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Electric-field controlled semiconductor spintronic devicesElectric-field controlled semiconductor spintronic devices
Tomas Jungwirth Institute of Physics ASCR
Alexander Shick
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 David Williams
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
e.g. GaAs valence band As p-orbitals large SO
Beff Bex + Beff
e.g. GaMnAs valence band FM & large SO
SpintronicsSpintronics
FerromagnetismFerromagnetism Coulomb repulsion & Pauli exclusion principle
spin coupled tomomentum andcrystal fields
macroscopicmoment
kx
ky
kx
ky
AuAu
Current spintronics - two terminal AMR or GMR devices
[010]
Magnetization[110]
[100]
[110][010]
Current
1. Current driven magnetization reversal
2. Spintronic transistor
3. Electric-field induced spin-polarization in non-magnetic systems
Coulomb blockade AMRspintronic SETin thin-film GaMnAs
Spin Hall effect inducededge spin polarizationin GaAs 2DHG
Electrical control of spintronic devicesElectrical control of spintronic devices
Parkin, US Patent (2004)
Magnetic race track memory
Yamanouchi et al., Nature (2004)
2 orders of magnitude lower criticalcurrents in dilute moment (Ga,Mn)As than in conventional metal FMsSinova, Jungwirth et al., PRB (2004)
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
Spin Hall effect
Spin-orbit only & electric fields only
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05
Detection through circularlypolarized electroluminescence
y
zx
applied electricalcurrent
induced transversespin accummulationspin (magnetization)
component
Testing the co-planar spin LED only first
p-n junction current only (no SHE driving current)
p -AlG a As
i-G a As
n- -d o p e d AlG a As
e tc he d
2DHG2DHG
2DEG2DEG
0
-10
-20
10
20
Cir
c. p
olar
izat
ion
[%] EL EL
peak
Bz=0• Can detect spin polarization due to Zeemen effect
• Zero perp-to-plane component of polarization at Bz=0 and Ip=0
0
-5
-10
5
10
Cir
c. p
olar
izat
ion
[%]
• In-plane HH spin-splitting due to SO-coupling
• Non-zero in-plane component of EL polarization at Bx=0 and Ip=0
-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
%
n
n
py
xz
LED 1
LED 2
10m channel
SHE experimentsSHE experiments
- show the SHE symmetries
- edge polarizations can be separated over large distances with no significant effect on the magnitude
1.5m channel
y
zx
applied electricalcurrent
induced transversespin accummulationspin (magnetization)
component
=0
Murakami et al. '03, Sinova et al.'04, Nomura et al. '05, ...
effSO BsH
p)V(cm2
1B
22eff
y
x
Ex
Theory: 8% over 10nm accum. lengthfor the GaAs 2DHG
Consistent with experimental 1-2% polarization over detection length of ~100nm
y [kF-1]
0 10 20 30 40 50
j yz (y)
/Ex
Sz (
y)/E
x
SSzzedgeedge L Lsoso ~ j ~ jzz
bulkbulk t tsoso
Spin injection from SHE GaAs channel Electrical measurement of SHE in Al
Valenzuela, Tinkham '06Kato et al. '04, Sih et al. '06
skewscattering
=0
Other SHE experiments:
100's of theory papers: transport with SO-coupling
intrinsic vs. extrinsic
Microscopic origin
Source Drain
GateVG
VDQ
Q
0
2
D'
D'
C2
QUC/QV&)Q(VdQU
TkC2
eB
2
Coulomb blockadeCoulomb blockade
• VVgg = 0 = 0
• VVgg 0 0
GG0
20 VCQ&
C2
)QQ(U
Q=ne - Q=ne - discretediscreteQQ00=C=CggVVgg - continuous - continuous
QQ00=-ne=-ne blocked blocked
QQ00=-(n+1/2)e=-(n+1/2)e open open
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
Wafer 1
0 -50 -100 -150-2
-1
0
1
2
Wafer 2
Int
[a.u.]
E [eV]
E [
eV]
0
2
4
6
8
10
1.48 1.49 1.50 1.51 1.520
2
4
6
8
10
p-AlGaAs
n-AlGaAs
GaAs/AlGaAs superlatticeGaAs substrate
etched
2DEG2DHG
i-GaAs
y
z GaAsp-AlGaAs
n-AlGaAs
GaAs/AlGaAs superlatticeGaAs substrate
etched
2DEG2DHG
i-GaAs
y
z GaAs
z [nm]
I
X
I
X
A
A
A
A
B
B
B
B
C
C
PLEL
p-AlGaAs
GaAs
Sub GaAs gap spectra analysis: PL vs EL
X : bulk GaAs excitons
I : recombinationwith impurity states
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:
Pauli exclusion principle & Coulomb repulsionPauli exclusion principle & Coulomb repulsion FerromagnetismFerromagnetism
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
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
Source Drain
GateVG
VDQ
Q
0
2
D'
D'
C2
QUC/QV&)Q(VdQU
TkC2
eB
2
Coulomb blockadeCoulomb blockade
• VVgg = 0 = 0
• VVgg 0 0
GG0
20 VCQ&
C2
)QQ(U
Q=ne - Q=ne - discretediscreteQQ00=C=CggVVgg - continuous - continuous
QQ00=-ne=-ne blocked blocked
QQ00=-(n+1/2)e=-(n+1/2)e open open
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 anisotropic magnetoresistanceCoulomb blockade anisotropic magnetoresistance
Band structure (group velocities, scattering rates, chemical potentialchemical potential) depend on M
Spin-orbit couplingSpin-orbit coupling
If lead and dot differentIf lead and dot different (different carrier concentrations in our (Ga,Mn)As SET)
Q
0
DL'
D' )M()M()M(&
e
)M(Q)Q(VdQU
GMMGG0
20
C
C
e
)M(V&)]M(VV[CQ&
C2
)QQ(U
electric && magneticmagnetic
control of Coulomb blockade oscillations
Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint
• CBAMR if change of |CBAMR if change of |((MM)| ~ )| ~ ee22//22CC
• In our (Ga,Mn)As ~ meV (~ 10 Kelvin)In our (Ga,Mn)As ~ meV (~ 10 Kelvin)
• 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
Ordinary Hall effectOrdinary Hall effect
Detected by measuring transverse voltage
Spin Hall effectSpin Hall effect
Spin-orbit coupling “force” deflects like-spinlike-spin particles
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
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
1.5 mchannel
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
Spin-orbit coupling “force” deflects like-spinlike-spin particles
I
_ FSO
FSO
_ __
majority
minority
VInMnAs
(r)Vkcm
sH imp22
2
SO
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;
spin and magnetization generation and detection
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 FM & large SO
SpintronicsSpintronics
FerromagnetismFerromagnetism Coulomb repulsion & Pauli exclusion principle