Spin Hall Effect induced by resonant scattering on impurities in

metals

Peter M LevyNew York University

In collaboration withAlbert Fert

Unite Mixte de Physique CNRS,and Universite Paris-Sud

0

0

Spin current

Spin current without charge current

Intrinsic SHE:

due to S-0 effects on the wave functions of the lattice

Extrinsic SHE:

due to S-0 terms of scattering potentials

Spin Hall Effect (SHE)

w

t = thickness

xy

DetectionFerromagnetic contact

nonmagnetic contact

Injection of spin-polarized current

V 0

S. Zhang, PRL 85, 393 (2000)

€

Velec

€

Velec +(1+ P)

2μ↑ +

(1 − P)

2μ↓

How the SHE could be used in spintronic applications:

Spintronics need currents that are spin polarized. The conventional method of obtaining a polarized current is to pass an ordinary charge current through aferromagnetic metal.

However, it is difficult to integrate ferromagnetic metals with CMOS [silicon-based]circuits that make up the active memory of computers. Therefore there is great interest in finding nonmagnetic metals or semiconductors which are capable of converting charge to spin currents. As we will see the Spin Hall Effect has this potential; this has lead to the current interest in this effect.

The origins of the SHE are the same as those that have produced the AnomalousHall Effect (AHE) which has been known for over 6-7 decades. The AHE is causedby ordinary charge currents and produces additional contributions to the ordinaryHall effect; it is caused by spin-orbit coupling effects on the band structure, defect scattering, and the expression for the electric current (anomalous velocity or side jump).

The SHE is caused by the same mechanisms but relies on the presence of a spin-polarized current.

Previous work on the SHE:

The term Spin Hall Effect was first used by Jorge Hirsch PRL 83, 1834 (1999).

The idea of a SHE was first proposed by M. I.Dyakonov and V. I. Perel, Phys. Lett. A 35, 459 (1971).

Shufeng Zhang made the first realistic calculation of the signal produced by thisEffect in metals with finite spin diffusion lengths. PRL 85, 393 (2000).

It was further studied by amongst others: J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A. H. MacDonald, PRL 92, 126603 (2004). Also, seearticles by Jairo Sinova in PRB and PRL 2004-2010; and Sinova’s Viewpoint article “Spin Hall effect goes electrical” in Physics 3, 82 (2010).

1/T

RH/R0

Introduction: Hall effect due to magnetic impurities in metals

Skew scattering

Mn impurities in Cu

No contribution to the Hall effect

Spin-polarizes the current

1981

The SHE of nonmagnetic Cu alloys

could be detected

using the spin-polarized current

induced by Mn impurities (0.01%)

Today

The SHE of nonmagnetic conductors

can be detected

by injecting a spin-polarized current

from a ferromagntic contact

€

rE =

(x ρ ±Mn + y ρ T ) my ρ xy

T

±y ρ xyT (x ρ ±

Mn + y ρ T )

r j ±

€

Vy ∝j+ − j−

j+ + j−

yρ xyT with

j+ − j−

j+ + j−

∝< SzMn >∝

H

T→

RH Vy/H 1/T

skew scat. identified by 1/T contrib. to RHscat

A. Fert and O. Jaoul, PRL 28, 303, 1972

H of skew scatt.

Side jump H c 0

Gd + Lu impuritiesNi + various impurities

R.Asomoza, AF et al, JLCM 1983

j =3/2

j =5/2

Spin-orbit split

5d states of Lu

SHE induced by resonant scattering on spin-orbit split impurity d levels

Partial wave phase shift analysis of resonant scattering (Friedel’s virtual bound state model)

E

EF

Accomodation of one 5d electron (Z5d=1 for Lu)

Skew scattering: scattering

probability to the right scattering probability to the left

H= xy/xx = constant, xx cI, xy cI

x

Re-emission to the right at

time t

Re-emission to the left at

time t+t

Side-jump y = vt of the center of mass

Scattering with side-jump: side-jump of the mass center of

the scattered electrons

H = y/ cI , xy= H xx (cI)2

H = y/

I cI

y

Re-emission probability to the right = p

Re-emission probability to the left = p(1-p)

*

*

the deflection angle H

is characteristic of the scattering asymmetry Ex j

IIxxHxyy

IHx cdtE

m

nedtj

0

2

H

x

y x

y

Ey

IIxxI

IIxx

IxxHxy

cc

cy

, as 1

2

Spin up el.

Spin up el.