vice versa Tom as Jungwirth University of Nottingham Institute of Physics Prague Mott nonrelativistic twospinchannel model of ferromagnets Dirac relativistic spinorbit coupling ID: 560658
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Slide1
Spintronics: How spin can act on charge carriers and vice versa
Tomas Jungwirth
University of Nottingham
Institute of Physics
PragueSlide2
“Mott“ non-relativistic two-spin-channel
model of ferromagnets“Dirac“ relativistic spin-orbit coupling
I
I
I
I
Mott, 1936
Dirac, 1928
Two paradigms for spintronics Slide3
SHE
& STT switchingSOT switching
-We see (anti)damping-like torque-SOT is field-like so we exclude it - non-relativistic STT in metals is dominated by the (anti)damping torque
-We also see (anti)damping-like torque-SOT is field-like but maybe there is some
(anti)damping-like SOT as well
Ralph, Buhrman,
et
al.
, Science
‘12
Miron et al., Nature ‘11Slide4
Ohmic “Dirac“ device: AMR
Magnetization-orientation-dependent scattering
Kelvin, 1857Slide5
Spin-orbit coupling
Slide6
Spin-orbit coupling
Slide7
Extraordinary magnetoresistance: AMR,
AHE, SHE, SOT.....B
V
I
_
+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _
F
L
Ordinary
magnetoresistance
:
response
to
external
magnetic
field
Acting
via
classical Lorentz force
Extraordinary
magnetoresistance
:
response to
internal
quantum-relativistic
spin-orbit
field
ordinary Hall effect 1879
I
_
F
SO
_
_
V
anomalous Hall effect 1881
anisotropic
magnetoresistance
M
Lord Kelvin 1857Slide8
Linear response:
g linear in Ej
Classical Boltzmann equation Non-equilibrium distribution function Steady-state current in linear response to applied electric field Slide9
Steady-state solution for elastic (impurity) scatteringSlide10
Constant quasi-particle relaxation time solution
Steady-state solution for elastic (impurity) scattering
g(i,k)=
if Slide11
Transport relaxation time solution: back-scattering dominates
Steady-state solution for elastic (impurity) scattering
g(i,
k)=
is isotropic: depends on
|
-
’
|
if Slide12
No relaxation time solution
Steady-state solution for elastic (impurity) scattering
is
an
isotropic: depends on k
,
k
’
if Slide13
AMR in
Rashba 2D systemRashba Hamiltonian
Eigenspinors Slide14
an
isotropic
AMR
in Rashba
2D system
isotropic
QM: 1st order Born approximationSlide15
Heuristic picture from back-s
cattering matrix elements
Rashba SOI
current
Back-scattering high resistivity
AMR
in
Rashba
2D
system
Rashba SOI
No back-scattering low resistivitySlide16
Mott, N. F. Proc. R. Soc.
Lond. A 1929
Dyakonov and Perel 1971Spin Hall effect in PMs
Electron spin-dependent scattering off Coulomb field of heavy atoms due to spin-orbit coupling
Polarimetry of high-energy electron beams in accelerators
Electron spin-dependent scattering off Coulomb field of dopands in a semiconductor due to spin-orbit coupling
j
c
Anomalous Hall effect in FMs
1881
Polarimetry of electrons in FMs
Kato,
Awschalom
,
et al., Science‘04
Wunderlich, Kaestner, Sinova
,
T
J, PRL‘05Slide17
j
c
js
Hirsch PRL‘99
Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effectSlide18
j
c
js
Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect
Hirsch PNAS‘05
- indexSlide19
Theoretical proposal of
intrinsic spin Hall effect
FM (Ga,Mn)As
Non-magnetic GaAs
TJ,
Niu
, MacDonald
, PRL’02
Murakami, Nagaosa, & S.-C. Zhang, Science’03
Proposed detection by polarized electroluminescence
Sinova
, TJ,
MacDonald
, et al. PRL’04
Proposed detection by magneto-optical Kerr effect
Intrinsic anoumalous Hall effect in (Ga,Mn)AsSlide20
Magneto-optical Kerr microscopy
Edge polarized electro-luminescence
Extrinsic SHE Kato,
Awschalom
, et al., Science‘04
Intrinsic SHE
Wunderlich, Kaestner, Sinova
,
T
J, PRL‘05Slide21
Optically generated spin current
Optically detected charge accummulation due to iSHE
Zhao et al., PRL‘06
fs pump-and-probe: iSHE generated before first scattering in the intrinsic GaAs
intrinsic iSHE
Werake et al., PRL‘11Slide22
AHE and SHESlide23
A
HE and SHESlide24
Skew scattering SHESlide25
Mott (skew) scattering SHE
SHE
A
MRSlide26
Skew scattering
A
HE (SHE)
: not constant, not isotropic, not even symmetric
no relaxation time solution
Approximation:Slide27
Skew scattering
AHE (SHE)Slide28
Spin orbit torque
M
I
e
Slide29
Field-like SOTCompare with AMR or skew-scattering SHE
E=
E
x
x
^Slide30
Field-like SOT
E=
E
x
x
^
isotropic
(
r
)Slide31
Field-like SOT
isotropic
(
r
)
g(i,
k)=Slide32
Field-like SOT
E=
E
x
x
^Slide33
Intrinsic spin Hall effect in PMs
FM (Ga,Mn)As
Non-magnetic GaAs
TJ,
Niu
, MacDonald
, PRL’02
Murakami, Nagaosa, & S.-C. Zhang, Science’03
Sinova
, TJ,
MacDonald
, et al. PRL’04
Intrinsic anoumalous Hall effect in FMs
Werake et al., PRL‘11
Wunderlich, Kaestner, Sinova
,
T
J, PRL‘05Slide34
Boltzmann theory : non-equilibrium distribution function
and equilibrium states
Linear response I.Slide35
Perturbation
theory: equilibrium distribution function
and non-equilibrium states
Linear response II. Slide36
Perturbation
theory: equilibrium distribution function
and non-equilibrium states
Linear response II. Slide37
Perturbation
theory: equilibrium distribution function and non-equilibrium states
Intrinsic SHE (AHE)
Linear response II.
0
0Slide38
p
z
p
x
p
y
p
z
p
x
p
y
E=
E
x
x
^
Heuristic picture: Bloch equations Slide39
Field-like SOT
Compare with AMR or skew-scattering SHE
E=
E
x
x
^Slide40
Intrinsic antidamping SOT from linear response II.
Compare with intrinsic SHE0
000Slide41
p
z
p
x
p
y
p
z
p
x
p
y
p
z
p
x
p
y
p
z
p
x
p
y
Intrinsic SHE: transverse spin current
Intrinsic SOT: spin
polarization
H
ex
=0
H
ex
>>
H
RSlide42
p
z
p
x
p
y
p
z
Intrinsic SHE: transverse spin current
Intrinsic SOT: spin
polarization
p
x
p
ySlide43
p
z
p
x
p
y
p
x
p
y
p
z
p
x
p
y
p
x
p
y
Intrinsic SOT is antidamping-like Slide44
SHE
& STT switchingSOT switching
-We see (anti)damping-like torque-SOT is field-like so we exclude it - non-relativistic STT in metals is dominated by the (anti)damping torque-We also see (anti)damping-like torque-SOT is field-like but maybe there is some (anti)damping-like SOT as well
and maybe we found it intrinsic SOT analogous to intrinsic SHE
Ralph, Buhrman,
et
al.
, Science
‘12
Miron et al., Nature ‘11