Spin Injection Hall Effect: a new member of the spintronic Hall family and its implications in...

Spin Injection Hall Effect: a new member of the spintronic Hall family and

its implications in nano-spintronics

Research fueled by:

Optical Spintronics MeetingHitachi-Cambridge,October 27th, 2009

JAIRO SINOVATexas A&M University

Institute of Physics ASCR

Hitachi CambridgeJoerg Wunderlich, X. Xu,

A. Irvine, et al

Institute of Physics ASCRTomas Jungwirth, Vít Novák, et al

Texas A&M L. Zarbo

2Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system?

Long standing paradigm: Datta-Das FET

Unfortunately it has not worked :•no reliable detection of spin-polarization in a diagonal transport configuration •No long spin-coherence in a Rashba spin-orbit coupled system

Towards a REALISTIC spin-based non-magnetic FET device

Ohno et al. Nature’99, others

Crooker et al. JAP’07, others Magneto-optical imaging

non-destructive

lacks nano-scale resolution and only an optical lab tool

MR Ferromagnet

electrical

destructive and requires semiconductor/magnet hybrid design & B-field to orient the FM

spin-LED

all-semiconductor

destructive and requires further conversion of emitted light to electrical signal

Spin detection in semiconductors

4

SHEB=0

charge current gives

spin current

Optical detection

SHE-1

B=0spin current

gives charge current Electrical

detection

js–––––––––––

+ + + + + + + + + +iSHEI

_ FSO

FSO

_ __

majority

minority

V

The family of spintronic Hall effects

AHEB=0

polarized charge current gives charge-spin

current

Electrical detection

J. Wunderlich, B. Kaestner, J. Sinova andT. Jungwirth, Phys. Rev. Lett. 94 047204 (2005)

Spin-Hall Effect

5

B. Kaestner, et al, JPL 02; B. Kaestner, et al Microelec. J. 03; Xiulai Xu, et al APL 04, Wunderlich et al PRL 05

Proposed experiment/device: Coplanar photocell in reverse bias with Hall probes along the 2DEG channelBorunda, Wunderlich, Jungwirth, Sinova et al PRL 07

Utilize technology developed to detect SHE in 2DHG and measure polarization via Hall probes

i pn

2DHG

Device schematics: materials

-

2DHGi p

n

Device schematics: trench

i

p

n2DHG

2DEG

Device schematics: n-etch

Vd

VH

2DHG

2DEG

Vs

9

Device schematics: materials

2DHG

2DEG

e

h

ee

ee

e

hh

h

h h

Vs

Vd

VH

10

Device schematics: SIHE measurement


2DHG

2DEG

e

h

ee

ee

e

hhh

h h

Vs

Vd

VH

Spin-injection Hall effect device schematics


Spin-injection Hall device measurements

trans. signal

σσooσσ++σσ-- σσoo

VL


Spin-injection Hall device measurements

trans. signal

σσooσσ++σσ-- σσoo

VL

SIHE ↔ Anomalous Hall

Local Hall voltage changes sign and magnitude along a channel of 6 μm

and high temperature operation

Zero bias-

σ+σ- σ+σ-

14

Persistent Spin injection Hall effect


Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling

The 2DEG is well described by the effective Hamiltonian:

Hence

For our 2DEG system:


What is special about α≈β

• spin along the [110] direction is conserved

• long lived precessing spin wave for spin perpendicular to [110]

The nesting property of the Fermi surface:


Effects of Rashba and Dresselhaus SO coupling

α= -β

[110]

[110]_

ky [010]

kx [100]

α > 0, β = 0[110]

[110]_

ky [010]

kx [100]

α = 0, β < 0[110]

[110]_

ky [010]

kx [100]


Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling

For the same distance traveled along [1-10], the spin precesses by exactly the same angle.

[110]

[110]_

[110]_


Similar wafer parameters to ours

Persistent state spin helix verified by pump-probe experiments

Weber et al. PRL 07

For arbitrary α,β spin-charge transport equation is obtained for diffusive regime

For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling Sx+ and Sz:

For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004);

Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004)

20

The Spin-Charge Drift-Diffusion Transport Equations


Spatial variation scale consistent with the one observed in SIHE

Spin-helix state when α ≠ β


Simple electrical measurement of out of plane magnetization

InMnAs

I

FSO

FSO

majority

minority

V

Spin dependent “force” deflects like-spin particles

ρH=R0B ┴ +4π RsM┴

Understanding the Hall signal in SIHE: Anomalous Hall Effect


Anomalous Hall effect (scaling with ρ )

37

Dyck et al PRB 2005

Material with dominant skew scattering mechanismMaterial with dominant scattering-independent mechanism

Ohio State University 2009 6

GaMnAs

Kotzler and Gil PRB 2005

Co films

Edmonds et al APL 2003


Intrinsic 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.

~τ0 or independent of impurity density

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. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.

independent of impurity density

Side jump scattering

Vimp(r)

Skew scattering

Asymmetric scattering due to the SO coupling of the electron or the impurity. Known as Mott scattering.

~1/ni Vimp(r)

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

E

SO coupled quasiparticles

STRONG SPIN-ORBIT COUPLED REGIME (Δso>ħ/τ)


Side jump scattering from SO disorder

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. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.

independent of impurity density

The terms/contributions dominant in the strong SO couple regime are strongly reduced (quasiparticles not well defined due to strong disorder broadening). Other terms, originating from the interaction of the quasiparticles with the SO-coupled part of the disorder potential dominate.

Better understood than the strongly SO couple regime

WEAK SPIN-ORBIT COUPLED REGIME (Δso<ħ/τ)

Skew scattering from SO disorder

~1/ni


Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii)

Crepieux et al PRB 01Nozier et al J. Phys. 79

Two types of contributions: i)S.O. from band structure interacting with the field (external and internal)•Bloch electrons interacting with S.O. part of the disorder

Lower bound estimate of skew scatt. contribution

AHE contribution to Spin-injection Hall effect


Local spin-polarization → calculation of AHE signal

Weak SO coupling regime → extrinsic skew-scattering term is dominant

Lower bound estimate

Spin-injection Hall effect: theoretical expectations


Further experimental tests of the observed SIHE

S. Datta, B. Das,Appl. Phys. Lett. 56 665 (1990).

… works only

- if channel is 1dimensional

- or under Spin Helix conditions for 2D channel

Comment 1: Datta-Das type device

SIHE Field Effect Transistor


SHE-1

B=0spin current gives

charge current


AHEB=0

polarized charge current gives charge-spin

current


SHEB=0

charge current gives spin current

Optical detection

SIHEB=0

Optical injected polarized current

gives charge current


The spintronic Hall family

32

- electrical detection method for Spin current

- large signal (comparable to AHE in metallic ferromagnets)

- high spatial resolution (~ < 50nm)

- nondestructive detection of spin WITHOUT magnetic elements

- linear with degree of spin polarization

- high temperature operation

- first electrical detection of the Spin Helix (coherently precessing spins)

- all electrical polarimeter (transfers degree of light polarization into an electrical signal)

SUMMARY

Drift-Diffusion eqs. with magnetic field perpendicular to 110 and time varying spin-injection

Spin Currents 2009

σ+(t)

B

Similar to steady state B=0 case, solve above equations with appropriate boundary conditions: resonant behavior around ωL and small shift of oscillation period

Jing Wang, Rundong Li, SC Zhang, et al

Semiclassical Monte Carlo of SIHENumerical solution of Boltzmann equation

Spin-independent scattering:

Spin-dependent scattering:

•phonons,•remote impurities,•interface roughness, etc.

•side-jump, skew scattering.

AHE

•Realistic system sizes (μm).•Less computationally intensive than other methods (e.g. NEGF).

Spin Currents 2009

Single Particle Monte Carlo

Spin Currents 2009

Spin-Dependent Semiclassical Monte CarloTemperature effects, disorder, nonlinear effects, transient regimes.Transparent inclusion of relevant microscopic mechanisms affecting spin transport (impurities, phonons, AHE contributions, etc.).Less computationally intensive than other methods(NEGF).Realistic size devices.

Effects of B field: current set-up

Spin Currents 2009

In-Plane magnetic fieldOut-of plane magnetic field

Spin Injection Hall Effect: a new member of the spintronic Hall family and its implications in...

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