JAIRO SINOVA

Research fueled by:

Denver March 9th 2007

Spin currents, spin-Hall spin accumulation, and anomalous Hall Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systemstransport in strongly spin-orbit coupled systems

Diluted Magnetic Semiconductors and Magnetization DynamicsDiluted Magnetic Semiconductors and Magnetization Dynamics

ONR N00014-06-1-0122

Tomas Jungwirth

Allan MacDonald, Qian Niu, Ken Nomura from U. of TexasMarco Polini from Scuola Normale Superiore, Pisa

Rembert Duine from Utretch Univeristy, The NetherlandsJoerg Wunderlich from Cambridge-HitachiLaurens Molenkamp et al from Wuerzburg

Brian Gallager, Richard Campton, and Tom Fox from U. of NottinghamMario Borunda and Xin Liu from TAMU

Ewelina Hankiewicz from U. Missouri and TAMUBranislav Nikolic, S. Souma, and L. Zarbo from U. of Delaware

Nikolai SinitsynAlexey Kovalev Karel Vyborny

Spin and Anomalous Hall Effect:•N. A. Sinitsyn, et al, "Charge and spin Hall conductivity in metallic graphene", Phys. Rev. Lett. 97, 106804 (2006).•N. A. Sinitsyn, et al, "Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach", Phys. Rev. B 75, 045315 (2007).•Mario F. Borunda, et al, "Absence of skew scattering in two-dimensional systems: Testing the origins of the anomalous Hall Effect", pre-print: cond-mat/0702289, submitted to Phys. Rev. Lett.

Diluted Magnetic Semiconductors/ Magnetization Dynamics:•T. Jungwirth, et al, "Theory of ferromagnetic (III,Mn)V Semiconductors", Rev. Mod. Phys. 78, 809 (2006)•J. Masek, et al, "Mn-doped Ga(As,P) and (Al,Ga)As ferromagnetic semiconductors", Phys. Rev. B 75, 045202 (2007).•J. Wunderlich, et al, “Local control of magnetocrystalline anisotropy in (Ga,Mn)As microdevices”, submitted to Phys. Rev. B •R. Duine, et al “Functional Keldysh Theory of spin-torques”, submitted to PRB

Aharonov-Casher effect•M. Koenig, et al, "Direct observation of the Aharonov-Casher phase", Phys. Rev. Lett. 96, 076804 (2006).•Alexey A. Kovalev, et al "Aharonov-Casher effect in a two dimensional hole ring with spin-orbit interaction", pre-print: cond-mat/0701534, submitted to Phys. Rev. B

ONR FUNDED TAMU SPIN PROGRAM ACTIVITY 2006-2007

OUTLINEOUTLINE Motivation:Motivation:

What is the problemWhat is the problem Challenges and outlook: ITRS 2005Challenges and outlook: ITRS 2005 ONR Spintronics TAMU programONR Spintronics TAMU program

Towards a comprehensive theory of anomalous transport:Towards a comprehensive theory of anomalous transport: The three spintronics Hall effectsThe three spintronics Hall effects

Similarities and differences: why is it so difficult Similarities and differences: why is it so difficult Anomalous Hall effect and Spin Hall effectAnomalous Hall effect and Spin Hall effect

AHE phenomenology and its long historyAHE phenomenology and its long history Three contributions to the AHEThree contributions to the AHE Microscopic approach: focus on the intrinsic AHEMicroscopic approach: focus on the intrinsic AHE Application to the SHE: theory, experiment, current statusApplication to the SHE: theory, experiment, current status

Equivalence of Kubo and Boltzmann: a success history of the Equivalence of Kubo and Boltzmann: a success history of the Graphene modelGraphene model

New results in 2D-Rashba systems: absence of skew scatteringNew results in 2D-Rashba systems: absence of skew scattering Diluted Magnetic Semiconductors: towards a higher TcDiluted Magnetic Semiconductors: towards a higher Tc

Experimental and theory trends of TcExperimental and theory trends of Tc Strategies to achieve higher TcStrategies to achieve higher Tc Using mathematical theorems to increase TcUsing mathematical theorems to increase Tc

A-C effect in mesoscopic rings with SO couplingA-C effect in mesoscopic rings with SO coupling

GETTING SMALLER IS NOT THE PROBLEM, GETTING HOTTER IS

Circuit heat generation is the main limiting factor for scaling device speed

Did we have this problem before: YesDid we solve it: Yes (but temporarily)

ITRS 2005

WHY IS CMOS SO HARD TO BEAT

International Technology Roadmap for Semiconductors 2005: EMERGING RESEARCH DEVICES

•N. A. Sinitsyn, et al, "Charge and spin Hall conductivity in metallic graphene", Phys. Rev. Lett. 97, 106804 (2006).•N. A. Sinitsyn, et al, "Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach", Phys. Rev. B 75, 045315 (2007).•Mario F. Borunda, et al, "Absence of skew scattering in two-dimensional systems: Testing the origins of the anomalous Hall Effect", pre-print: cond-mat/0702289, submitted to Phys. Rev. Lett.

Spin and Anomalous Hall Effect:

The spintronics Hall effectsThe spintronics Hall effects

AHE

SHEcharge current

gives spin current

polarized charge current gives charge-spin

current

SHE-1

spin current gives

charge current

Anomalous Hall Anomalous Hall transporttransport

Commonalities:

•Spin-orbit coupling is the key•Same basic (semiclassical) mechanisms

Differences:

•Charge-current (AHE) well define, spin current (SHE) is not•Exchange field present (AHE) vs. non-exchange field present (SHE-1)

Difficulties:

•Difficult to deal systematically with off-diagonal transport in multi-band system•Large SO coupling makes important length scales hard to pick•Farraginous results of supposedly equivalent theories•The Hall conductivities tend to be small

Anomalous Hall effect: where things Anomalous Hall effect: where things started, the long debatestarted, the long debate

MπRBR sH 40

Simple electrical measurement Simple electrical measurement of magnetizationof magnetization

Spin-orbit coupling “force” deflects like-spinlike-spin particles

I

_ FSO

FSO

_ __

majority

minority

VInMnAs

controversial theoretically: semiclassical theory identifies three contributions (intrinsic deflection, skew scattering, side jump scattering)

Intrinsic deflectionIntrinsic deflection

Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling.

Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure)

E

Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step.

Related to the intrinsic effect: analogy to refraction from an imbedded medium

Side jump scattering

Skew scattering

Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators.

THE THREE CONTRIBUTIONS TO THE AHE: THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACHMICROSCOPIC KUBO APPROACH

Skew scattering

Side-jump scattering

Intrinsic AHE

SkewσH

Skew (skew)-1 2~σ0 S where S = Q(k,p)/Q(p,k) – 1~

V0 Im[<k|q><q|p><p|k>]

Vertex Corrections σIntrinsic

Intrinsicσ0 /εF

n, q

n, q m, p

m, pn’, k

n, q

n’n, q

= -1 / 0

Averaging procedures:

= 0

Success of intrinsic AHE approach in strongly SO

coupled systems• DMS systems (Jungwirth et al PRL 2002)• Fe (Yao et al PRL 04)• Layered 2D ferromagnets such as SrRuO3 and

pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 71, 19 (2001),Taguchi et al., Science 291, 2573 (2001), Fang et al Science 302, 92 (2003), Shindou and Nagaosa, Phys. Rev. Lett. 87, 116801 (2001)]

• Colossal magnetoresistance of manganites, Ye et~al Phys. Rev. Lett. 83, 3737 (1999).

• Ferromagnetic Spinel CuCrSeBr: Wei-Lee et al, Science (2004)

Berry’s phase based AHE effect is quantitative-

successful in many instances BUT still not a theory that

treats systematically intrinsic and extrinsic

contribution in an equal footing.

Experiment AH 1000 (cm)-1

TheroyAH 750 (cm)-1

Spin Hall effectSpin Hall effect

Take now a PARAMAGNET instead of a FERROMAGNET: Spin-orbit coupling “force” deflects like-spinlike-spin particles

I

_ FSO

FSO

_ __

V=0

non-magnetic

Spin-current generation in non-magnetic systems Spin-current generation in non-magnetic systems without applying external magnetic fieldswithout applying external magnetic fields

Spin accumulation without charge accumulationSpin accumulation without charge accumulationexcludes simple electrical detectionexcludes simple electrical detection

Carriers with same charge but opposite spin are deflected by the spin-orbit coupling to opposite sides.

Spin Hall Effect(Dyaknov and Perel)

InterbandCoherent Response

(EF) 0

Occupation # Response

`Skew Scattering‘(e2/h) kF (EF )1

X `Skewness’

[Hirsch, S.F. Zhang] Intrinsic

`Berry Phase’(e2/h) kF

[Murakami et al,

Sinova et al]

Influence of Disorder`Side Jump’’

[Inoue et al, Misckenko et al, Chalaev et al.] Paramagnets

First experimentalFirst experimental observations at the end of 2004observations at the end of 2004

Wunderlich, Kästner, Sinova, Jungwirth, PRL 05

Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system

-1

0

1

CP

[%]

Light frequency (eV)1.505

1.52

Kato, Myars, Gossard, Awschalom, Science Nov 04

Observation of the spin Hall effect bulk in semiconductors

Local Kerr effect in n-type GaAs and InGaAs: Local Kerr effect in n-type GaAs and InGaAs: (weaker SO-coupling, stronger disorder)(weaker SO-coupling, stronger disorder)

OTHER RECENT EXPERIMENTS

“demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current”

Sih et al, Nature 05, PRL 05

Valenzuela and Tinkham cond-mat/0605423, Nature 06

Transport observation of the SHE by spin injection!!

Saitoh et al APL 06

SHE at room temperature in HgTe systems Stern et al PRL 06 !!!

Need to match the Kubo to the Need to match the Kubo to the BoltzmannBoltzmann

Kubo: systematic formalismKubo: systematic formalism Botzmann: easy physical Botzmann: easy physical

interpretation of different interpretation of different contributionscontributions

Intrinsic + Extrinsic:Intrinsic + Extrinsic:Connecting Microscopic and Semiclassical Connecting Microscopic and Semiclassical

approachapproach

Sinitsyn et al PRL 06, PRB 07

AHE in Rashba systems with disorder:AHE in Rashba systems with disorder: Dugaev et al PRB 05Dugaev et al PRB 05 Sinitsyn et al PRB 05Sinitsyn et al PRB 05 Inoue et al (PRL 06)Inoue et al (PRL 06) Onoda et al (PRL 06)Onoda et al (PRL 06)

Borunda et al (cond-mat 07)Borunda et al (cond-mat 07)

All are done using same or equivalent linear response formulation–different or not obviously equivalent answers!!!

Semiclassical Boltzmann equation

' ''

( )l ll l l l

l

f feE f f

t k

2' ' '

' '' ''' '

' ''

2| | ( )

...

l l l l l l

l l l ll l l l

l l

T

V VT V

i

Golden rule:

' 'l l ll J. Smit (1956):Skew Scattering

In metallic regime:

Kubo-Streda formula summary

2 R+II Rxy x y-

R A AR A A

x y x y x y

e dGσ = dεf(ε)Tr[v G v -

4π dε

dG dG dG-v v G -v G v +v v G ]

dε dε dε

I IIxy xy xyσ =σ +σ

2 +I R A Axy x y-

R R Ax y

e df(ε)σ =- dε Tr[v (G -G )v G -

4π dε

-v G v (G -G )]

2' ' '

2| | ( )l l l l l lV

Golden Rule:

Coordinate shift:

0 0' ' ' '

' '

( ) ( )v ( )l l ll l l l l l l l l

l ll l

f f feE eE r f f

t

ModifiedBoltzmannEquation:

( , )l k

Iml l l l lz

y x x y

u u u uF

k k k k

Berry curvature:

' ' ' '',ˆ arg

'l l l l l l l lk kr u i u u i u D V

k k

' ''

lll l l l l

l

v F eE rk

velocity:

l ll

J e f v

current:

' 'l l l lV T

Semiclassical approach II

Sinitsyn et al PRL 06, PRB 06

Armchair edge

Zigzag edge

EF

Success in graphene

2 R+II Rxy x y-

R A AR A A

x y x y x y

e dGσ = dεf(ε)Tr[v G v -

4π dε

dG dG dG-v v G -v G v +v v G ]

dε dε dε

I IIxy xy xyσ =σ +σ

2 +I R A Axy x y-

R R Ax y

e df(ε)σ =- dε Tr[v (G -G )v G -

4π dε

-v G v (G -G )]

In metallic regime:IIxyσ =0

Kubo-Streda formula:

2 32 42 4

I so so FF Fxy 2 2 22 22 2 22 2 2

F soF so F so F so

e V-e Δ (vk )4(vk ) 3(vk )σ = 1+ +

(vk ) +4Δ 2πn V4π (vk ) +Δ (vk ) +4Δ (vk ) +4Δ

Single K-band with spin up

x x y y so zKH =v(k σ +k σ )+Δ σ

Sinitsyn et al PRL 06, PRB 06 SAME RESULT OBTAINED USING BOLTMANN!!!

Comparing Boltzmann to Kubo in the chiral basis

0 0' ' ' '

' '

( ) ( )v ( )l l ll l l l l l l l l

l ll l

f f feE eE r f f

t

For single occupied linear Rashba band; zero for both occupied !!

Non-equilibrium Green’s function formalism (Keldysh-LB)

Advantages:•No worries about spin-current definition. Defined in leads where SO=0•Well established formalism valid in linear and nonlinear regime•Easy to see what is going on locally•Fermi surface transport

SHE in the mesoscopic regime

Landauer-Keldish approachLandauer-Keldish approach

B.K. Nicolić, et al PRL.95.046601, Mario Borunda and J. Sinova unpublished

Diluted Magnetic Semiconductors/ Magnetization Dynamics

•T. Jungwirth, et al, "Theory of ferromagnetic (III,Mn)V Semiconductors", Rev. Mod. Phys. 78, 809 (2006)•J. Masek, et al, "Mn-doped Ga(As,P) and (Al,Ga)As ferromagnetic semiconductors", Phys. Rev. B 75, 045202 (2007).•J. Wunderlich, et al, “Local control of magnetocrystalline anisotropy in (Ga,Mn)As microdevices”, submitted to Phys. Rev. B •R. Duine, et al “Functional Keldysh Theory of spin-torques”, submitted to PRB

Dilute Magnetic Semiconductors: the simple picture

5 d-electrons with L=0 S=5/2 local moment

moderately shallow acceptor (110 meV) hole

Jungwirth, Sinova, MJungwirth, Sinova, Mašek, Kučera, ašek, Kučera, MacMacDDonaldonald, , Rev. Mod. Phys. (2006)Rev. Mod. Phys. (2006), ,

http://unix12.fzu.cz/mshttp://unix12.fzu.cz/ms

- Mn local moments too dilute (near-neghbors cople AF)

- Holes do not polarize in pure GaAs

- Hole mediated Mn-Mn FM coupling

FERROMAGNETISM MEDIATED BY THE CARRIERS!!!

Ga

As

Mn

Ferromagnetic: x=1-8%

Ga1-xMnxAs

Low Temperature - MBE

courtesy of D. Basov

Inter-stitial

Anti-site

Substitutioanl Mn:acceptor +Local 5/2

moment

As anti-site deffect: Q=+2e

Interstitial Mn: double donor

BUT THINGS ARE NOT THAT SIMPLE

Curie temperature limited to ~110K.Curie temperature limited to ~110K.

Only metallic for ~3% to 6% MnOnly metallic for ~3% to 6% Mn

High degree of compensationHigh degree of compensation

Unusual magnetization (temperature dep.)Unusual magnetization (temperature dep.)

Significant magnetization deficitSignificant magnetization deficit

1996 1998 2000 20020

40

80

120

[4][3][2]

[1]

Cu

rie

tem

per

atu

re (

K)

Time

But are these intrinsic properties of GaMnAs ??

“110K could be a fundamental limit on TC” As

GaMn

Mn Mn

Problems for GaMnAs (late 2002)

Can a dilute moment ferromagnet have a high Curie temperature ?

The questions that we need to answer are:

1. Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ?

2. Is there an extrinsic limit from the ability to create the material and its growth (prevents one to reach the optimal spot in the phase diagram)?

Magnetism in systems with coupled dilute moments and delocalized band electrons

(Ga,Mn)As

cou

plin

g s

tren

gth

/ F

erm

i en

erg

y

band-electron density / local-moment density

Theoretical Approaches to DMSsTheoretical Approaches to DMSs• First Principles Local Spin Density Approximation (LSDA) PROS: No initial assumptions, effective Heisenberg model can be

extracted, good for determining chemical trends

CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually)• Microscopic Tight Binding models

•Phenomenological k.p Local Moment

PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), good agreement with LDA+U calculations

CONS: difficult to capture non-tabulated chemical trends, hard to reach large system sizes

PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated, CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN)

As

GaMn

Mn Mn

Tc linear in MnGa local moment concentration; falls rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole density for compensation < 50%.

Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005)

3/1pxT MnMFc

Intrinsic properties of (Ga,Mn)As

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

160

180

TC(K

)

Mntotal

(%)

8% Mn

Open symbols as grown. Closed symbols annealed

High compensatio

n0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

160

180

TC(K

)

Mneff

(%)

Linear increase of Tc with Mneff = Mnsub-MnInt

Tc as grown and annealed samples

• Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample

• Charge compensation not so important unless > 40%

• No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

- Effective concentration of uncompensated MnGa moments has to increase beyond 6% of the current record Tc=173K sample. A factor of 2 needed 12% Mn would still be a DMS

- Low solubility of group-II Mn in III-V-host GaAs makes growth difficult

Low-temperature MBEStrategy A: stick to (Ga,Mn)As

- alternative growth modes (i.e. with proper

substrate/interface material) allowing for larger

and still uniform incorporation of Mn in zincblende GaAs

More Mn - problem with solubility

Getting to higher Tc: Strategy A

Find DMS system as closely related to (Ga,Mn)As as possible with

• larger hole-Mn spin-spin interaction

• lower tendency to self-compensation by interstitial Mn

• larger Mn solubility

• independent control of local-moment and carrier doping (p- & n-type)

Getting to higher Tc: Strategy B

conc. of wide gap component0 1

latti

ce c

onst

ant (

A)

5.4

5.7

(Al,Ga)As

Ga(As,P)

(Al,Ga)As & Ga(As,P) hosts

d5 d5

local moment - hole spin-spin coupling Jpd S . s

Mn d - As(P) p overlap Mn d level - valence band splitting

GaAs & (Al,Ga)As

(Al,Ga)As & Ga(As,P)GaAs

Ga(As,P)

MnAs

Ga

Smaller lattice const. more importantfor enhancing p-d coupling than larger gap

Mixing P in GaAs more favorable

for increasing mean-field Tc than Al

Factor of ~1.5 Tc enhancement

p-d coupling and Tc in mixed

(Al,Ga)As and Ga(As,P)

Mašek, et al. PRB (2006)Microscopic TBA/CPA or Microscopic TBA/CPA or

LDA+U/CPALDA+U/CPA

(Al,Ga)As

Ga(As,P)

Ga(As,P)

10% Mn

10% Mn

5% Mn

theory

theory

Using DEEP mathematics to find a new material

3=1+2

Steps so far in strategy B:

• larger hole-Mn spin-spin interaction : DONE BUT DANGER IN PHASE DIAGRAM

• lower tendency to self-compensation by interstitial Mn: DONE

• larger Mn solubility ?

• independent control of local-moment and carrier doping (p- & n-type)?

IIIIII = I + II = I + II Ga = Li + Zn Ga = Li + Zn

GaAs and LiZnAs are twin SC

Wei, Zunger '86;Bacewicz, Ciszek '88;Kuriyama, et al. '87,'94;Wood, Strohmayer '05

Masek, et al. PRB (2006)

LDA+U says that Mn-doped are also twin DMSs

Additional interstitial Li in

Ga tetrahedral position - donors

n-type Li(Zn,Mn)As

No solubility limit for group-II Mn

substituting for group-II Zn

theory

Electron mediated Mn-Mn coupling n-type Li(Zn,Mn)As -

similar to hole mediated coupling in p-type (Ga,Mn)As

L

As p-orb.

Ga s-orb.As p-orb.

EF

Comparable Tc's at comparable Mn and carrier doping and

Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As

Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family

Wunderlich et al, submitted to PRB 07

COLLABORATION BETWEEN INDIVIDUAL ONR PROJECTS:1st benefit of this meeting (UCSD+TAMU)

Aharonov-Casher effect: corollary of Aharonov-Bohm effect

with electric fields instead

Control of conductance through a novel Berry’s phase effect induced by gate voltages instead of magnetic fields

•M. Koenig, et al, "Direct observation of the Aharonov-Casher phase", Phys. Rev. Lett. 96, 076804 (2006).•Alexey A. Kovalev, et al "Aharonov-Casher effect in a two dimensional hole ring with spin-orbit interaction", pre-print: cond-mat/0701534, submitted to Phys. Rev. B

HgTe RHgTe Ringing-Structures-Structures

Three phase factors:

Aharonov-Bohm

Berry

Aharonov-Casher

effexttottotext

tot

BBBBB

b

B

s

;,

,for 1

toparallelanti and parallel

,and

0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

160

180

q1867

nHall

= 1,79*1012 cm-2

nSdH

= 1,74*1012 cm-2

µ= 301000 cm2/Vs

Rxx

()

B (T)

0,0

0,5

1,0

1,5

2,0

2,5

Rxy (k

)

High Electron MobilityHigh Electron Mobility

> 3 x 105 cm2/Vsec

= 2.0 V , A sym . C ase

Rashba Effect in HgTeRashba Effect in HgTe

0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

(nm - 1)

20

40

60

80

100

120

140

160

()

(meV

)

= 0.2 V , S ym. C ase

22

11

22

0.0 0.05 0.1 0.15 0.2 0.25(nm - 1)

0

5

10

15

(meV

)

= 2.0 V= 2.0 V

Rashba splitting energy

meV 30max, RmeV 30max, R

8 x 8 kp band structure model

A. Novik et al., PRB 72, 035321 (2005).

Y.S. Gui et al., PRB 70, 115328 (2004).

HgTe RHgTe Ringing--StructuresStructures

Modeling E. Hankiewicz, J. Sinova,

Concentric Tight Binding Model + B-field

EXPERIMENT

THEORY

Semiconductor nano-spintronics (TAMU): ONR AWARD N00014-06-1-0122

Scientific objectives Rationale and motivation

Task 1- Develop quantitative theories of spin transport and accumulation in spin-orbit coupled systems: spin-Hall and anomalous Hall effect and spin-transport phenomena

Task 2- Develop quantitative theories for novel spintronics materials that couple semiconducting properties and ferromagnetic properties

Task 3- Develop a theory of spin Coulomb drag in systems with spin-orbit coupling

Task 1- Possibility of manipulating spin and spin currents by solely electrical means in a controlled fashion. New switching devices.

Task 2- Allows control of new transport phenomena such as anisotropic tunneling magneto-resistance by gates. New memory devices.

Task 3- Allows for longer spin coherence times in spin transport and makes larger spin based devices more likely to impact the IT field.

Task 1- Possibility to create new logical switching devices with lower dissipative heat consumption, increasing reliability and speed.

Task 2- Novel MRAM devices for larger memory density capabilities and reliability (no mechanical parts)

Task 3- Allows for larger size devices in the mesoscopic range.

Navy/DoD relevance Accomplishments 2006/2007

• Theory of anomalous Hall effect in graphene.• Discovery of Aharonov-Casher phase in

transport measurements.• Extensive review of diluted magnetic

semiconductors and analysis of ferromagnetic temperature trends

• Prediction of new DMS materials with room temperature ferromagnetism possibilities.

• Extended theory of spin accumulation in coherent mesoscopic devices.

EXTRASEXTRAS

Keeping Keeping ScoreScore

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid:

• Ferromagnetic transition temperatures Magneto-crystalline anisotropy and coercively Domain structure Anisotropic magneto-resistance Anomalous Hall effect MO in the visible range Non-Drude peak in longitudinal ac-conductivity • Ferromagnetic resonance • Domain wall resistance • TAMR

BUT it is only a peace of the theoretical mosaic with many remaining challenges!!

TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

● Energy dependence of Jpd

● Localization effects

● Contributions due to impurity states: Flatte’s approach of starting from isolated impurities

● Systematic p and xeff study (need more than 2 meff data points)

Possible issues regarding IR absorption