spin-injection hall effectpeople.physics.tamu.edu/sinova/talks/spie_august_2010.pdf · spie...

Research fueled by:

JAIRO SINOVATexas A&M University

Institute of Physics ASCR

Hitachi CambridgeJörg Wunderlich, A. Irvine, et al

Institute of Physics ASCRTomas Jungwirth, Vít Novák, et al

Spin-injection Hall Effect:a new paradigm in using spin-orbit coupling to

create a spin FET with pure spin-currents

University of UtrechtUtrecht, January 8th 2010SPIE conference

Spintronics IIIAugust 1st 2010Sand Diego, CA

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

I. Technology motivation

II. Spin injection Hall effect•Making the device•Basic observation; analogy to AHE•The effective Hamiltonian•Spin-charge Dynamics

III. iSHE FET•Gating action of iSHE•iSHE AND-gate with pure spin current

Spin-injection Hall Effect:a new paradigm in using spin-orbit coupling to

create a spin FET with pure spin-currents

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

Circuit heat generation is one key limiting factor for scaling device speed

3

Industry has been successful in doubling of transistor numbers on a chip approximately every 18 months (Moore’s law). Although expected to continue for several decades several major challenges will need to be faced.

The need for basic research in technology development


International Technology Roadmap for Semiconductors

Basic Research Inc.

1D systems

Single electron systems (FETs)

Spin dependent physics

Ferromagnetic transport

Molecular systems

New materials

Strongly correlated

systems

Nanoelectronics

The need for basic research in technology development


Spin-orbit coupling interaction

5

(one of the few echoes of relativistic physics in the solid state)

HSO = −µB · Beff

This gives an effective interaction with the electron’s magnetic moment

Consequences•Effective quantization axis of the spin depends on the momentum of the electron. Band structure (group velocities, scattering rates, etc.) mixed strongly in multi-band systems

•If treated as scattering the electron gets asymmetrically scattered to the left or to the right depending on its “spin”

Classical explanation (in reality it is quantum mechanics + relativity )

E = −1e∇V (r)• “Impurity” potential V(r) Produces

an electric field

∇V

Beff

ps

Beff = − kcm

× EIn the rest frame of an electronthe electric field generates and effective magnetic field

• Motion of an electron


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 (Dyakonov-Perel mechanism)

Towards a realistic spin-based non-magnetic FET device

Beff = − kcm

× E

E


Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism).

New paradigm using SO coupling: SO not so bad for dephasing

Beff = − kcm

× E

E

1) Can we use SO coupling to manipulate spin AND increase spin-coherence?

2) Can we detect the spin in a non-destructive way electrically?

3) Can this effect be exploited to create a realistic spin-FET?

Use the persistent spin-Helix state and control of SO coupling strength(Bernevig et al 06, Weber et al 07, Wünderlich et al 09)

Use AHE to measure injected current polarization at the nano-scale electrically (Wünderlich, et al 09, 04)

YES (Wünderlich, Irvin, JS, Jungwirth et al 2010)

Vd

VH

2DHG

2DEG

Vs

22

Device schematic – Hall measurement


2DHG

2DEG

e

h

e eee

e

hhh

h h

Vs

Vd

VH

Spin-injection Hall effect device schematics


Spin-injection Hall device measurements

10

trans. signal

σoσ+σ- σo

VL


Spin-injection Hall device measurements

11

trans. signal

σoσ+σ- σo

VL

SIHE ↔ Anomalous Hall

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

H2DEG =2

k2

2m+ α(kyσx − kxσy) + β(kxσx − kyσy) + λ

∗σ × (k ×∇Vdis(r))

λ∗ =P 2

3

1

E2g

− 1(Eg + ∆so)2

≈ 5.3A

2for GaAs β = −Bk2

z B = 10 eV A3 α = λ∗Ez


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

a 2DEG is well described by the effective Hamiltonian:

Something interesting occurs when

H2DEG ≈2

k2

2m+ α(ky − kx)(σx + σy)

• spin along the [110] direction is conserved• long lived precessing spin wave for spin perpendicular to [110]

E↓(k) = E↑(k + Q) Q =4mα

2

The nesting property of the Fermi surface:

Bernevig et al PRL 06, Weber et al. PRL 07

Schliemann et al PRL 04

H2DEG =2

k2

2m+ α(kyσx − kxσy) + β(kxσx − kyσy)


Effects of Rashba and Dresselhaus SO couplingα = -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]_


Persistent state spin helix verified by pump-probe experiments

Similar wafer parameters to ours

Sz/x−(x[110]) = S0z/x− exp[qx[110]]

L1/2 = 2m|α ± β|/2|q| =L2

1L22 + L4

2

1/4and θ =

12

arctan

2L2

1L22 − L4

1/4

L22 − L2

1/2


Spatial variation scale consistent with the one observed in SIHE

Spin-helix state when α ≠ β

Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

ρxy = − σxy

σ2xx + σ2

xy

≈ −σxy

σ2xx

≈ −σxyρ2xx ≈ −Aρxx − Bρ2

xx


Simple electrical measurement of out of plane magnetization

InMnAs

17

Spin dependent “force” deflects like-spin particles

ρH=R0B +4π RsM

Understanding AHE in SIHE: AHE basics

I

_ FSO

FSO

_ __majority

minority

V

σAH

xy ≈ B + Aσxx


Cartoon of the mechanisms contributing to AHE σAH

xy ≈ B + Aσxx

independent of impurity density

xc =∂ε(k)∂k

+e

E × Ω

Ωz(k, n) = 2Im

∂

∂ynk

∂

∂xnk

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

SO coupled quasiparticles

Intrinsic deflection B

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 scatteringVimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ)

B

Skew scattering

Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering.

~σ~1/niVimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ) A


Contributions understood in simple metallic 2D models

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Semi-classical approach:Gauge invariant formulation

Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07

Kubo microscopic approach:in agreement with semiclassical

Borunda, Sinova, et al PRL 07, Nunner, JS, et al PRB 08

Non-Equilibrium Green’s Function (NEGF) microscopic approach

Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08

σAH

xy ≈ B + Aσxx


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)ii)Bloch electrons interacting with S.O. part of the disorder

Lower bound estimate of skew scatt. contribution

AHE contribution to Spin-injection Hall effect

H2DEG =2

k2

2m+ α(kyσx − kxσy) + β(kxσx − kyσy) + λ

∗σ × (k ×∇Vdis(r))

Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09


Local spin-polarization → calculation of AHE signal Weak SO coupling regime → extrinsic skew-scattering term is dominant

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Lower bound estimate

Spin-injection Hall effect: theoretical expectations


22

SiHE: continuous shift of spin injection

VH2I

VbVH1

σ+σ-σ+σ- σ+

σ-

R[Ω

]

I ph[n

A]

Spin polarized charge current


iSHE with spin-helix state

23

B

spin polarizedcharge current

pure spin diffusive current:no particle current, no Joule heating

generalized Boltzmann MC simulation


Spin Hall Transistor

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Manipulation2µm long gate: reverse biased pn-junction

Spin injectorreverse biased pn-junction+ light spotof 2µm diameter

DetectionHall crosses 1 2


iSHE transistor: GATING

Channel closed

Channel opened

Gating action of iSHE

Spin polarized charge current

Pure spin diffusive current


2 Detectors and 1 Gate

σ-


2 Detectors and 2 Gates

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σ-


SiHE AND spin logic gatecharge currentpure spin current:

no particle current


Summary of spin-injection Hall effect

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• Basic studies of spin-charge dynamics and Hall effect in non-magnetic systems with SO coupling • Spin-photovoltaic cell: solid state polarimeter on a semiconductor chip requiring no magnetic elements, external magnetic field, or bias

• SIHE-FET with pure spin currents in the active region

•SiHE-AND gate


Next step ....

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Electrical injec,on through barrier from Fe

Electrical detec,on by SIHE Scho:ky barrier: Kamil Olejnik (HCL, IOP Prague)MgO barrier: Sankara Rutala (CNRS, Thales, UPSUD, Orsay, France)


Allan MacDonald U of Texas

Tomas JungwirthTexas A&M U.

Inst. of Phys. ASCRU. of Nottingham

Joerg WunderlichCambridge-Hitachi

Laurens MolenkampWürzburg

Xiong-Jun LiuTexas A&M U.

Mario BorundaTexas A&M Univ.

Harvard Univ.

Nikolai SinitsynTexas A&M U.

U. of TexasLANL

Alexey KovalevTexas A&M U.

UCLA

Liviu ZarboTexas A&M Univ.

Xin LiuTexas A&M U.

Ewelina Hankiewicz(Texas A&M Univ.)

Würzburg University

Principal Collaborators

Gerrit BauerTU Delft

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Bryan GallagherU. of Nottingham

and many others


The Spin-Charge Drift-Diffusion Transport EquationsFor 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)

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spin-injection hall effectpeople.physics.tamu.edu/sinova/talks/spie_august_2010.pdf · spie...

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