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Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systems Diluted Magnetic Semiconductors and Magnetization Dynamics ONR N00014-06-1-0122. JAIRO SINOVA. Denver March 9 th 2007. Research fueled by:. Alexey Kovalev. Nikolai Sinitsyn.

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slide1

Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systemsDiluted Magnetic Semiconductors and Magnetization DynamicsONR N00014-06-1-0122

JAIRO SINOVA

Denver March 9th 2007

Research fueled by:

slide2

Alexey Kovalev

Nikolai Sinitsyn

Tomas Jungwirth

Karel Vyborny

Allan MacDonald, Qian Niu, Ken Nomura from U. of Texas

Marco Polini from Scuola Normale Superiore, Pisa

Rembert Duine from Utretch Univeristy, The Netherlands

Joerg Wunderlich from Cambridge-Hitachi

Laurens Molenkamp et al from Wuerzburg

Brian Gallager, Richard Campton, and Tom Fox from U. of Nottingham

Mario Borunda and Xin Liu from TAMU

Ewelina Hankiewicz from U. Missouri and TAMU

Branislav Nikolic, S. Souma, and L. Zarbo from U. of Delaware

slide3

ONR FUNDED TAMU SPIN PROGRAM ACTIVITY 2006-2007

  • 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. B75, 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. B75, 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
outline
OUTLINE
  • Motivation:
    • What is the problem
    • Challenges and outlook: ITRS 2005
    • ONR Spintronics TAMU program
  • Towards a comprehensive theory of anomalous transport:
    • The three spintronics Hall effects
      • Similarities and differences: why is it so difficult
    • Anomalous Hall effect and Spin Hall effect
      • AHE phenomenology and its long history
      • Three contributions to the AHE
      • Microscopic approach: focus on the intrinsic AHE
      • Application to the SHE: theory, experiment, current status
    • Equivalence of Kubo and Boltzmann: a success history of the Graphene model
    • New results in 2D-Rashba systems: absence of skew scattering
  • Diluted Magnetic Semiconductors: towards a higher Tc
    • Experimental and theory trends of Tc
    • Strategies to achieve higher Tc
    • Using mathematical theorems to increase Tc
  • A-C effect in mesoscopic rings with SO coupling
slide5

GETTING SMALLER IS NOT THE PROBLEM, GETTING HOTTER IS

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

slide6

Did we have this problem before: Yes

Did we solve it: Yes (but temporarily)

slide9

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. B75, 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.
slide10

The spintronics Hall effects

SHE

charge current gives

spin current

AHE

SHE-1

polarized charge current gives

charge-spin current

spin current gives

charge current

anomalous hall transport
Anomalous Hall transport
  • 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
slide12

majority

_

_

_

FSO

_

FSO

I

minority

V

Anomalous Hall effect: where things started, the long debate

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

Simple electrical measurement

of magnetization

InMnAs

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

intrinsic deflection
Intrinsic deflection

E

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)

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.

Side jump scattering

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

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.

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 microscopic kubo approach

n’, k

n, q

m, p

m, p

n, q

n, q

= -1/0

n’n, q

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH

Skew scattering

Skew

σHSkew (skew)-1 2~σ0 S where

S = Q(k,p)/Q(p,k) – 1~

V0 Im[<k|q><q|p><p|k>]

Averaging procedures:

Side-jump scattering

Vertex Corrections

 σIntrinsic

Intrinsic AHE

= 0

Intrinsic

σ0 /εF

success of intrinsic ahe approach in strongly so coupled systems
Success of intrinsic AHE approach in strongly SO coupled systems

Experiment

sAH  1000 (W cm)-1

Theroy

sAH  750 (W cm)-1

  • 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.

slide16

_

_

_

FSO

_

non-magnetic

FSO

I

V=0

Spin Hall effect

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

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

Spin-current generation in non-magnetic systems

without applying external magnetic fields

Spin accumulation without charge accumulation

excludes simple electrical detection

slide17

Spin Hall Effect

(Dyaknov and Perel)

Interband

Coherent 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

slide18

First experimentalobservations at the end of 2004

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:

(weaker SO-coupling, stronger disorder)

1.52

Wunderlich, Kästner, Sinova, Jungwirth, PRL 05

Experimental observation of the spin-Hall effect in a two

dimensional spin-orbit coupled semiconductor system

CP [%]

1.505

Light frequency (eV)

slide19

OTHER RECENT EXPERIMENTS

Transport observation of the SHE by spin injection!!

Valenzuela and Tinkham cond-mat/0605423, Nature 06

Saitoh et al APL 06

Sih et al, Nature 05, PRL 05

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

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

slide20

Intrinsic + Extrinsic:Connecting Microscopic and Semiclassical approach

Sinitsyn et al PRL 06, PRB 07

  • Need to match the Kubo to the Boltzmann
  • Kubo: systematic formalism
  • Botzmann: easy physical interpretation of different contributions

AHE in Rashba systems with disorder:

Dugaev et al PRB 05

Sinitsyn et al PRB 05

Inoue et al (PRL 06)

Onoda et al (PRL 06)

Borunda et al (cond-mat 07)

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

slide21

Kubo-Streda formula summary

Semiclassical Boltzmann equation

Golden rule:

In metallic regime:

J. Smit (1956):

Skew Scattering

slide22

Semiclassicalapproach II

Golden Rule:

Modified

Boltzmann

Equation:

velocity:

Sinitsyn et al PRL 06, PRB 06

current:

Berry curvature:

Coordinate shift:

slide23

Success in graphene

EF

Armchair edge

Zigzag edge

slide24

Single K-band with spin up

Kubo-Streda

formula:

In metallic regime:

Sinitsyn et al PRL 06, PRB 06

SAME RESULT OBTAINED USING BOLTMANN!!!

slide27

SHE in the mesoscopic regime

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
landauer keldish approach
Landauer-Keldish approach

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

diluted magnetic semiconductors magnetization dynamics
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. B75, 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
slide30

Dilute Magnetic Semiconductors: the simple picture

5 d-electrons with L=0

S=5/2 local moment

moderately shallow

acceptor (110 meV)

 hole

-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!!!

Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms

slide31

Ga1-xMnxAs

As anti-site deffect: Q=+2e

Substitutioanl Mn:

acceptor +Local 5/2 moment

Interstitial Mn:

double donor

BUT THINGS ARE NOT THAT SIMPLE

Anti-

site

Mn

As

Inter-

stitial

Ga

Low Temperature

- MBE

Ferromagnetic: x=1-8%

courtesy of D. Basov

slide32

Mn

Mn

Mn

As

Ga

Problems for GaMnAs (late 2002)

  • Curie temperature limited to ~110K.
  • Only metallic for ~3% to 6% Mn
  • High degree of compensation
  • Unusual magnetization (temperature dep.)
  • Significant magnetization deficit

“110K could be a fundamental limit on TC”

But are these intrinsic properties of GaMnAs ??

slide33

Can a dilute moment ferromagnet have a high Curie temperature ?

  • The questions that we need to answer are:
  • Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ?
  • 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)?
slide34

Magnetism in systems with coupled dilute moments

and delocalized band electrons

coupling strength / Fermi energy

band-electron density / local-moment density

(Ga,Mn)As

slide35

Theoretical 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

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

  • Phenomenological k.p  Local Moment

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)

slide36

Mn

Mn

Mn

As

Ga

Intrinsic properties of (Ga,Mn)As

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

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%.

slide37

Linear increase of Tc with Mneff = Mnsub-MnInt

High compensation

8% Mn

Tc as grown and annealed samples

Open symbols as grown. Closed symbols annealed

  • 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
slide38

Getting to higher Tc: Strategy A

- 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 MBE

Strategy 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

slide39

Getting to higher Tc: Strategy B

  • 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)
slide40

d5

d5

Mn

As

Ga

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

5.7

(Al,Ga)As

lattice constant (A)

Ga(As,P)

5.4

0

1

conc. of wide gap component

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

Mn d - As(P) poverlap

Mn d level - valence band splitting

GaAs & (Al,Ga)As

Ga(As,P)

GaAs

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

slide41

(Al,Ga)As

p-d coupling and Tc in mixed

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

theory

10% Mn

Ga(As,P)

Smaller lattice const. more important

for 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

10% Mn

Ga(As,P)

5% Mn

theory

Mašek, et al. PRB (2006)

Microscopic TBA/CPA or LDA+U/CPA

slide42

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)?

Using DEEP mathematics to find a new material

3=1+2

slide43

III = I + II  Ga = Li + Zn

GaAs and LiZnAs are twin SC

Wei, Zunger '86;

Bacewicz, Ciszek '88;

Kuriyama, et al. '87,'94;

Wood, Strohmayer '05

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

Masek, et al. PRB (2006)

slide44

No solubility limit for group-II Mn

substituting for group-II Zn

theory

Additional interstitial Li in

Ga tetrahedral position - donors

n-type Li(Zn,Mn)As

slide45

EF

L

As p-orb.

Ga s-orb.

As p-orb.

Electronmediated Mn-Mn coupling n-type Li(Zn,Mn)As -

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

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

slide47

COLLABORATION BETWEEN INDIVIDUAL ONR PROJECTS:

1st benefit of this meeting (UCSD+TAMU)

slide48

Aharonov-Casher effect:

corollary of Aharonov-Bohm effect with electric fields instead

  • 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

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

hgte r ing structures
HgTe Ring-Structures

Three phase factors:

Aharonov-Bohm

Berry

Aharonov-Casher

high electron mobility
High Electron Mobility

m> 3 x 105 cm2/Vsec

rashba effect in hgte
Rashba Effect in HgTe

8 x 8 k×p band structure model

Rashba splitting energy

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

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

hgte r ing structures1
HgTe Ring-Structures

EXPERIMENT

THEORY

Modeling E. Hankiewicz, J. Sinova,

Concentric Tight Binding Model + B-field

slide53

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.

Navy/DoD relevance

Accomplishments 2006/2007

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.

  • 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.
keeping score
Keeping Score

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

slide56
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

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