnetic electrodes, whose magnetic 

moments are aligned parallel in an applied saturating field Hs, is much higher than its 

conductance G(0) in zero field when the moments are antiparallel. This is called tunneling JMR 

and the relative change in the resistance of the junction, i.e., the so-called JMR ratio, is defined 

as 

 1

1 1

)0(

)()0(

−

− − − = G

HGG

JMR S . (10) 

10
Looking at the ratio of the resistances at low temperatures, the JMR ratio is enhanced, but it 

reverts to the usual bulk JMR ratio at high temperatures. Extending these ideas provides an 

explanation of an enhancement of the JMR observed in granular systems at low temperatures 

(13, pp. 261–7, 270). 

The field of spintronics can be divided into two categories: those that cover the emerging 

applications and those covering already well-established schemes and materials. The second 

group is also called magnetoelectronics and typically covers paramagnetic and ferromagnetic 

metals and insulators that utilize MR effects. Examples are magnetic read heads in computer 

hard drives, nonvolatile MRAM, and circuit isolators. There is a large class of emerging 

materials that characterize the first category of spintronics. Examples are ferromagnetic 

semiconductors, organic semiconductors, organic ferromagnets, high-temperature 

superconductors, and nanotubes. These materials can bring novel functionalities to the traditional 

devices (7, p. 325). We will look at the first category in this study, because we want to examine 

the usefulness of EPR and Barkhausen Noise Analysis (BNA) with these materials, but we also 

want to investigate some of the emerging materials as the promise of their usefulness is very 

great. 

The occurrence of ferromagnetism in magnetic semiconductors is neither a new nor rare 

phenomenon, and was extensively studied several decades ago in materials such as manganites, 

semiconductor spinels (e.g., CdCr2Se43), the europium chalcogenides (e.g., EuO), and the lead 

chalcogenides (e.g., Pb1-x-ySnyMnxTe4). The recent resurgence of interest in ferromagnetic 

semiconductors has largely been ignited by the discovery of ferromagnetism in the Mn-doped 

III-IV semiconductors, Ga1-xMnxAs and In1-xMnxAs. 

Mean field theories developed to understand the origins of ferromagnetism in the III-Mn-V 

semiconductors have lead to predictions of ferromagnetism in a much wider class of 

magnetically doped semiconductors. In addition to the mean field approach that relies on carriermediated ferromagnetism, first principles calculations have also predicted the existence of 

ferromagnetic ground states in many different materials. These predictions have created intense 

interest in the crystal growth of magnetic semiconductors such as (Zn,Cr)Te, magnetic III-V 

nitrides, phosphides, antimonides, magnetic group IV semiconductors, and various other 

complex phosphides and oxides. 

Magneto-transport in Ga1-xMnxAs will be examined in this project. Magneto-transport 

measurements in III-Mn-V ferromagnetic semiconductors provide a convenient means of 

probing the ferromagnetic properties. The Hall effect in these materials has contributions from 

both the standard Hall voltage and the “anomalous Hall effect” (AHE) and is described by 

ρ = Hxy + A μ 0MRBR , (11) 

where RH is the ordinary Hall coefficient, RA is the AHE coefficient, and M is the sample 

magnetization. A detailed understanding of the AHE in Ga1-xMnxAs is relatively recent, wherein 

the AHE originates not in the interplay between spin-orbit coupling and elastic scattering, but 

rather from an intrinsic Berry’s phase effect related to the presence of the spin-orbit coupling 

 

3Se = selenium. 

4Te = tellurium. 

11
itself. Berry’s phase effect is the phenomenon that any “vector” that is parallel-transported 

(moved keeping the same direction) along a path back to the original place may acquire an angle 

with respect to its initial direction prior to transport. This angle is a geometric property. (14) 

This theory also addresses all aspects of the anisotropic magnetoconductivity tensor in these 

ferromagnetic semiconductors. An interesting consequence of this anisotropic 

magnetoconductivity tensor is the “planar Hall effect,” wherein a transverse electric field arises 

in a measurement geometry identical to that used for AMR (see section 1) measurements (i.e., 

the magnetic field is in plane). While this planar effect is very small in metallic ferromagnets, it 

is extremely large in Ga1-xMnxAs. This “giant planar Hall effect” is an elegant and sensitive 

probe of the angle-dependent magnetization and also provides a means of studying magnetic 

domain reversals. Quite remarkably, the large domain sizes in Ga1-xMnxAs enable the 

observation of Barkhausen jumps (small discontinuities in the magnetic hysteresis loop caused 

by domain wall movements (15)), even in devices as large as a few microns. Ongoing 

measurements of this planar Hall effect show that the signals tend to be even larger in more 

insulating digital Ga1-xMnxAs alloys. The Barkhausen jumps will be examined in this project 

using a Stressscan 5000 instrument. 

Since one of the main goals of semiconductor spintronics is to obtain optical or electrical control 

of ferromagnetism, it is important to identify ferromagnetic semiconductors wherein there exists 

a clear coupling between the carrier density and ferromagnetic order. The best way to do this is 

to carry out multiple complementary measurements that probe the ferromagnetic transition. 

Some of the common tools that can be used to obtain these measurements are the anomalous Hall 

effect, magnetic circular dichroism, temperature-dependent conductivity, magneto-optical Kerr 

effect, and superconducting quantum interference device (SQUID) magnetometry. (3) 

Magnetic domains, and the boundaries that separate them (domain walls (DWs)), play a central 

role in the science of magnetism. Understanding and controlling domains is important for many 

technological applications in spintronics and may lead to new devices. Negative intrinsic 

resistivity of an individual domain wall in epitaxial (Ga,Mn)As microdevices have been studied. 

Steady and pulsed magnetic fields have been applied to trap and carefully position an individual 

DW within each separate device studied. This procedure reproducibly enables high-resolution 

MR measurements across an individual wall. Negative intrinsic DW resistance that scales with 

channel width has been consistently observed. This appears to come from sizeable quantum 

corrections to the MR. Precise extraction of the domain wall resistance (DWR) can be achieved 

by averaging the measured longitudinal resistances, 

( ) 2/ D

xx

U

xx += RRR , (12) 

which compensates obscure contributions from the transverse voltages. The difference between 

R and 

( )

A

Lt R

0

0 ρ = , (13) 

a simple, idealized prediction for the longitudinal resistance, clearly displays the presence of 

effects beyond those associated with a simple resistivity discontinuity at the DW. 

12
There are two fundamental contributions to this difference called the “eddy-like” and “intrinsic” 

DW resistivities. To date, the experimental results obtained from the various methods are 

conflicting. Both positive and negative DWRs are reported. There are several scattering 

mechanisms that can produce positive DWR, including reflection of carriers by the DW, a 

“zigzag” current redistribution inside the wall due to the Hall effect, and spin-dependent 

scattering analogous to the GMR effect in magnetic layers. Negative DWR could possibly arise 

from electronic coherence in ferromagnetic metals. This could be due to the suppression of 

dephasing of weakly localized electrons at a DW, effectively reducing the intrinsic resistivity of 

DWs. In addition, a semiclassical model has been developed that can theoretically yield either 

positive or negative DWR. (16) 

6. Proposed Research Plan 

There have been essentially nine sets of experiments performed in this area. In the first set, 

contacts were normal metals and current was passed through “spin filters,” which are barriers 

whose conductance depends on spin (17). The second was the first to measure the spin 

polarization of the current originating in a ferromagnetic metal film. In these experiments, 

electrons tunneled through a nonmagnetic insulating barrier film into a superconducting metal 

film that acted as a “spin polarized” detector when a magnetic field, H, was applied to the 

structure (18). In the third, instead of analyzing the spin polarization of the tunneling current 

using a superconducting film in an applied field, experimenters replaced the superconducting 

film with another ferromagnetic metal film (19). The next three sets of experiments dealt with 

how spins interact. They interact mainly through spin coupling and spin-orbit coupling. If these 

influences could be eliminated, the orientation of a carrier’s spin can last a long time. 

The context of the fourth set of experiments was the excitation of a non-equilibrium population 

of spin-polarized electrons in the skin depth of a normal metal when microwave radiation is 

absorbed in an electron-spin resonance experiment, and the diffusion of these electrons from the 

skin into the bulk of the metal. A spin diffusion length was defined such that the generated spin 

imbalance would relax over it. This length was 

 s DL s = τ , (14) 

where D is the electron diffusion constant and s τ is the spin relaxation time. The fifth set of 

experiments measured this spin diffusion length directly through a transport experiment, using 

ferromagnetic metal contacts to inject spins into a normal metal (20). The sixth experiment 

measured the spin diffusion length of carriers injected into a paramagnetic metal from a 

ferromagnetic contact (21). 

The seventh set of experiments tested the dependence of the GMR effect (stated on page four) on 

the relative orientation of moments in simple sandwich structures consisting of two 

ferromagnetic layers separated by a normal metal. They showed that the GMR affects scales 

simply as the projection of the magnetic moment of one layer upon the magnetic moment of the 

other (22, 23). The resistance derives from electron scattering events that are spin defined (24). 

These events fall into two categories: spin-defined scattering at interfaces where the films meet 

and spin scattering within the interior (bulk) of the films. The eighth set of experiments 

13
attempted to identify which of these categories is more important. They indicated that for 

homogeneous layers the spin scattering is primarily at the interfaces. This was done by inserting 

thin layers of a second ferromagnetic material at the interfaces in ferromagnetic/nonmagnetic/ 

ferromagnetic sandwiches. It was generally observed, for many different combinations of metals 

that the MR varies exponentially on the thickness of the interface layer, with a characteristic 

lengthξ . It was found that lengthξ was extremely short and was typically ≈1.5 to 3 Ǻ at room 

temperature, and thatξ became even shorter at lower temperatures. The GMR effect was thus 

clearly shown to be determined by the character of the ferromagnetic/nonmagnetic interfaces 

(25); however, magnetic defects within the interior of a film, such as magnetic impurities in the 

nonmagnetic metal layer or inhomogeneities within the ferromagnetic layer, can also contribute 

measurable spin scattering. 

In this project, I will demonstrate, by the insertion of thin magnetic layers at the interfaces in 

sandwich structures, that the magnitude of the GMR effect is determined largely by the character 

of the magnetic/nonmagnetic interfaces. These magnetic layers can be inserted between any 

magnetic and nonmagnetic layer and will be approximately 2.5 Ǻ thick. It has been show that 

“dusting” a nonmagnetic/magnetic interface with thin Co layers, just 2.5 Ǻ thick, almost doubles 

the MR of the nonmagnetic/magnetic/nonmagnetic sandwich, making it comparable to the 

sandwich in which the nonmagnetic layers are completely replaced by Co. The thickness 

dependence is well described by a function of the form 

 ⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − −+=

Δ

ξ

i t ba

R

R exp1 , (15) 

where the length scaleξ is extremely short and is only ≅2.3 Ǻ (25, p. 1642). This relates well to 

the EPR part of this project, because spin injection (what EPR measures) and MR (what is being 

examined here) both relate to an understanding of spintronics. 

The samples will be prepared by direct current (DC) magnetron sputtering in a high vacuum 

system with a base pressure of ≅2×10-9 Torr. DC magnetron sputtering is the ejection of atoms or 

groups of atoms from the surface of the cathode of a vacuum tube as the result of heavy-ion 

impact (26). The structures will be deposited at ≅2 Ǻ/s in an argon pressure of 3.3 mTorr at 

≅40 °C. Series of up to 19 multilayers will be prepared sequentially under computer control. The 

composition of alloy layers will be checked using energy dispersive x-ray diffraction (EDXD), a 

technique in which an energy spectrum is obtained from the x-rays scattered from a 

polychromatic x-ray beam through a fixed angle by a polycrystalline sample (27). The resistance 

of the samples will be measured using a low frequency alternating current (AC) lock-in 

technique with a four-in-line contact geometry and spring-loaded, gold-plated contacts. A lock-in 

technique is one in which one or both of the frequencies of two coupled oscillating systems are 

shifted and automatically held so that the two frequencies have the ratio of two integral numbers 

(27). The current and magnetic field will be in the plane of the films with the magnetic field 

parallel or perpendicular to the current. The MR, ∆R /R, is defined as the maximum change in 

resistance observed over the field range of interest divided by the high field resistance. 

The structures that will be prepared for this study will be comprised of exchange-biased 

sandwiches (EBS) of the form FI / S / FII / FeMn, in which one of the magnetic layers, FII, is 

exchange coupled to an antiferromagnetic layer of FeMn. Therefore, we will be able to evaluate 

14
the importance of interface scattering by introducing thin layers of, for example, Co at the Py/Cu 

interfaces in Py/Cu/Py sandwiches. Py stands for permalloy, a typical example being Ni81Fe19. If 

spin-dependent interface scattering is the main mechanism creating the GMR, thin layers of Co 

will produce a large increase in MR. On the other hand, if bulk scattering lies at the origin of 

GMR, much thicker layers of Co will be required to substantially change the MR effect (25). In 

this experiment, one of the following elements, Ni, Co, Fe, Pd, Pt, Cu, Mn, rhodium (Rh), or 

ruthenium (Ru), will be used for the thin layers introduced at the Py/Cu interface (6, pp. 58–63). 

DC magnetron sputtering and molecular beam epitaxy (MBE) are experimental methods that 

have been used in the study of spin transport polarization and are described here because they 

may be needed to answer some of the questions about the mechanisms of spintronics. 

MBE is a powerful tool for developing new semiconductor material systems. It was used to grow 

semiconductor structures layer by layer, with precise control over the composition of the layers 

and high levels of background purity. The high degree of compositional control derives from 

accurate control of the temperature and, therefore, of the flow of atoms and molecules that are 

deposited to make the semiconductor structures. A number of factors contribute to the 

background purity, including the ability of MBE systems to achieve background pressures of 

10-11 Torr. The principal restriction to what can be grown in an MBE system is the number of 

material supplies available. These are usually evaporation furnaces (or sometimes gas injectors) 

that are located in “ports” that are adjacent to the growth station. However, changing the 

materials being used often requires breaking the vacuum, which is both time-consuming and 

expensive. In addition, there is always a danger of cross-contamination. (28) 

Preparing well-defined heterostructures on a nanometer scale has not only led to fundamentally 

new phenomena, such as the quantum Hall effect and the fractional quantum Hall effect, but has 

also led to new technologies, such as the double heterojunction laser, higher electronic device 

speeds, and “band gap” engineering of materials. These heterostructures can be grown under 

clean and controlled conditions by MBE. Epitaxy is the crystalline growth of one material on the 

same (homoepitaxy) or different material (heteroepitaxy). 

The MBE process is described schematically in figure 3. Under UHV conditions, the various 

constituents are coevaporated onto a clean crystalline substrate surface, which serves as seed 

crystal and is usually heated to provide high mobility of the impinging particles for crystalline 

growth. Group III/V (III=Al,Ga,In; V=P,As,Sb) and group II/VI (II=Pb,Cd,Hg5; VI=S,Se,Te6) 

compounds are widely used in conventional MBE, especially with group IV semiconductors, 

silicon (Si) and germanium (Ge). Covalent bonding is exhibited in these crystals in all three 

space directions (3-D materials), and dangling bonds occur at their surfaces, which have to be 

matched at these 3-D/3-D heterojunctions. This is shown in figure 4. 

 

5Hg = mercury. 

6S = sulfur. 

15
Figure 3. The basic principle of MBE showing coevaporation of atoms or 

molecules from two different sources onto a heated substrate. 

NOTE: Picture printed with permission from C. Kreis, PhD. thesis. 

Figure 4. Heterojunction , with dangling bonds at the interface, of a 

lattice mismatched 3-D crystal. 

NOTE: Picture printed with permission from C. Kreis, PhD. thesis. 

The lattice mismatch, Δa , is defined as 

s

sf

a

aa

a − =Δ , (16) 

where af and as denote the in-plane lattice parameter of film and substrate, respectively. It is of 

crucial importance for the quality of the junction, since the length and angle of the covalent 

bonds at the interface can not easily be altered. The covalent interaction at the interface usually 

causes strong disturbances at the interface, like strain, structural imperfections, and dangling 

bonds (i.e., edge dislocations), for a lattice mismatch of only 1%. These disturbances introduce a 

considerable defect density and greatly limit the possible choice of material combinations. (29) 

Ploog grew ferromagnet/semiconductor heterojunctions that allowed electrical spin injection at 

room temperature. The most promising results were obtained from the MnAs/GaAs and 

Fe3Si/GaAs heterostructures. In addition, the observation of a small out-of-plane magnetization 

component MnAs/GaAs(001) heterostructure led to a promising new concept for application in 

future magnetologic devices (30). I will examine “hybrid” ferromagnetic/semiconductor 

heterostructures that integrate conventional semiconductors with ferromagnetic semiconductors 

and ferromagnetic metals. These are important for semiconductor spintronics. In particular, I will 

16
look at hybrid heterostructures that combine conventional III-V and II-VI semiconductors with 

the ferromagnetic semiconductor (Ga,Mn)As and the ferromagnetic metal MnAs. I will focus on 

the characteristics of two novel classes of heterostructures: 

1. (Ga,Mn)As/AlAs/MnAs magnetic tunnel junctions (MTJs) that provide an all electrical 

scheme for probing spin injection from metals into GaAs 

2. n-ZnSe/(Ga,Mn)As heterojunction diodes that unexpectedly exhibit a magnetically driven 

photoconductivity 

The injection of a spin-polarized current into semiconductors is an important requirement for 

semiconductor spintronic devices. Spin injection through a tunnel barrier can be probed by 

measuring the TMR in a semiconductor sandwiched between a double barrier MTJ with one 

tunnel barrier serving as the spin injector and the second as the spin detector. By varying the 

characteristics of the semiconductor (doping, thickness, etc.), one may probe a number of useful 

physical parameters, such as spin diffusion length that are directly related to semiconductor 

spintronics. 

As a precursor to this experiment, spin-polarized tunneling in epitaxial single barrier MTJs 

comprised of a ferromagnetic metal, MnAs, and a ferromagnetic semiconductor, Ga1-xMnxAs, 

separated by a non-magnetic semiconductor, AlAs, have been studied. The hybrid MTJ provides 

a built-in control experiment since we can measure the TMR in both the paramagnetic and 

ferromagnetic states of Ga1-xMnxAs. An unusual feature of the hybrid metal/semiconductor 

MTJs—not the precursor experiment that has only one ferromagnetic substance—arises from the 

highly mismatched conductivities of the two ferromagnetic components: MnAs and Ga1-xMnxAs. 

Most studies of MTJs probe tunneling between materials with similar conductivity. 

The MTJ samples have been fabricated by MBE on p+ – GaAs(001) substrates after the growth 

of a 40 nm-thick, p-GaAs buffer layer. The best configuration has been found to be Ga1-xMnxAs 

(x=0.03; thickness, 120 nm), GaAs (thickness, 1 nm), AlAs (thickness = 1,2,5 and 10 nm), 

GaAs (thickness, 1 nm), and MnAs (thickness, 45 nm) grown sequentially at 250 °C. Standard 

photolithography and wet-etching techniques have been used to define 300-μm diameter mesas 

(flat surfaces) for vertical transport measurements. Each mesa will be etched down into the 

p-GaAs region. Between the top MnAs layer and the back of the p-GaAs, a four-probe method 

will be used to measure the DC current-voltage characteristics of the mesas. These measurements 

are carried out in a continuous flow helium cryostat over a range of 4.2 K to 300 K with an inplane magnetic field ranging up to 2 kG provided by an electromagnet. Additional transport 

measurements down to 330 mK are carried out in a He3

 cryostat with a superconducting magnet. 

Lastly, magnetization measurements have been carried out on 10-mm2 pieces of the unpatterned 

wafer using a Quantum Device superconducting quantum interference magnetometer. 

d AlAs

Quantitatively, the change in the tunnel resistance is given by 

, 1

2

MG

MG

P

PA

PP

PP

R

RR

TMR − = − = (17) 

17
where RA and RP are the junction resistances with antiparallel and parallel moments, respectively. 

PG and PM are the spin polarizations of Ga1-xMnxAs and MnAs, respectively. From recent 

Andreev tunneling estimates of spin polarization, PG ≈85% and PM ≈40%, while the ideal TMR 

predicted by Julliere’s model is ≈100%. This suggests that the spin-dependent tunneling process 

observed in previous experiments of this kind is fairly efficient, ≈30% of the ideal TMR. 

Detailed information about the AlAs barrier can be obtained through the analysis of 

conductance-voltage (G-V) curves (31). 

Even though I will be carrying out an experiment from set eight in this project, I will describe the 

ninth set of experiments for completeness. This ninth set of experiments was carried out to 

measure the GMR in a perpendicular geometry. The perpendicular geometry yields larger 

effects, because there is no shunting of the current through normal metals; all of the current must 

undergo spin scattering at every interface to traverse the layered structure (32, 33). An immediate 

benefit of the perpendicular transport experiments is clarification of the physics of the transport 

process. In this geometry, a given electron can pass through many layers before “forgetting” its 

spin orientation (34). 

With these experiments as a background, I will carry out experiments that combine the concepts 

and techniques developed in them to further investigate the concept of spin polarization transport 

in such materials as the Heusler alloys, and interpret and apply the results. As stated previously, 

a set eight type of experiment will be carried out. 

It has been shown by Kammerer that the spin polarization of the Heusler alloy Co2MnSi (61%) at 

10 K exceeds that of conventional transition metals, such as Ni80Fe20 (47%) and Co30Fe20 (37%) 

(35). Another result, due to Panchula, is that surface segregation of Mn and Sb reduces the spin 

polarization of the purported half-metal NiMnSb (36). For example, I will examine the effect of 

magnetic defects within the interior of a film, such as magnetic impurities in the nonmagnetic 

metal layer or inhomogeneity within the ferromagnetic layer, on the quantity and quality of spin 

scattering. I intend to focus on EPR and perturbation techniques and to examine the effect of 

domain wall movements on spin polarization dynamics, in addition to the set of experiments 

described above. I intend to use either an electromagnetic X-band (EMX) Series EPR 

spectrometer (produced by the Bruker BioSpin Corporation) at the U.S. Army Research 

Laboratory or the EPR spectrometer in the Chemistry Department at the University of Delaware. 

Since EPR can be used to make spin polarization measurements, I propose to make some of 

these measurements on selected Heusler alloys and decide if they can be used to make spintonic 

devices, such as those described in the Anticipated Results and Conclusions section of this 

article. Other experimental approaches that may be attempted in this study are injecting spin 

defects into a normal metal and observing the nuances using EPR and possibly other methods, 

such as Andreev reflection, an Aharonov-Bohm ring, a spin-polarized electron emitter, a 

compact analyzer of electron spin polarization, spin-polarized metastable-atom deexcitation 

spectroscopy (SPMDS), cyclotrons, a spin-guide source, a resonant interband tunneling device, 

point contact spectroscopy, a spin-polarized scanning tunneling microscope, and/or 

inhomogeneous doping. It won’t be possible to use all of these methods in this project, but a 

familiarity with each one will be obtained and examined to see if any, or all of them, can be 

useful to understanding the mechanisms of spintronics. 

18
In particular, Andreev reflection is a scattering process, at an interface with a superconductor, 

responsible for a conversion between a dissipative quasi-particle current and a dissipationless 

supercurrent. This is a phase-coherent scattering process in which the reflected particle carries 

information about both the phase of the incident particle and the macroscopic phase of the 

superconductor. The advantage of this technique is the detection of polarization in a much wider 

range of materials than those which can be grown for detection in F/I/S or F/I/F tunnel junctions, 

where F stands for ferromagnetic, I stands for insulator, and S stands for semiconductor. (6) 

A molecule in which the total spin of the electrons is one (S=1) is said to be in a triplet state. 

Two factors determine whether the ground state of a molecule is a singlet or triplet, namely, the 

orbital energies of the valence electrons and the strengths of the electrostatic exchange 

interactions between electrons of parallel spin. If two orbitals are sufficiently close together, the 

exchange energy predominates and the ground state of the molecule is a triplet. If there were 

only exchange and electrostatic interactions between electrons, the three sublevels of a triplet 

state would be exactly degenerate (split apart) and the EPR spectra would be very similar to 

those of radicals with spin of 1⁄2. The most important single fact about triplet states is that the 

magnetic dipole-dipole forces between the two unpaired electrons remove the degeneracy and 

lead to highly anisotropic spectra in most molecules. (37) 

EPR can characterize the electron spin polarization of the excited quartet state of strongly 

coupled triplet-doublet spin systems. These systems (molecules) usually consist of a nitroxide 

radical or a paramagnetic metal bound to a chromophore, such as a porphyrin, phthalocyanine, or 

fullerene. They can be excited to produce an interacting triplet-doublet spin pair. The electron 

spin polarization is associated with electronic relaxation. These systems usually relax to the 

lowest triplet-quartet state by intersystem crossing from the trip doublet. When spin-orbit 

coupling is the main mechanism for this relaxation path, it leads to spin polarization of the trip 

quartet. Analytical expressions for this polarization have been derived using first- and secondorder perturbation theory, which have, subsequently, been used to calculate powder spectra for 

typical sets of magnetic parameters. 

Our system consists of a strongly exchange coupled triplet-doublet pair, which can be described 

by the spin Hamiltonian: 

( ) ( , 3

1 2 ,

2

,

2

FFTT FT ,Tz T Tx Ty Ω ⎟ Ω −+ SSESSDSSJBgSgSH Ω

⎠

⎞ ⎜

⎝

⎛ −+−+= ) rr r r r β (18) 

where the T refers to the triplet spin and orbitals involved, and F refers to the doublet spin and to 

the orbital carrying the unpaired electron. To simplify the expressions, we use the notation, 

. The first part of the Hamiltonian is the Zeeman energy; the second part is the exchange 

interaction; and the third and fourth parts are the zero-field energy. J denotes the exchange 

interaction between the triplet and doublet, and and are their respective g tensors. D and 

E are the zero-field splitting parameters of the triplet spin state. Here the dipolar coupling 

between the triplet and doublet is much weaker than the zero-field splitting of the triplet and is 

ignored in the Hamiltonian, as are hyperfine interactions (38). To derive the expression for the 

zero-field energy (parts three and four), principal axes with principal values –X, –Y, and –Z were 

used to diagonalize the zero-field tensor, resulting in the expression 

h = 1

T g F g

. (19) 222 −−− ZSYSXS zyx

19
However, since the trace of a Hamiltonian in a principal axis system is zero (X+Y+Z=0), the 

zero-field splitting can be rewritten in terms of just two independent constants, D and E, as 

shown in equation 18 (37). 

The exchange coupling between the triplet and doublet is much larger than the difference in their 

Zeeman energies, ff Δ βBgJ , and the Zeeman energy is much larger than the zero-field 

splitting, ω ff , ED and 

β ≈ βBgBg = hω, T F (20) 

where and are the values of the respective triplet and doublet g tensors along the d

of the magnetic field and Δg is their difference. 

T g F g irection 

Therefore, the eigenfunctions of the Hamiltonian are separated into trip-doublet, D, and tripquartet, Q, substrates using the following “ket” notation: 

( ) 2 , 3

1

2

1 , D =+ + −TT 0αβ =+ TQ +α

2

3 , , (21) 

( ) 2 , 3

1

2

1 , D =− − −TT 0βα ( ),2

3

1

2

1 , Q + +=+ TT 0αβ (22) 

 ( ),2

3

1

2

1 , Q − +=− TT 0βα (23) 

 . 2

3 , =− TQ − β (24) 

whereT± and T0 are the triplet spin states, andα and β are eigenstates of the doublet spin. 

The spin polarization associated with these states depends on the pathway by which they are 

populated. If the two electrons of the triplet state have different exchange interactions with the 

third electron, the trip-doublet state (the two D kets in equations 21–24) acquires some singlet 

character from the sing-doublet state. Therefore, the transition from the sing-doublet to the tripdoublet is partially allowed and it is assumed that this is the dominant decay pathway for the 

sing-doublet. This assumption is supported by the observation that in systems such as porphyrin 

dimmers containing a paramagnetic center, this effect leads to intersystem crossing (ISC) rates, 

which are orders of magnitude faster than rates in corresponding diamagnetic complexes. It is 

possible, however, that in some systems spin-orbit coupling also plays a significant role in the 

decay of the excited sing-doublet. In these cases, an additional multiplet contribution to 

polarization of the trip-quartet state would be seen. Here we assume that this contribution is 

negligible and that following light excitation to the sing-doublet, the initial relaxation 

predominantly populates the trip-doublet sublevels. Ensuing doublet-quartet ISC, it then 

populates the quartet state (Q kets in equations 21–24). It is proposed that the main mechanism 

of this latter crossing process is spin-orbit coupling accompanied by fast internal conversion. 

“Internal conversion” is the effect caused by the spin-independent, intramolecular processes 

leading to relaxation between different orbital configurations. Because the time scales of these 

20
two intramolecular processes are very different, the problem can be stated in terms of a static 

spin Hamiltonian, in which the spin-orbit coupling acts as a perturbation. In the molecular 

frameΩ , the spin-orbit contribution has the form 

= ΩΩ ,, + SLSLH ΩΩ ,, FFFTTTSO

r r r r λ λ , (25) 

whereλ T and λ F are the spin-orbit coupling parameters and the vector operators, and LΩ,T

r LΩ,Fr , 

describe the angular momentum for the orbitals in which the triplet and doublet spins reside. 

Rigorously speaking, this Hamiltonian is correct only for the one-center approximation of the 

spin-orbit interactions. However, for multicenter systems, one can use “effective” orbitals to 

represent the spin-orbit interaction in the form used in equation 25. 

The basic postulates of this model can be summarized as follows: 

• The trip-quartet state, Q kets in equations 21–24, is populated from the trip-doublet state, 

D kets in equations 21–24, due to intersystem crossing. 

• The spin-spin interaction of the triplet and doublet parts of the system is fixed spatially 

with respect to one another, and, hence, does not vary. Therefore, the quartet spin 

polarization does not arise from level crossing (i.e., it is not due to variation of the 

exchange interaction) or from fluctuations of the dipolar interactions. 

• The spin polarization is generally by internal processes rather than by intermolecular 

motion and interactions, because of the strong exchange coupling between the triplet and 

doublet spins. 

• The degree of quartet-doublet mixing described by a static spin-orbit coupling Hamiltonian 

(equation 25) limits the rate of the doublet-quartet transitions. 

The properties of most strongly exchange-coupled, triplet-doublet systems at low temperatures 

are characterized by these postulates. In addition, several approximations are introduced below in 

order to derive analytical expressions using perturbation theory. 

Experimentally, liquid crystal solvents can be used to provide macroscopic ordering of EPR 

samples, and the ordering is maintained when the liquid crystal is frozen to the glass phase or 

crystalline solid phase in the magnetic field. The spectra of the samples thus prepared 

demonstrate the θ dependence of the net polarization and the 2 sin ( 3/1cos ) 2 θ − dependence of 

the multiplet contribution given by equation 26 for the traceless diagonal part of the quartet 

density matrix,Δρ Q , describing the populations of the quartet state, 

() ( ) ( ) 32

3

2 2 2

2

2

1 sin

3

1 sin 3/1cos ρ Q θ Qz pSp θ Qz Q ⎟ + θ SpSS Qz ⎠

⎞ ⎜

⎝

⎛ ∝Δ + − − , (26) 

where θ is the angle between the z directions in molecular and laboratory coordinate systems. 

+= SSS FTQ is the operator for the total spin of the quartet state, where T refers to the triplet 

spin and orbitals involved and F refers to the doublet spin and to the orbital carrying the unpaired 

electron. 

21
The parameters p1, p2, and p3 arise from the spin-orbit coupling induced quartet-doublet mixing 

and are given by 

( )

2

1

1

4

p

JJBg

p ΔΔ −+

+ = β , (27) 

( )

22

2 2

2 6 −+

−+

ΔΔ

Δ+Δ −= Tz p

λ (28) 

and 

 , p3 = 0 (29) 

where indicates the exchange integral. 1 J Δ+ and Δ− are the energy differences between the tripquartet and trip-doublet states, respectively, of different orbital configurations and can be written 

as 

( ) ( ) 1 0 2 1 QEDE JJ + =Δ − = ΔTz + + (30) 

and 

− =Δ ( 1 )− (DEQE 0 ) = ΔTz − − JJ 1 .2 (31) 

The spin-orbit coupling parameter is 

= λλ TTz LΩ,Tz .01 (32) 

The first-order operator, , corresponds to the net polarization, while the second-order 

operator, , describes the multiplet component, and the third-order operator describes a 

combination of both the net and the multiplet components. The largest of the three amplitudes is 

p2 associated with the multiplet polarization, while p3 is zero to within our linear approximation. 

(38) 

SQz

2 SQz

Since the net polarization is proportional to while the multiplet polarization follows θ 2 sin

⎟

⎠

⎞ ⎜

⎝

⎛ −

3

1

cos 2 θ , (33) 

as seen above in the expression for Δρ Q , only net polarization occurs when the molecular z axis 

is at the “magic angle.” (39). 

The magic angle is 54.7° and use of it provides spectra with much better resolution. The magic 

angle is used primarily with nuclear magnetic resonance (NMR) in the magic angle spin NMR 

(MAS NMR) method, but is also employed with EPR. Under normal conditions, a solid sample 

would yield only an extremely broad featureless spectrum with a large contribution to the 

broadening arising from static dipolar interactions. Much of this initial broadening can be 

removed in solids by using high power proton (electrons for EPR) irradiation, often termed 

dipolar decoupling. But line widths of 5-10 KHz (NMR) or more can still remain. This 

broadening is due to chemical shift anisotropy. The observed broad envelope is a result of 

22 
contributions from the many individual chemical shifts of nuclei (electrons for EPR) in 

molecules oriented differently within the sample. The anisotropy can be effectively removed if 

the sample is spun rapidly at an angle of 54.7° with respect to the external magnetic field. (40) 

On the other hand, for θ=0 (i.e., the z-direction parallel to the external magnetic field), no net 

polarization will be observed. This is because, with the molecule in this orientation, the spin 

states coupled by the spin-orbit interaction have the same projection along the field direction. 

Thus, the rate of decay of the two doublet sublevels with m=+1/2 and m=–1/2 are identical. 

However, there is net polarization in the quartet state for other molecular orientations relative to 

the magnetic field since the projection of the spin states differ and, therefore, the ISC rates from 

the two levels are also different. This effect also contributes to the concentration of the net 

polarization at the center of the spectrum, because the orientations for which the net polarization 

is strongest have their m ↔±= ± 2/32/1 transitions at the center of the spectrum. (39) 

The multiplet polarization is maximal when θ=0 (i.e. when the molecular symmetry axis is 

parallel to the external field); while the net contribution is maximal when the symmetry axis is 

perpendicular to the field. Hence, the net polarization is very weak and the multiplet polarization 

is very strong when the order parameter of the symmetry axis is Szz=0.7. Conversely, for negative 

valued parameters, Szz =–0.3, orientations with θ close to 90° are more likely and the net 

polarization is stronger. It was experimentally seen that the strength of the multiplet polarization 

for various valued parameters depends on the value of the zero-field splitting parameter E. When 

E=0, strong net polarization is observed for both positive and negative valued parameters, but the 

spectral positions of the maxima change. For positive valued parameters, features corresponding 

to the z component of the zero-field splitting tensor are dominant, while for negative valued 

parameters, the features from the x and y components of the tensor are most prominent. When the 

sample is rotated 90°, the distribution of orientations with respect to the field becomes broader 

and more isotropic. However, the relative intensity of the net and multiplet contributions is 

inverted when the sample is rotated, regardless of the sign of the parameter. 

In the above discussion, the molecular axis about which effective spin-orbit coupling occurs was 

defined to be the molecular z axis. This direction may not necessarily be associated with the 

largest zero-field splitting, even though this direction will normally correspond to one of the 

principal zero-field splitting (ZFS) axes. Therefore, the z axis of the ZFS tensor, defined by the 

largest principal value, may be parallel to any one of the molecular axes x, y, or z. The scheme 

where the large principal value of the ZFS tensor corresponds to the molecular z axis was 

compared to a scheme where the axes correspond as follows: 

, (34) 

,

ZFS mol → yx

 (35) ZFS mol → zy

and 

 . (36) ZFS mol → xz

This change in ordering of the principal values of the ZFS tensor led to an inversion of the 

multiplet polarization, while the net polarization was unaffected by this change. This is because 

the sign of the multiplet contribution to the spectrum for a given orientation depends on both 

23
⎟

⎠

⎞ ⎜

⎝

⎛ −

3

1

cos 2 θ and the sign of the zero-field splitting, while the sign of net polarization is 

independent of these parameters. The latter is a result of the fact that the sign of the net 

polarization is determined by the sign of J, which is positive if the trip-quartet is lower in energy 

than the trip-doublet. Therefore, a variety of multiplet polarization patterns can be expected from 

molecules of different structure. On the other hand, net polarization is always predicted to be 

positive within a first-order perturbation treatment. 

In summary, the first-order (linear) perturbation treatment leads to the following conclusions 

about the net and multiplet contributions to the spin polarization: 

• The magnetic field dependence, spectral positions, and kinetic behavior of the two 

contributions are different and allow them to be separated. 

• The ratio of their maximal intensities is proportional to the square of the spin-orbit 

coupling divided by the energy gap between the two lowest excited electronic 

configurations. 

• The net polarization is predicted to be absorptive if the exchange interaction is positive. 

• The orientation dependence of the multiplet and net contributions are opposite. 

Second-order perturbation is mainly caused by two effects: off-diagonal terms of the spin 

Hamiltonian due to the spin orbit coupling and dipolar coupling of the triplet electrons. Both of 

these effects can modify the wave functions of the doublet and quartet states and introduce 

additional terms in the expressions for net polarization. Another consequence of second-order 

terms is that they cause a shift of the zero-field spin energy levels. Two limiting situations 

generate second-order (quadratic) terms: 

1. When the exchange interaction of the higher excited states is negligible compared to the 

orbital energy gap, Tz J1 pp Δ

2. When the doublet-quartet splitting of higher orbital states is significant, 1 J Tz ≤Δ

The most important result of the second-order perturbation treatment is that the two polarization 

parameters dependent upon net polarization, p1 and p3 are both inversely proportional to the 

Zeeman energy,ω , and are, therefore, inversely proportional to the magnetic field strength: 

Bg

D

pp eff

β 31 ∝∝ , (37) 

where is a zero-field splitting parameter (41) and B is the magnetic field intensity. There are 

crucial differences between the first- and second-order terms for net polarization if the spin-orbit 

interactions in different planes are comparable. In this case, the second-order terms mix doublet 

and quartet states of the same orbital configuration. Therefore, they are roughly proportional to 

the overall zero-field splitting parameter. 

Deff

Putting first- and second-order perturbation together, it is seen that the net polarization 

contributes to both the central peak and the outer wings of the spectrum. However, under some 

conditions, it can be considered that the central peak comes purely from net polarization, while 

the outer wings of the spectrum show only multiplet polarization. Spin polarization of the excited 

24
doublet states can also occur. It can also happen that the net polarization of the quartet state can 

be generated by spin orbit coupling and can be observed while the excited doublet state remains 

unpolarized. (38) 

The standard Monte Carlo method, sometimes called the method of statistical trials, has been 

used to study the dependence of MR and resistivity on temperature and field (42). The Monte 

Carlo method is based on random selections and was not practical before the advent of 

computers. This method can be illustrated by finding the area of a plane figure, S: Let the figure 

be completely within the unit square, choose at random N points in the square, and designate the 

number of points lying inside S by N’. Geometrically, the area of S is approximately equal to the 

ratio N’/N. The greater the N, the greater the accuracy of this estimate (43). 

A Monte Carlo method developed for spin dynamics was applied to study spin-polarized 

transport properties of a 2-D electron gas in a semiconductor spin field-effect transistor (SFET) 

structure. The specific symmetry of spin-orbit terms (Rashba and Dresselhaus) leads to strong 

anisotropy of spin dynamics in the low field regime. Results derived from this study provided 

useful information to assist in optimization of the SFET performance (44). Monte Carlo 

simulations have also been performed to study the in-plane transport of spin-polarized electrons 

in III-V semiconductor quantum wells in the range 77-300 K (45). The Monte Carlo method has 

also been used to model spin injection through a Schottky barrier, where it was found that the 

injected current can maintain substantial spin polarization to a length scale of 1 μm at room 

temperature without external fields (46). The electron spin polarization was described by the spin 

density matrix, while the spatial dynamics of the electron was treated semi-classically. The 

coherent dynamics of the current spin polarization and spin dephasing were determined by the 

spin-orbit interaction. The electric field in the device was evaluated self-consistently with the 

charge distribution. The phonon and impurity electron momentum scattering mechanisms were 

incorporated in the simulation. The steady state spatial distribution of the current spinpolarization vector was simulated. The estimated value of the spin dephasing length at room 

temperature was of the order of 0.2 μm in the In0.52Al0.48As / In0.53Ga0.47As / In0.52Al0.48As FET 

structure with the quantum well grown in the (0, 0, 1) crystallographic direction (47). 

7. Anticipated Results and Conclusions 

The anticipated results are both of a theoretical nature and a practical nature. A robust spin 

injection into Si will be attempted. To date, control of spin in GaAs and in III-V ferromagnetic 

semiconductors has been achieved. We would like to extend this control to Si. This would add 

significantly to the current information technology. Important materials advances in improving 

the compatibility of Si/III-V structures suggest that this extension to Si might be able to be 

accomplished. Another result from this research might be that the effects of magnetic interfaces 

and material inhomogeneities on spin-polarized transport may be observed and understood. A 

comprehensive transport calculation in the created devices would provide valuable insights into 

both the spin polarization being measured and how it is reduced from the moment it was 

generated. 

25
Another result will be accurate band-structure-derived calculations of spin relaxation times in 

both metals and semiconductors. Accurate calculations of the g factor, which has not been 

accomplished even for the elemental metals, may be carried out. A characterization of spin 

relaxation and decoherence (individual spin dephasing) of localized or confined electrons, when 

the hyperfine-interaction mechanism dominates, may be developed. Studying single-spin 

relaxation and decoherence may enhance the development of quantum computing. 

Another result may be the realization of an all-optical NMR spectrometer. To accomplish this, 

periodically optically excited electron spins will play the role of the resonant radio waves. The 

operation of a spin laser has been demonstrated. The laser previously demonstrated was a 

vertical-cavity surface-emitting laser (VCSEL). It was optically pumped in the gain medium, 

which was two quantum wells with 50% spin-polarized electrons. The results of this current 

project may be able to be used in the development of such an all-optical NMR instrument. 

Major results of this research should be in the area of spintronic devices. This area will be 

developed because of the concept that the flow of spin-polarized carriers, rather than applied 

magnetic field, can be used to manipulate magnetization of ferromagnetic materials. Coherent 

microwave oscillations in nanomagnets form a basis for these devices. These oscillations are the 

result of both the reversal of magnetization and the driving of a spin-polarized current. Results 

about spin-transfer torque should be forthcoming. It has already been realized in geometries that 

possess a very large current density. It is expected that much smaller switching currents will be 

required to demonstrate spin-transfer torque (together with other cooperative phenomena) in 

ferromagnetic semiconductors. This effect will be experimentally tested. We will show that 

reversal of magnetization in (In,Mn)As can be manipulated by modifying the carrier density 

using a gate voltage in a field-effect transistor structure. (7, pp. 385–6) 

Another spintronic device is the spin valve. It is a GMR device, which consists of two 

ferromagnetic layers sandwiching a thin nonmagnetic metal layer with one of the magnetic 

layers being “pinned”, i.e., the direction of the magnetization of the layer is relatively insensitive 

to moderate magnetic fields. The other magnetic film is called the “free” layer and the direction 

of its magnetization can be changed by applying relatively small magnetic fields. In this device, 

the resistance typically rises 5% to 10% as the orientation of the magnetization of the 

ferromagnetic layers changes from parallel to antiparallel. Pinning in the “pinned” layer is 

achieved by using an antiferromagnetic layer in contact with it. NiMnSb is a candidate material 

for spin valves. Its coercive field is of great importance, since it defines the operating magnetic 

field range of active devices. Thus, it is desirable that the grown films possess a low Hc, coercive 

field. 

Yet another spintronic device is the MTJ. It also consists of two ferromagnetic layers 

sandwiching, this time, a very thin insulating layer, such as Al2O3. The tunneling resistance is 

modulated by a magnetic field in the same way as the resistance of a spin valve and changes, 

usually 20% to 40%. It requires saturation magnetic fields equal or less than those required for 

spin valves. 

The spin transistor is a theoretical device that has initiated a vigorous search for electrical spin 

injection from ferromagnetic films into semiconductors. It consists of two ferromagnetic layers 

sandwiching a narrow semiconductor channel. In this device, spin-aligned electrons are injected 

from one of the magnetic films, called the emitter, into the semiconductor channel. After 

traveling through this channel, they are detected by the other magnetic film, called the collector. 

26
A gate electrode over the semiconductor channel creates a field that causes a magnetic 

interaction, making the spins precess. When the gate voltage is off, the aligned spins can 

propagate from the emitter to the collector through the semiconductor channel. When the gate 

voltage is on, the spins precess and current passes through the semiconductor channel only if the 

spins are aligned with the magnetization of the collector (2). Three important examples of the 

spin transistor are the Datta-Das SFET, the magnetic bipolar transistor, and the hot-electron spin 

transistor (7). Datta and Das have proposed a spin transistor that is a hybrid semiconductor 

device employing a direct electrical spin injection from a ferromagnetic substance into a 

nonmagnetic superconductor (5). The spin injection and spin detection are carried out by a 

ferromagnetic source and drain, and by spin precession about the built-in structure inversion 

asymmetry (Bychkov-Rashba) field in the asymmetric, quasi-one-dimensional channel of the 

ordinary field-effect transistor. Here the precession vector is 

( ) ( nkk ) BR

r r r r 2α ×=Ω , (38) 

where k

r

 is the wave vector for a Bloch state propagating in the plane, n

r

 is the confinement unit 

vector of the quantum well, and α BR is a parameter depending on spin-orbit coupling and the 

asymmetry of the confining electrostatic potentials arising from the growth process of the 

heterostructure. The attractive feature of the Datta-Das SFET is that spin-dependent device 

operation is not controlled by external magnetic fields, but by gate bias, which controls the spin 

precession rate. 

The magnetic bipolar transistor (MBT) is a bipolar transistor with spin-split carrier bands and, in 

general, an injected spin source. A related device structure, a spin-polarized injection current 

emitter (SPICE), has semiconductors with no equilibrium spin, while the spin source is provided 

by a ferromagnetic spin injector attached to the emitter. Another ferromagnetic metal, a spin 

detector, is attached to the base/collector junction to modulate the current flow. In both 

configurations, the aim is to control current amplification by spin and magnetic field. 

The current amplification (gain), 

B

C

I

I β = , (39) 

is typically approximately 100 in practical transistors. This ratio depends on many factors, such 

as the doping densities, carrier lifetimes, diffusion coefficients, and structure geometry. In an 

MBT, β also depends on the spin splitting, 2qς , and the non-equilibrium polarization, δPE . 

This additional dependence of β in an MBT is called magnetoamplification. An important 

prediction is that non-equilibrium spin can be injected at low bias all the way from the emitter, 

through the base, to the collector in order to make an effective control of β by δPE possible. 

The MBT is, in effect, a magnetic heterostructure transistor, since its functionality depends on 

tenability of the band structure of the emitter, base, or collector. The advantage of the MBT is 

that the band structure can be tuned during the device operation by magnetic field or spin 

injection signals rather than being built in, but can be tuned during the device operation by 

magnetic field or spin injection signals. 

27
The MBT has an equilibrium and non-equilibrium (magnetization) in the emitter, base, or 

collector. The two main physical phenomena associated with the low-injection theory of spinpolarized transport through MBTs are electrical spin injection and spin control of current 

amplification (magnetoamplification). A source spin can be injected from the emitter to the 

collector. If the base of an MBT has an equilibrium magnetization, the spin can be injected from 

the base to the collector by intrinsic spin injection. The resulting spin accumulation in the 

collector is proportional to 

( TkqV ) Bbe exp / , (40) 

where q is the proton charge, is the bias in the emitter-base junction, and is the thermal 

energy. To control the electrical current through MBTs, both the equilibrium and the nonequilibrium spin can be used. The equilibrium spin controls the magnitude of the equilibrium 

electron and hole densities, thereby controlling the currents. The current amplification is 

increased (decreased) by increasing the equilibrium spin polarization of the base (emitter). A 

spin-valve effect can arise if there is a non-equilibrium spin in the emitter, and the base or the 

emitter has an equilibrium spin. This spin-valve effect can lead to a giant magnetoamplification 

effect, where the current amplifications for the parallel and antiparallel orientations of the 

equilibrium and non-equilibrium spins differ significantly. (8, p. 115314–1) 

Vbe Tk B

The third type of spin transistor, the hot-electron spin transistor, relies on transport of hot, or 

non-thermalized, carriers. They have the potential of serving several different purposes. First, 

they could be used as a diagnostic tool to characterize spin- and energy-dependent interfacial 

properties, scattering processes, and electronic structure relevant to spin devices. Secondly, they 

are of interest for their ability to sense magnetic fields, their possible memory applications, and 

their potential as a source of ballistic hot-electron spin injection. Two proposed types of hotelectron spin transistors are the spin-valve transistor and the magnetic tunneling transistor. 

The spin-valve, or Monsma transistor, integrates metallic ferromagnets and semiconductors. It is 

a three-terminal structure consisting of a metallic base, B, made of a ferromagnetic multilayer in 

a current perpendicular to the plane (CPP) GMR geometry surrounded by a silicon emitter, E, 

and collector, C, with two Schottky contacts formed at E/B and B/C interfaces. This threeterminal structure, which has a small current gain (a small change in the base current leads to a 

large change in the collector current) of approximately 2, is in contrast to the two-terminal 

structure of a conventional semiconductor transistor that has a large current gain. Forward 

bias, , controls the emitter current, , of spin-unpolarized electrons, which are injected into a 

base region as hot carriers. The scattering processes in the base, together with the reverse 

bias, , influence how many of the injected electrons can overcome the B/C Schottky barrier 

and contribute to the collector current, . The magnetoresistive response is usually expressed 

using magnetocurrent (MC), defined as the change in collector current normalized to the 

minimum value 

VEB E I

VBC

CI

( )

↑↓

↑↑ ↑↓ − =

C

C C

I

II

MC , (41) 

28
analogous to the expressions for GMR or TMR structures, where (parallel) and ↑↓ (antiparallel) denote the relative orientation of the magnetizations. The large values of MC (>200%) 

and the sensitivity of ≈130% per G measured at room temperature demonstrate a capability for 

magnetic-field sensors. 

↑↑

Figure 5 below illustrates a specific example of a spin-valve transistor, the photo-diode. It relies 

on photons to excite electrons within a sandwich of metal layers. Two of these layers are 

ferromagnetic, which selectively filter the electrons that pass through them based on their 

magnetic orientation (spin). Having two ferromagnetic layers provides a means to first polarizing 

and then analyzing the electron current, and allows for switching the output current of the device 

from low to high by an external magnetic field. The metal sandwich (yellow) sits on a 

semiconductor collector (orange), and the metal/semiconductor interface serves as a barrier to 

filter the hot electrons (48). It is hoped that the results of this current project will lead to a 

refinement of this type of hot-electron transistor. 

Figure 5. Spin-valve photo-diode (48). 

The second example of the hot-electron transistor is the magnetic tunneling transistor. It has a 

tunneling junction instead of a Schottky barrier emitter. This addition of a tunnel junction, 

combined with a variable, , allows exploration of hot-electron transport over an energy range 

of several eV. At a large bias, the ratio 

VBE

VEB

 

E

C

I

I , (42) 

important for the device performance, can be substantially increased over that of the spin-valve 

transistor. 

I will discuss two particular realizations of the magnetic tunnel transistor. The first has four 

regions. Region 1 is the emitter, region 2 is the Al2O3 tunnel barrier, region 3 is the base, and 

region 4 is a semiconductor collector that has a Schottky barrier at the interface with the base. 

Different coercive fields in regions 1 and 3 ensure independent switching of the corresponding 

magnetizations in the applied magnetic field. After an initial decrease of MC with electron 

29
energy, at VEB ≈ 0.3 V larger than the base/collector Schottky barrier, there is an onset of hotelectron transport into L valleys accompanied by an increase in MC. A large MC alone, 

measured in various hot-electron spin transistors, is not sufficient to demonstrate spin injection in 

a semiconductor collector. For conclusive evidence spin detection in a collector region is needed. 

This was first achieved using optical detection with a spin LED structure added to the collector. 

Measurements at T=1.4 K and B=2.5 T, after a background subtraction, showed majority spin 

injection with Pcirc ≈ 10%. 

The second realization of the magnetic tunnel transistor is more similar to the original spin-valve 

transistor. In this case, the emitter was nonmagnetic (Cu) while the base was a magnetic 

multilayer (F1/N/F2). The resulting strong spin-filtering effect can be inferred from the 

transmitted hot carriers with a spin-dependent exponential decay within the Fi layer, where i=1,2. 

The resulting magnetocurrent can be expressed as 

( ), 1

2

21

21

NN

NN

PP

PP

MC − = (43) 

which is analogous to TMR using Julliere’s model, but with the redefined definition of spin 

polarization. At VEB ≈ 0.8 V and at T=77 K, the measured MC exceeds 3400%, while, using the 

last equation, the polarization of the transmitted electrons can be estimated to exceed 90%, even 

with a ferromagnet only ≈ 3 nm thick. Increased spin injection, even at room temperatures, are 

expected to result from future studies of hot-electron spin transistors. Other semiconductor 

collectors will probably be used in future studies, as well. It would be particularly desirable to 

demonstrate hot-electron spin injection in Si and to facilitate an integration with the 

complementary metal-oxide semiconductor (CMOS) technology. (7, pp. 380–384) 

Furthermore, it was demonstrated by Hong and Wu that the spin dependent collector current in a 

hot-electron spin-valve transistor can be manipulated through changing Schottky barrier 

characters such as height and width (49). This result will be useful for device design. 

Also, electrical spin injection has been demonstrated from ferromagnetic thin films into a 2-D 

electron gas semiconductor system. However, the spin injection was inefficient. This inefficiency 

is perhaps mainly due to the conductivity mismatch of the ferromagnetic metal and the 

semiconductor, and secondly due to the low spin polarization of the Py, which was only 35%. It 

has been proposed that this conductivity mismatch can be improved with the introduction of a 

tunnel barrier between the ferromagnetic layer and the semiconductor. On the other hand, the 

spin polarization of the emitter contact can be improved using ferromagnetic materials which are 

called half-metals and are expected to present 100% spin polarization. (2) 

Another possible result could be the world’s first plastic magnet suitable for use as a storage 

medium in consumer products. Spintronics could be the idea behind the development of such a 

material, which could eventually replace more costly metals in computer hard drives. A new 

magnetic polymer, called PANiCNQ, has already been developed for this purpose by the 

University of Durham in the United Kingdom. They have discovered a method to induce 

magnetism in their material, showing some promise for its future use as a magnetic recording 

medium. Like most plastics, this material is cheap to synthesize, easy to process, and can be 

molded into any desired shape. It could be used in such products as portable music or video 

players, hand-held computers, or recording media for digital cameras. These devices don’t 

require high recording densities. Prior magnetic plastics have either worked only in oxygen-free 

30
environments at temperatures too low for practical use or offered very weak magnetism at higher 

temperatures. The Durham researchers made their magnetic compound by combining emeraldine 

base polyaniline (PANi), a conductive plastic, and tetracyanoquinodimethane (TCNQ), a 

polymer. Over a three-month period, they detected an increase in the material’s magnetism to the 

point that a magnet would pick up powdered PANiCNQ. Then, they found that they could 

change the proportions of PANi and TCNQ to alter the compound’s magnetism as needed. The 

new compound was neither highly nor uniformly magnetic, but they contend that these problems 

can be solved. In conventional magnetism, a material’s electron spins line up to exert a force on 

some types of metals. The Durham team paralleled this mechanism by creating an alignment of 

free radicals. The usefulness of this new compound for hard drives is questionable since they are 

already one of the cheapest forms of storage, but plastics are inexpensive to mass produce and 

eventually might be useful in some sort of storage medium. It may be possible to make the 

technique yield more PANiCNQ and to make the material more magnetic. It will probably take 

between 5 and 10 years to make the compound available for commercial use. (50) 

Further applications of this project may occur in the field of quantum computing. Quantum 

computing offers the potential for dealing with certain intractable problems of conventional 

digital computing. A quantum computer would contain thousands of devices and would probably 

be built with solid-state technology. The challenge for solid-state quantum computing is to find a 

way to use devices without precise knowledge of their physical characteristics. Quantum 

computing is implemented with “qubits,” physical systems that are in either of two 

distinguishable quantum states that represent information: one state is zero and the other a one. 

The power in this system comes from the processing of many variables simultaneously by using 

a superposition of quantum states. Wave functions-solutions of the quantum Schrödinger 

equation for qubits-define the states in the case of quantum computing. A qubit’s states can be 

identified with zero and one, and their wave functions written as φ 0 and φ1 . A qubit can also be 

represented by the superposition of the two states: 

ψ = φ + ba φ10 , (44) 

where a and b are complex numbers satisfying . This superposition principle offers a 

means of carrying a much larger amount of information. Another quantum phenomenon, called 

entanglement, ties the wave functions of the qubits in a register together in a way that makes it 

possible to affect each member of the superposition, creating great power on quantum 

computing. 

1 22 ba =+

Most of the successful experimental demonstrations of qubits have used superconducting 

devices. An experiment using a superconducting Coulomb box as the qubit provides an example. 

A Coulomb box is a structure with a capacitance so small that the energy needed to add a single 

electron to it is the dominant energy in the operation of a circuit. The box in this experiment is 

called a “Cooper-pair box,” because the energy of the electrons can be lowered by the formation 

of Cooper pairs. The box can exchange charge with a reservoir through Josephson junctions. 

Solid-state technology produces devices on a planar surface. Neighboring qubits on a surface 

might interact with one another through overlapping wave functions, or through a capacitive 

link, used with superconducting qubits. However, it is difficult to see how to provide the long 

point-to-point connections that quantum computing requires. 

31
Decoherence is another quantum phenomenon that must be addressed. It is an unwanted 

interaction of quantum information with extraneous entities that destroy the information that the 

system is processing. An error-correction method that compares redundant qubits at each step 

has been proposed to combat decoherence. Forming accurate superpositions requires specifying 

separate timing sequences for each qubit and tailoring interaction times to each pair. The 

quantum computing alternative can be described as redundancy in quantum error correction and 

may be an anticipated result of this spintronics project. (50, pp. 65–69) 

The technique for manipulating and measuring DWs that will be investigated in this project may 

be useful in ferromagnetic semiconductor devices for magnetic logic and memory. The technique 

may also provide a new path for measuring quantum signatures of DW motion at low 

temperatures, where macroscopic quantum tunneling should be seen. (16) 

Another possible outcome of this research could be a liquid state NMR computer, which is based 

on nuclear spin states of molecules in solution. A five-qubit order finding algorithm has been 

demonstrated for this concept. One problem associated with the NMR computer is scalability, 

since the signal-to-noise ratio decreases exponentially as the size of the molecule increases. (5) 

32
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35
Acronyms 

2-D two-dimensional 

3-D three-dimensional 

AC alternating current 

AHE anomalous Hall effect 

AMR anisotropic magnetoresistance 

BNA Barkhausen Noise Analysis 

CCMS Center for Computational Materials Science 

CMOS complementary metal-oxide semiconductor 

CPP current perpendicular to the plane 

DC direct current 

DWR domain wall resistance 

DWs domain walls 

EBS exchange-biased sandwiches 

EDXD energy-dispersive X-ray diffraction 

EMX electromagnetic X-band 

EPR electron paramagnetic resonance spectroscopy 

F ferromagnetic 

fcc face-centered-cubic 

FET field-effect transistor 

FM ferromagnetic 

GMR giant magnetoresistance 

G-V conductance-voltage 

I insulator 

ISC intersystem crossing 

JMR junction magnetoresistance 

LED light emitting diode 

MAS NMR magic angle spin nuclear magnetic resonance 

MBE molecular beam epitaxy 

MBT magnetic bipolar transistor 

36 
MC magnetocurrent 

MR magnetoresistance 

MRAM magnetic random access memory 

MTJ magnetic tunnel junction 

NMR nuclear magnetic resonance 

PANi polyaniline 

PLD pulsed laser deposition 

Py permalloy 

S semiconductor 

SFET spin field-effect transistor 

SPICE spin-polarized injection current emitter 

spin electronics spintronics 

SPMDS spin polarization, spin-polarized metastable-atom deexcitation 

spectroscopy 

SQUID superconducting quantum interference device 

TCNQ tetracyanoquinodimethane 

TMR tunnel magnetoresistance 

UHV ultra-high vacuum 

VCSEL vertical-cavity surface-emitting laser 

XPS X-ray Photoelectron Spectroscopy 

ZFS zero-field splitting 

37
Bibliography 

Battle et al. J. of Applied Physics 2002, 91, 10163–10168. 

Bobo et al. J. of Applied Physics 1998, 83, 6685–6687. 

Caballero et al. J. of Vacuum. Science Technology A 1998, 16, 1801–1805. 

Comstock. J. of Materials Science: Materials in Electronics 2002, 13, 509–523. 

Koller et al. J. of Applied Physics 2003, 93, 8549–8551. 

Landry et al. Applied Physics Letters 2001, 78, 501–503. 

Mitsuzuka et al. J. of Applied Physics 1999, 85, 5807–5809. 

Moodera and Mathon. J. of Magnetism and Magnetic Materials 1999, 200, 248–273. 

Moodera et al. Applied Physics Letters 1997, 70, 3050–3052. 

Prinz. Physics Today, April 1995, pp 58–63. 

Ritchie et al. J. of Magnetism and Magnetic Materials 2002, 247, 187–197. 

Zhang. Physical Review Letters 1999, 83, 640–643. 

Zhu and Zheng. Spin Dynamics in Confined Magnetic Structures. Topics in Applied 

Physics 2002, 83, 289–326. 

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