Spin Hall Effect induced by resonant
scattering on impurities in
metals
Peter M Levy
New York University
In collaboration with
Albert Fert
Unite Mixte de Physique CNRS,
and Universite Paris-Sud
Spin Hall Effect (SHE)
Spin current without
charge current
  0
Spin current
  0
Intrinsic SHE:
Extrinsic SHE:
due to S-0 effects on the wave
functions of the lattice
due to S-0 terms of scattering
potentials
V 0
Ferromagnetic contact
Velec 
x

nonmagnetic contact
Detection
(1 P)
(1 P)
 

2
2
Injection of spin-polarized current
y
Velec
w
t = thickness

S. Zhang, PRL 85, 393 (2000)
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 a
ferromagnetic 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 Anomalous
Hall Effect (AHE) which has been known for over 6-7 decades. The AHE is caused
by ordinary charge currents and produces additional contributions to the ordinary
Hall 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 spinpolarized current.
Previous work on the SHE:
The idea of a SHE was first proposed by M. I.Dyakonov and V. I. Perel,
Phys. Lett. A 35, 459 (1971).
The term Spin Hall Effect was first used by Jorge Hirsch PRL 83, 1834 (1999).
Shufeng Zhang made the first realistic calculation of the signal produced by this
Effect 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, see
articles by Jairo Sinova in PRB and PRL 2004-2010; and Sinova’s Viewpoint
article “Spin Hall effect goes electrical” in Physics 3, 82 (2010).
Introduction: Hall effect due to magnetic impurities in metals
Skew scattering
RH/R0
1/T
No contribution to the Hall effect
Mn impurities in Cu
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
Nonmagnetic impurities T with large spinorbit induce SHE revealed by the Mninduced current spin polarization
Mn impurities +field polarize the
current without inducing Hall
effect by themselves
Cu + y nonmagnetic impurities T + x Mn impurities
(y 100-2000 ppm, T=Ir,Lu,Ta, Au) ( x  100 ppm)
r (x   y  ) my 
r
E
j

T
Mn
T
 y xy
(x   y  )
Mn

T
T
xy
j  j  T
j  j
H
Mn
Vy 
yxy with
 Sz   
j  j 
j  j 
T
RH  Vy/H 1/T
skew scat. identified by 1/T contrib. to RH
scat
R.Asomoza, AF et al,
JLCM 1983
Ni + various impurities
Gd + Lu impurities
Side jump H
c  0
H of skew scatt.
A. Fert and O. Jaoul,
PRL 28, 303, 1972
SHE induced by resonant scattering on spin-orbit split impurity d levels
E
Partial wave phase shift analysis of resonant scattering
(Friedel’s virtual bound state model)
Spin-orbit split
5d states of Lu
j =5/2
j =3/2
EF
Accomodation of
one 5d electron
(Z5d=1 for Lu)
Skew scattering:
scattering
probability to the right 
scattering probability to the left
Scattering with side-jump:
side-jump of the mass center of
the scattered electrons
H= xy/xx = constant, xx cI, xy  cI
H = y/  cI , xy= H xx  (cI)2
Re-emission
probability to the
left = p(1-p)
Side-jump y = vt of the
x
y
*
Ex
j
scattering asymmetry
Re-emission
to the right at
time t
 I  cI
dt ne2
 j x H 
E y dt  0   xy   H  xxI  cI
I m
H
*
H = y/
Spin
up el.
the deflection angle H
is characteristic of the
x
y
Re-emission
probability to
the right = p
Ey
center of mass
Re-emission
to the left at
time t+t
Spin
up el.
x
y

y I
 xy   H    xx  cI2

as   c I1 ,  xxI  c I
I
xx