Spin-orbit coupling based spintronics: Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in Extraordinary magnetoresistance studies in semiconductors semiconductors Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmond Andrew Rushforth, Devin Giddings Hitachi Cambridge University of Texas and Texas A&M Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova, et al. David Williams, et a. Institute of Physics ASCR ander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, t Novák, Miroslav Cukr, Kamil Olejník, et al.
Transcript
Spin-orbit coupling based spintronics: Extraordinary Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductorsmagnetoresistance studies in semiconductors
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds,
Andrew Rushforth, Devin Giddings et al.
Hitachi Cambridge University of Texas and Texas A&M
Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova, et al. David Williams, et a.
Institute of Physics ASCR
Alexander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen,
Vít Novák, Miroslav Cukr, Kamil Olejník, et al.
Extraordinary magnetoresistance
B
V
I
_
+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ FL
Ordinary magnetoresistance:
response to external magnetic field via classical Lorentz force
Extraordinary magnetoresistance:
response to internal spin-polarization via quantum-relativistic spin-orbit coupling
e.g. ordinary (quantum) Hall effect
anisotropic magnetoresistance
V
BBeffeff
pss
Discovered in the 19th century in TM ferromagnets– classical unsettled CMP field- now accessible in semiconductors
effSO BsH
p)V(cm2
1B
22eff
I
_ FSO__
V
M+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _
anomalous Hall effect
Conventional ferromagnetic metals
itinerant 4s:no exch.-split
no SO
localized 3d:exch. split
SO coupled
ss sd
sdss
Mott’s model of transportAb initio Kubo (CPA) formula forAMR and AHE in FeNi alloys
- carriers with both strong carriers with both strong SO coupling and SO coupling and exchange splittingexchange splitting
- simpler band structure
- SO topology of holes dominated by As p-orbitals as in hosts (Mn on Ga sublattice)
favorable for exploring physical origins
Origin of R[M I]> R[M || I] non-crystalline AMR in GaMnAs
~(k . s)2 ~Mx . sx
SO-coupling – spherical model FM exchange spiitting
hot spots for scattering for states moving M R[M I]> R[M || I] (opposite to most metal FMs)
Boltzmann eq. in relax. time approximation 1st order Born approximation
4-band spherical Kohn-Luttinger model
ky
kxk
x
kx
k y
k y
M
M
1/k (M)
M
[110]
current
))
theory
exp.
spherical model: non-crystalline AMR only
full 6-band Hamiltonian:non-crystalline andcrystalline AMR
In metallic GaMnAs:
also magnitudes and relative strengths of non-crystalline and crystalline AMR terms consistent with experiment
Mcurrent
)
Rushforth et al. ‘07
Family of new AMR effects: TAMR – anisotropic TDOS
TAMR – discovered in GaMnAs
AuGaMnAs
AuAlOx Au
predicted and observed in metals
[100]
[010]
[100]
[010]
[100]
[010]
Gould, et al., PRL'04, Brey et al. APL’04,Ruster et al.PRL’05, Giraud et al. APL’05, Saito et al. PRB’05,
[010]
M[110]
[100]
[110][010]
Shick et al.PRB'06, Bolotin et al. PRL'06, Viret et al. EJP’06, Moser et al. 06, Grigorenko et al. ‘06
GMMGG0
20
C
C
e
)M(V&)]M(VV[CQ&
C2
)QQ(U
electric && magneticmagnetic
control of Coulomb blockade oscillations
Coulomb blockade AMR – anisotropic chemical potential
Q
0
'D
'
e
)M(Q)Q(VdQU
Wunderlich et al. ‘06
Predicted stronger CBAMR for metals
Source Drain
GateVG
VDQ
[010]
M[110]
[100]
[110][010]
Karplus&Luttinger intrinsic AHE mechanism revived in GaMnAs
Experiment AH 1000 (cm)-1
TheroyAH 750 (cm)-1
AHE mechanisms
intrinsic AHE in pure Fe: ab initio Kubo eq.
I_ FSO
FSO
_ __
VJungwirth et al. PRL ‘02,APL ’03, Edmonds et al. APL ’03, Chun et al. PRL ‘07
Yao et al. PRL ‘04
Karplus&Luttinger PR ‘54
Co [Kotzler&Gil PRB ‘05]
SrRuO3 and pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 01,Taguchi et al., Science 01, Fang et al Science 03, Shindou and Nagaosa, PRL 01]
Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04]
- AHE SHE
I
_ FSO
FSO
_ __
V=0
non-magnetic
- All Semiconductor systems including 2D with “model” SO
- Optical methods: polarized EL
Cubic (2DHG) and linear (2DEG) in k Rashba model
Kato Sci ’04, Wunderlich et al PRL’05, PRB’06, Sih et al. NatPhys ‘05
Solvable analytically
p -AlG a As
i-G a As
n- -d o p e d AlG a As
e tc he d
2DHG2DHG
2DEG2DEG
I
_ FSO
FSO
_ __
V
Exploring SHE & AHE fenomenologies in 2D non-magnetic SC
p -AlG a As
i-G a As
n- -d o p e d AlG a As
e tc he d
2DHG2DHG
2DEG2DEG
p -AlG a As
i-G a As
n- -d o p e d AlG a As
e tc he d
2DEG2DEG
2DHG2DHG
+
-
Gate
zx
+
-
2DHG 2DEG
Gate
SHE AHE
2D “model” systems ideal to explore intrinsic vs. extrinsic AHE/SHE
semicalssical Boltzmann eq.
intrinsic skew scattering side jump
group velocity distribution function
quantum Kubo formula
int. skew side jumpsc.
Extrinsic skew scattering term: - absent in 2DEG for two-band occupation
- absent in 2DHG for any band occupation
Borunda et al. ‘07
Optical means of exploring EMR fundamentals on systems with simpleyet topologically distinct SO-bands
SO-coupling and electric field controlled spintronics:
1. Coulomb blockade AMR
Spintronic transistor - magnetoresistance controlled by gate voltage
Strong dependenceon field anglehints to AMR origin
Huge hysteretic low-field MR
Sign & magnitudetunable by smallgate valtages
Wunderlich, Jungwirth, Kaestner et al., cond-mat/0602608
Bptp
B90
B0
I
AMR nature of the effect
normal AMR Coulomb blockade AMR
Single electron transistor
Narrow channel SETdots due to disorder potential fluctuations
(similar to non-magnetic narrow-channel GaAs or Si SETs)
CB oscillationslow Vsd blockeddue to SE charging
magnetization angle
CB oscillation shifts by magnetication rotations
At fixed Vg peak valleyor valley peak
MR comparable to CBnegative or positive MR(Vg)
GMMGG0
20
C
C
e
)M(V&)]M(VV[CQ&
C2
)QQ(U
electric && magneticmagnetic
control of Coulomb blockade oscillations
n-1 n n+1 n+2n-1 n n+1 n+2
EC
QQindind = = nnee
QQindind = (= (n+1/2)n+1/2)eeQ0
Q0
e2/2C
Coulomb blockade AMR
Q
0
'D
'
e
)M(Q)Q(VdQU
[010]
M[110]
[100]
[110][010]
SO-coupling (M)
• CBAMR if change of CBAMR if change of ||((MM)| ~ )| ~ ee22//22CC ~ 10Kelvin from exp. consistent
• In room-T ferromagnet change of |In room-T ferromagnet change of |((MM)|)|~100Kelvin~100Kelvin
• CBAMR works with dot both ferro CBAMR works with dot both ferro or paramegneticor paramegnetic
Different doping expected in leads an dots in narrow channel GaMnAs SETs
Calculated doping dependence of(M1)-(M2)
• Huge, hysteretic, low-field MR tunable by small gate voltage changes • Combines electrical transistor action with permanent storage
• Non-hysteretic MR and large B - chemical potential shifts due to Zeeman effect Ono et al. '97, Deshmukh et al. '02
• Small MR - subtle effects of spin-coherent and resonant tunneling through quantum dots Ono et al. '97, Sahoo '05
CBAMR SET
Other FERRO SETs
I
_ FSO
FSO
_ __
V=0
non-magnetic
Spin-current generation in non-magnetic systems Spin-current generation in non-magnetic systems without applying external magnetic fieldswithout applying external magnetic fields
Spin accumulation without charge accumulationexcludes simple electrical detection
BB ( (A,CA,C): ): 3D electron – 3D electron – 2D hole 2D hole recombinationrecombination
Bias dependent emission wavelength for 3D electron – 2D hole Bias dependent emission wavelength for 3D electron – 2D hole recombination recombination [A. Y. Silov et al., APL 85, 5929 (2004)][A. Y. Silov et al., APL 85, 5929 (2004)]
++--
NO perp.-to-plane component of polarization at B=0NO perp.-to-plane component of polarization at B=0
BB≠0 behavior consistent with SO-split HH subband≠0 behavior consistent with SO-split HH subband
In-plane
detection angle
Perp.-to plane
detection angle
Circularly polarized EL
Light polarization due to recombination with SOLight polarization due to recombination with SO--split split holehole--subbandsubband in a in a pp--nn LED under forward biasLED under forward bias
spin operators of holes: j=3s
-0.2 0.0 0.2-0.50
-0.25
0.00
0.25
0.50
<sx>HH+
<sx>HH-
<sz>HH--
<<sszz>>HHHH++
<S
>
ky [nm-1]
spin-polarization of HH+ and HH- subbands
-0.2 0.0 0.2-0.50
-0.25
0.00
0.25
0.50
-0.2 0.0 0.2-0.50
-0.25
0.00
0.25
0.50
<sx>HH+
<sx>HH-
<sz>HH--
<<sszz>>HHHH++
<S
>
ky [nm-1]
spin-polarization of HH+ and HH- subbands
inin--planeplane polarization
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
ky [nm-1]
3D electron-2D hole Recombination
-0.2 0.0 0,2
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
ky [nm-1]
3D electron-2D hole Recombination
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
ky [nm-1]
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
0
20
E [
meV
]
a
HH+
HH-LH
- +
-20
0
20
ky [nm-1]
3D electron-2D hole Recombination
-0.2 0.0 0,2
s=1/2 electrons to j=3/2 holes plus selection rules
circular polarization of emitted light
Microscopic band-structure calculations of the 2DHG:
total wf antisymmetric = orbital wf antisymmetric * spin wf symmetric (aligned)
FEROFERO MAGMAG NETNET
ee--
• RobustRobust (can be as strong as bonding in solids)(can be as strong as bonding in solids)
• Strong coupling to magnetic fieldStrong coupling to magnetic field (weak fields = anisotropy fields needed (weak fields = anisotropy fields needed only to reorient macroscopic moment)only to reorient macroscopic moment)
Non-relativistic many-body1. Introduction
Spin-orbit couplingSpin-orbit coupling (Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit)
ee--
effSO BsH
p)V(cm2
1B
22eff
V
BBeffeff
pss
FM without SO-couplingGaAs valence band As p-orbitals large SO
BexBeff Bex + Beff
GaMnAs valence band tunable FM & large SO
AMRAMR (anisotropic magnetoresistance)
Band structure depends on Band structure depends on MM
Ferromagnetism: sensitivity to magnetic field
SO-coupling: anisotropies in Ohmic transport characteristics
M || <100>
M ||
<01
0>
GaMnAs
ky
kx
spinspin-valve-valve
TMR (tunneling magnetoresistance)
Based on ferromagnetism only
no (few) spin-up DOS available at EF large spin-up DOS available at EF
Gould, Ruster, Jungwirth, et al., PRL '04, '05
[100]
[010]
[100]
[010]
[100]
[010]
(Ga,Mn)As(Ga,Mn)As
AuAu
- no exchange-bias needed
- spin-valve with ritcher phenomenology than TMR
Tunneling AMR: anisotropic tunneling DOS due to SO-coupling
MRAMMRAM
[010]
Magnetization[110]
[100]
[110][010]
Current
Magnetisation in plane
y
x
jt
z
Wavevector dependent tunnelling probabilityT (ky, kz) in GaMnAs Red high T; blue low T.
xz
y
jt
constriction
Magnetization perp. to plane
Magnetization in-plane
Giddings, Khalid, Jungwirth, Wunderlich et al., PRL '05
thin film
TAMR in metals
Bolotin,Kemmeth, Ralph, cond-mat/0602251
Shick, Maca, Masek, Jungwirth, PRB '06
NiFe TAMR TMR
TMR ~TAMR >>AMR
ab-initio calculations
Viret et al., cond-mat/0602298 Fe, Co break junctions TAMR >TMR
EXPERIMENT
Spin Hall Effect
2DHG
2DEG VT
VD
Single Electron TransistorSingle Electron Transistor
• In room-T ferromagnet change of |In room-T ferromagnet change of |((MM)|~100K )|~100K
• Room-T conventional SET (e2/2C >300K) possible
-0.08 0.00 0.080
20
RC [
M
]
-BC1 -BC2BC2
BC1
B [ T ]
POWER“OFF”
Electrical operation mode
“READ”:measure RC
at VG = VG1
“1” (M1)
“0” (M0)
“WRITE”permanently
POWER “ON”
POWER“OFF”
Electrical operation mode
Electrical operation mode
“READ”:measure RC
at VG = VG1
“1” (M1)
“0” (M0)
“WRITE”permanently
POWER “ON”
M1 -M1
M0 M0
VG = VG1 = 1.04V
1.00 1.01 1.02 1.03 1.046
8
10
12
14
16
18
20
VG0VG1
RC [
M
]
VG [ V ]
electric modeelectric mode
magneticmagneticnonnon--volatilevolatile
modemode
0.6 0.8 1.00
25
50
RC [
M
]
VG [ V ]
““00””
““11””
MM00(a)
(b)
(c)
MM11
Magnetic non-volatile mode
VG = VG1 : M0 (“0”) M1 (“1”)
[[InverseInverse:: VG = VG0 : M0 (“1”) M1 (“0”)]
M0 : B B0 0 BC1 < B0 < BC2
M1 : B B1 0 B1 < -BC2
Electric modeM = M1 : VG0 (“0”) VG1 (“1”)
[[InverseInverse:: M = M0 : VG0 (“1”) VG1 (“0”)]
(d)
Magnetic non-volatile mode
VG = VG1 : M0 (“0”) M1 (“1”)
[[InverseInverse:: VG = VG0 : M0 (“1”) M1 (“0”)]
M0 : B B0 0 BC1 < B0 < BC2
M1 : B B1 0 B1 < -BC2
Electric modeM = M1 : VG0 (“0”) VG1 (“1”)
[[InverseInverse:: M = M0 : VG0 (“1”) VG1 (“0”)]
(d)
CBAMR CBAMR new device concepts new device concepts
Electrically generated spin polarization in normal semiconductors Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECTSPIN HALL EFFECT
B
V
I
_
+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ FL
Lorentz force deflect chargedcharged--particles towards the edge
Spin-current generation in non-magnetic systems Spin-current generation in non-magnetic systems without applying external magnetic fieldswithout applying external magnetic fields
Spin accumulation without charge accumulationexcludes simple electrical detection
Microscopic theory and some interpretationMicroscopic theory and some interpretation
- weak dependence on impurity scattering time
- SSzzedgeedge ~ j ~ jzz
bulkbulk / v / vFF
ttsoso=h/=h/soso : (intrinsic) spin-precession time
LLsoso=v=vFF t tsoso : spin-precession length
SSzzedgeedge L Lsoso ~ j ~ jzz
bulkbulk t tsoso
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05
experimentally detected
non-conserving (ambiguous)theoretical quantity
spin * velocity
-1
0
1
Pol
ariz
atio
n in
%
1.505 1.510 1.515 1.520
-1
0
1
Energy in eV
Pol
ariz
atio
n in
%
1.5m
channel
n
n
py
xz
LED1
LED2
10m channel
SHE experiment in SHE experiment in GaAs/AlGaAs 2DHGGaAs/AlGaAs 2DHG
- shows the basic SHE symmetries
- edge polarizations can be separated over large distances with no significant effect on the magnitude
- 1-2% polarization over detection length of ~100nm consistent with theory prediction (8% over 10nm accumulation length)
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05
1.5mchannel
n
n
p yxz
Conventionally generated spin polarization in non-magnetic semiconductorsConventionally generated spin polarization in non-magnetic semiconductors: spin injection from ferromagnets, circular polarized light sources,
external magnetic fields
SHESHE: small electrical currents in simple semiconductor microchips
SHE microchip, 100A
high-field lab. equipment, 100 A
Spin and Anomalous Hall effectsSpin and Anomalous Hall effects
MπR4BR s0H
Simple electrical measurement Simple electrical measurement of magnetizationof magnetization
Skew scattering off impurity potential Skew scattering off impurity potential (Extrinsic SHE/AHE)
skewscattering
lsdr
rdV
err
mc
k
mc
seBH effSO
)(1
bands from l=0 atomic orbitals weak SO(electrons in GaAs)
bands from l>0 atomic orbitals strong SO(holes in GaAs)
SO-coupling from host atoms SO-coupling from host atoms (Intrinsic SHE/AHE)
E
Intrinsic AHE approach explains many experimentsIntrinsic AHE approach explains many experiments
• (Ga,Mn)As systems [Jungwirth et al. PRL 02, APL 03]
• Fe [Yao, Kleinman, Macdonald, Sinova, Jungwirth et al PRL 04]
• Co [Kotzler and Gil PRB 05]
• Layered 2D ferromagnets such as SrRuO3 and pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 01,Taguchi et al., Science 01, Fang et al Science 03, Shindou and Nagaosa, PRL 01]
• Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04]
Experiment AH 1000 (cm)-1
TheroyAH 750 (cm)-1
Hall effects familyHall effects family
• OrdinaryOrdinary: carrier density and charge; magnetic field sensing
• QuantumQuantum: text-book example a strongly correlated many-electron system with e.g. fractionally charged quasiparticles; universal, material independent resistance
• Spin and AnomalousSpin and Anomalous: relativistic effects in solid state;
