spintronics: how spin can act on charge carriers and vice versa
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Spintronics: How spin can act on charge carriers and vice versa. Tom as Jungwirth. University of Nottingham. Institute of Physics Prague. Two paradigms for spintronics . “Mott“ non-relativistic two-spin-channel model of ferromagnets. I. I. Mott, 1936. - PowerPoint PPT PresentationTRANSCRIPT
Spintronics: How spin can act on charge carriers and vice versa
Tomas Jungwirth
University of Nottingham
Institute of Physics Prague
“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
SHE & STT switching SOT 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 ‘11
Ohmic “Dirac“ device: AMR
Magnetization-orientation-dependent scattering
Kelvin, 1857
Spin-orbit coupling
Spin-orbit coupling
Extraordinary magnetoresistance: AMR, AHE, SHE, SOT.....
B
V
I
_+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ FL
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
_ FSO__
Vanomalous Hall effect 1881
anisotropic magnetoresistance
M
Lord Kelvin 1857
)(21
jiijsAMR
)(21
jiijAAHE
)()( MM jiij
)()2( ,,0 jkn
iknd
d
njiji EgvkdeEj
Linear response: g linear in Ej
nknknknknd
d
kn
knkn
knkn ffWkdE
EfvEe
t
f
dt
df)(
)2(
)(,,,,,
,
,0
,0,,
)( ,0,, knknkn Effg
Classical Boltzmann equation
Non-equilibrium distribution function
Steady-state current in linear response to applied electric field
k
E kn
,
tk
Steady-state solution for elastic (impurity) scattering
Constant quasi-particle relaxation time solution
Steady-state solution for elastic (impurity) scattering
g(i,k)=
if
Transport relaxation time solution: back-scattering dominates
Steady-state solution for elastic (impurity) scattering
g(i,k)=
is isotropic: depends on | - ’| if
No relaxation time solution
Steady-state solution for elastic (impurity) scattering
is anisotropic: depends on k, k’ if
AMR in Rashba 2D system
Rashba Hamiltonian Eigenspinors
)(21
jiijsAMR
anisotropic
AMR in Rashba 2D system
isotropic
.)( constererd rkirki
QM: 1st order Born approximation
)(1 rV
)(rMV xx
M
Heuristic picture from back-scattering matrix elements
Rashba SOI
current
Back-scattering high resistivity
AMR in Rashba 2D system
M
M
)(rMV xx )(rMV yy
Rashba SOI
No back-scattering low resistivity
Mott, N. F. Proc. R. Soc. Lond. A 1929 Dyakonov and Perel 1971
Spin 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
jc
Anomalous Hall effect in FMs 1881
Polarimetry of electrons in FMs
Kato, Awschalom, et al., Science‘04Wunderlich, Kaestner, Sinova, TJ, PRL‘05
jc js
Hirsch PRL‘99
Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect
jc js
Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect
Hirsch PNAS‘05
- index
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’03Proposed detection by polarized electroluminescence
Sinova, TJ, MacDonald, et al. PRL’04Proposed detection by magneto-optical Kerr effect
Intrinsic anoumalous Hall effect in (Ga,Mn)As
Magneto-optical Kerr microscopy Edge polarized electro-luminescence
Extrinsic SHE Kato, Awschalom, et al., Science‘04
Intrinsic SHE Wunderlich, Kaestner, Sinova, TJ, PRL‘05
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‘11
AHE and SHE
)(21
jiijAAHE
AHE and SHE
Skew scattering SHE
Mott (skew) scattering SHE
jiijll )2('
jiija
ll )3(' SHE
AMR
Skew scattering AHE (SHE)
)3('a
ll : not constant, not isotropic, not even symmetric no relaxation time solution
Approximation:
Skew scattering AHE (SHE)
Spin orbit torque
M
Ie
Field-like SOT
Compare with AMR or skew-scattering SHE
)()2( ,,0 jkn
iknd
d
ni Egvkdej
)()2( ,,0 jkn
iknd
d
ni Egkds
s
E=Ex x
Field-like SOT
s
E=Ex x
isotropic
(r)
.)( constererd rkirki
)()2( ,,0 jkn
iknd
d
ni Egkds
Field-like SOT
isotropic
(r)
.)( constererd rkirki
g(i,k)=
)()2( ,,0 jkn
iknd
d
ni Egkds
Field-like SOT
s
E=Ex x
sMJdtMd ex
yEmes xtr ˆ21
3
MJH exex
Rex HH
Intrinsic spin Hall effect in PMs
FM (Ga,Mn)As Non-magnetic GaAs
TJ, Niu, MacDonald, PRL’02 Murakami, Nagaosa, & S.-C. Zhang, Science’03Sinova, TJ, MacDonald, et al. PRL’04
Intrinsic anoumalous Hall effect in FMs
Werake et al., PRL‘11Wunderlich, Kaestner, Sinova, TJ, PRL‘05
Boltzmann theory : non-equilibrium distribution function and equilibrium states
Linear response I.
pAmce
mpA
cep
mˆ
2ˆ
)ˆ(21 2
2
ccevEietU ti .ˆ)(ˆ
ti
ll
ti
ll
til
ll eelvElli
eelt
''
|ˆ|''||)(|
mp
mpr
iHr
iv
ˆ]
2ˆ
,ˆ[1],ˆ[1ˆ2
)ˆ(2ˆ 2
rVm
pH tA
ceE ti
1 tie
iEcA
Perturbation theory: equilibrium distribution function and non-equilibrium states
Linear response II.
tA
ceE ti
1
)]ˆ(ˆ
[2ˆ
)]ˆ(ˆ[)ˆ(21 2
2 zmpA
ce
mpA
cepzA
cep
m
ti
ll
ti
ll
til
ll eelvElli
eelt
''
|ˆ|''||)(|
)ˆ(]ˆˆ[2ˆ 2
rVpzm
pH SO
)ˆ(ˆ
]]ˆˆ[2ˆ
(,ˆ[1],ˆ[1ˆ2
zmppz
mpr
iHr
iv
ccevEietU ti .ˆ)(ˆ
tieiEcA
Perturbation theory: equilibrium distribution function and non-equilibrium states
Linear response II.
)()(|ˆ|)( 0 llzyll
zy ftjtJ
ti
ll
ti
ll
til
ll eelvElli
eelt
''
|ˆ|''||)(|
Perturbation theory: equilibrium distribution function and non-equilibrium states
Intrinsic SHE (AHE)
xE
zyj
Linear response II.
0 0
pz
pxpy
pz
pxpy
E=Ex x
0, yeffB tEpB xxyeff ~~, xz Es ~
xz Es ~
00
)(1
2
2
dtds
dtsd
Bsdt
ds
zy
eqeffz
y
Heuristic picture: Bloch equations
Field-like SOT
Compare with AMR or skew-scattering SHE
)()2( ,,0 jkn
iknd
d
ni Egvkdej
)()2( ,,0 jkn
iknd
d
ni Egkds
s
E=Ex x
Intrinsic antidamping SOT from linear response II.
Compare with intrinsic SHE
0 0
0 0
pz
pxpy
pz
pxpy
pz
pxpy
pz
pxpy
Intrinsic SHE: transverse spin current
Intrinsic SOT: spin polarization
Hex=0
Hex >> HR tEpB xxyeff ~~,
tEpB xxyeff ~~, xz Es ~
xz Es ~
xz Es ~
xz Es ~
pz
pxpy
pz
Intrinsic SHE: transverse spin current
Intrinsic SOT: spin polarization
tEpB xxyeff ~~, xz Es ~
xz Es ~
pxpy
tEpB xxyeff ~~,
xz Es ~
xz Es ~
Mxsd
z eEMJ
ss cos2 22
pxpz eEp
ss
sin
2 22
2
,
dtdB yeff /,
2)( equileffB
dtdB yeff /,
2)( equileffB
pz
pxpypxpy
tEpB xxyeff ~~, xM ˆ||
pz
pxpypxpy
tEpB xxyeff ~~,
)]ˆ([~ MzEMsMJdtMd ex
Intrinsic SOT is antidamping-like
yM ˆ||
0zs
0zs
SHE & STT switching SOT 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