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Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems. Tom as Jungwirth. Universit y of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds , Andrew Rushforth, et al. Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Ma š ek, - PowerPoint PPT Presentation
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Anisotropic magnetoresistance and spin-injection Halleffect in 2D spin-orbit coupled systems
Tomas Jungwirth
University of Nottingham Bryan Gallagher, Richard Campion, Kevin
Edmonds, Andrew Rushforth, et al.
Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
Institute of Physics ASCRKarel Výborný, Jan Zemen, Jan Mašek,
Vít Novák, Kamil Olejník, et al.
University of Texas Allan MaDonald, et al.
Texas A&MJairo Sinova, et al.
Extraordinary magnetoresistance: AMR, AHE
B
V
I
_
+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ FL
Ordinary magnetoresistance:response in normal metals to external magnetic field via classical Lorentz force
Extraordinary magnetoresistance:response to internal spin polarization in ferromagnets via quantum-relativistic spin-orbit coupling
ordinary Hall effect 1879 I
_ FSO__
Vanomalous Hall effect 1881
anisotropic magnetoresistance
M
Lord Kelvin 1857
Spin-orbit coupling
nucleus rest frame electron rest frame
vI QrE3
04 r
Q
30
4 r
rIB
EvEvB 200
1
c EvSS
2B
mc
egH B
SO
Lorentz transformation Thomas precession
2 2
From 1950’s microscopic model interpretations – often controversial
itinerant 4s:no exch.-split
no SO
localized 3d:exch. split
SO coupled
ss sd
sdss
AMR: Mott’s model of transport in metals
Smit 1951
AHE
(then partly forgotten till 2000’s)
Karplus&Luttinger 1954
Smit 1955
Berger 1970
From 1990’s numerics based on relativistic ab initio band strucrure & Kubo formula
Numerically successful but difficult to connect with microscopic models due to complex bands in metals Banhart&Ebert EPL‘95
Khmelevskyi ‘PRB 03
AMR
AHE
Scattering considered essential for both AMR and AHE alloys like FeNi (treated in CPA)
AMR sensors: dawn of spintronics in early 1990’s
In mid 1990’s replaced in HDD by GMR or TMR but still extensively used in e.g. automotive industry
Inductive read/write element
Magnetoresistive read element
Mn-d-like localmoments
As-p-like holes
Mn
Ga
As
From late 1990’s AMR and AHE studied in novel ferromagnetsFerromagnetic DMS GaMnAs with much simpler 3D band structure than metals
Bso
Bex + Bso
Jungwirth et al. RMP’06Dietl et al. Semicond. and Semimet. ‘08
Semiquantitative numerical description of AMR and AHE in GaMnAs
Jungwirth et al. RMP’06Dietl et al. Semicond. and Semimet. ‘08
M
[110]
current))
Spherical model: non-crystalline AMR only
Anisotropic scattering rate:non-crystalline and crystalline AMR
Mcurrent
)
AMR in GaMnAs DMS: from full numerics to microscopic mechanism
Rushforth et al. PRL‘07
AMR in GaMnAs DMS: from full numerics to microscopic mechanism
M
current
Non-crystalline AMR mechanisms:
1) Polarized SO bands 2) Polarized impurities & SO bands
Leading AMR mechanism in DMSs
Rushforth et al. PRL‘07
current
MGa
Microscopic mechanism of AHE in GaMnAs DMS
AHE explained by the revived intrinsic mechanism
Jungwirth et al PRL‘02
Experiment AH 1000 (cm)-1
TheroyAH 750 (cm)-1
Note: Inspired to explain AHE in pure Fe,etc by intrinsic AHE
Yao et al PRL‘04
2D SO-coupled systems simplest band-structures offermost detailed and complete understanding of the AMR and AHE
Rashba SO-coupled 2DEG
AMR in 2D SO-coupled systems
We will discuss a detailed theory analysis in Rashba-Dresselhaus 2D systems
Experimentally not studied in 2D systems yet; we will comment on experiments in related 3D DMS systems
Trushin, Vyborny et al PRB in press (arXiv:0904.3785)
AHE in 2D SO-coupled systems
Detailed theory analysis completed
We will discuss 2D AHE related experiment: Spin-injection Hall effect in a planar photo-diode
Nagaosa et al RMP ‘to be published (arXiv:0904.4154)
Heuristic link between spin-texture of 2D SO bands, impurity potentials and AMR
Short-range magnetic impurity potential
Short-range electro-magnetic impurity potential
Non-crystalline AMR>0 in Rashba 2D system
Rashba Hamiltonian
Eigenspinors
Non-crystalline AMR>0 in Rashba 2D system
Scattering matrix elements
( )
current
Large non-crystalline AMR>0 in Rashba 2D system with electro-magnetic scatterrers
Scattering matrix elements of
( )
current
current
Negative and positive and crystalline AMR in Dresselhaus 2D system
Dresselhaus
Rashbacurrent
curre
nt
AMR in (Ga,Mn)As modeled by j=3/2 Kohn-Luttinger Hamiltonian
KL Hamiltonian
Heavy holes
Magnetic part of the impurity potential
Scattering matrix elements of
Compare with spin-1/2
Rashba Kohn-Luttinger
Negative AMR in (Ga,Mn)As due to electro-magnetic MnGa impiruties
current
AMR in 2D Rashba system from exact solution to integral Boltzmann eq.
= const. for
independent of
or
averages to 0 over Fermi cont.
quasiparticle life-time
AMR in 2D Rashba system from exact solution to integral Boltzmann eq.
transport life-time
transport life-time is a good first approximation to AMR
AMR in 2D Rashba system from exact solution to integral Boltzmann eq.
analytical solution to the integral Boltzmann eq.
contains only cos and sin harmonics
jqs
––– – –– – –– – –
+ + + + + + + + + +AHE
Ferromagnetic(polarized charge current) jq
SHE
nonmagnetic(unpolarizedcharge current)
p -AlG a As
i-G a As
n- -d o p e d AlG a As
e tc he d
2DHG2DHG
2DEG2DEG
Spintronic Hall effects in magnetic and non-magnetic (2D) systems
Wunderlich et al. IEEE 01, PRL‘05
Co/Pt
Spin-injection Hall effect: Hall measurement of spin-polarized electrical current injected into non-magnetic system
Wunderlich et al. Nature Phys. in press, arXives:0811.3486
– – – – + + + +
+ + + + – – – –
jqs
nonmagneticSpin-polarizer(e.g. ferromagnet, light)
29
i pn
2DHG
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
-
2DHGi p
n
30
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
i
p
n2DHG
2DEG
31
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
2DHG
2DEG
e
h
ee
ee
e
hh
h
h h
VH
32
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
Optical spin-generation area near the p-n junction
Simulated band-profile
p-n junction bulit-in potential (depletion length ) ~ 100 nm self-focusing of the generation area of counter-propagating e- and h+
Hall probes further than 1m from the p-n junction safely outside the spin-generation area and/or masked Hall probes
2DHG2DEG
e
h
ee
ee
e
h hh
hh
Vb
VH2
VL
2DHG2DEG
ee
hh
eeee
eeee
ee
hh hhhh
hhhh
Vb
VH2
VL
))(V(2 dis
*22
rkkkkkm
kH yyxxyxxy
2DEG
Spin transport in a 2DEG with Rashba+Dresselhaus SO
GaAs, for A 2o
3.5)(
11
3 22
2*
sogg EE
P GaAs, for AeV with 30
102 BkB z zE*
Schliemann, et al., Phys. Rev. Lett. 94, 146801 (2003)Bernevig, et al., Phys. Rev. Lett. 97, 236601 (2006)Weber, et al., Phys. Rev. Lett. 98, 076604 (2007)
weak spin orbit coupling regime:
System can be described by a set of spin-charge diff. Equation:
5meV)( ,
Spin dynamics in a 2DEG with Rashba Dresselhaus SO
2~~
4~~~
arctan,)~~~
(||,)exp(|| 21
22
41
22
21
21414
22
22
1LL
LLLLLLqiqq
]exp[)( ]011[]011[ xqxpZ
Steady state solution for the out of plane spin-polarization component
22/1 ||2
~ mL
SO-length ~1m
Spin-diffusion along the channelof injected spin- electrons
see also Bernevig et al., PRL‘06
Spin-diffusion along the channelof injected spin- electrons
Local spin-dependent transverse deflection due to skew scattering ~10nm
SO-length (~1m) >> mean-free-path (~10 nm)
))(V(2 dis
*22
rkkkkkm
kH yyxxyxxy
2DEG
GaAs, for A 2o
3.5)(
11
3 22
2*
sogg EE
P GaAs, for AeV with 30
102 BkB z zE*
Skew-scattering Hall effect
Spin injection Hall effect: theoretical estimate
Local spin polarization calculation of the Hall signal
Weak SO coupling regime extrinsic skew-scattering term is dominant
)(2)( ]011[*
]011[ xpnn
ex z
iH
A. Crepieux and P. Buno, PRB ’01
Large Hall angles – comparable to AHE in metals
0123
SIHE device realization
n3,n2,n1: local SIHE n0: averaged-SIHE / AHE
Spin-generation area
2DHG2DEG
e
h
ee
ee
e
h hh
hh
Vb
VH2
VL
2DHG2DEG
ee
hh
eeee
eeee
ee
hh hhhh
hhhh
Vb
VH2
VL
5.5m
Unmasked and masked SIHE devices
0 25 50 750
10
20R
L [k]
tm [s]
-50
-25
0
25
50
- 0 +
-50
-25
0
25
50
RH
2 [
]
Vb= 0V
Vb= -10V
2DHG2DEG
e
h
ee
ee
e
h hh
hh
Vb
VH2
VL
2DHG2DEG
ee
hh
eeee
eeee
ee
hh hhhh
hhhh
Vb
VH2
VL
Measured SIHE phenomenology
+
+
-+
+
-
Skew scattering
-
-Bso+
+
-+
+
-
Skew scattering
-
-Bso
-1.0 -0.5 0.0 0.5 1.0-2
-1
0
1
2
H [ 1
0-3 ]
H1
-1.0 -0.5 0.0 0.5 1.0
-10
-5
0
5
10
H [ 1
0-3 ]
H2
0 10 20 30 40 50-10
-5
0
5
10
H0 (x3) H2
tm [s]
H [
10-3
]
H1 (x3) H3 (x3)
- +
SIHE: spatially dependent, linear, strong
-20
-10
0
10
20
H2 H3
VH [
V]
0 20 40 60 80-4-2024
I [A
]
tm [s]
-0 - 0
Vb=-0.5V Vb=+0.5V
(a)
-20
-10
0
10
20
H2 H3
V
H [
V]
0 20 40 60 80-4-2024
tm [s]
I [A
]
-0 - 0
Vb=-5V Vb=+5V
SIHE vs AHE
0 30 60 90 120 150 180-5
0
5 100K 160K (x2) 220K (x3)
H [1
0-3]
tm [s]
SIHE survives to high temperatures
-
+
Spin-detection in semiconductors
Ohno et al. Nature’99, others
Magneto-optical imaging
non-destructive
lacks nano-scale resolution and only an optical lab tool
MR Ferromagnet
electrical
requires semiconductor/magnet hybrid design & B-field to orient the FM spin-LED
all-semiconductor
requires further conversion of emitted light to electrical signal
Datta-Das transistor
Ohno et al. Nature’99, others
Crooker et al. JAP’07, others Magneto-optical imaging
non-destructive
lacks nano-scale resolution and only an optical lab tool
MR Ferromagnet
electrical
requires semiconductor/magnet hybrid design & B-field to orient the FM spin-LED
all-semiconductor
requires further conversion of emitted light to electrical signal
Spin-detection in semiconductors
Spin-injection Hall effect
non-destructive
electrical
100-10nm resolution with current lithography
in situ directly along the SC channel & all-SC requiring no magnetic elements in the structure or B-field
Spin-photovoltaic cell: polarimeter on a SC chip requiring no magnetic elements, external magnetic field, or bias; form IR to visible light depending on the SC
Spin-detection tool for other device concepts (e.g. Datta-Das transistor)
Basic studies of quantum-relativistic spin-charge dynamics and AHE also in the intriguing strong SO regime in archetypal 2DEG systems
Application of SIHE