Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems
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Transcript Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems
Anisotropic magnetoresistance and spin-injection Hall
effect in 2D spin-orbit coupled systems
Tomas Jungwirth
Institute of Physics ASCR
Karel Výborný, Jan Zemen, Jan Mašek,
Vít Novák, Kamil Olejník, et al.
Hitachi Cambridge, Univ. Cambridge
Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
University of Nottingham
Bryan Gallagher, Richard Campion, Kevin
Edmonds, Andrew Rushforth, et al.
Texas A&M
Jairo Sinova, et al.
University of Texas
Allan MaDonald, et al.
Extraordinary magnetoresistance: AMR, AHE
Ordinary magnetoresistance:
response in normal metals to external
magnetic field via classical Lorentz force
B
Extraordinary magnetoresistance:
response to internal spin polarization in ferromagnets
via quantum-relativistic spin-orbit coupling
anisotropic
magnetoresistance
_ _ _ _ _ _ _ _ _ _
_
Lord Kelvin 1857
FL
+++++++++++++
V
I
M
__
FSO
I
ordinary Hall effect 1879
V
anomalous Hall
effect 1881
Spin-orbit coupling
nucleus rest frame
E
Q
40 r
r
3
1
B 0 0 v E 2 v E
c
Lorentz transformation Thomas precession
electron rest frame
I Qv
H SO
0 I r
B
4 r 3
g B
e
SB
S vE
2
2
2mc
From 1950’s microscopic model interpretations – often controversial
AMR: Mott’s model of transport in metals
ss
sd
ss
sd
itinerant 4s:
no exch.-split
no SO
Smit 1951
localized 3d:
exch. split
SO coupled
AHE
Karplus&Luttinger 1954
(then partly forgotten till 2000’s)
Berger 1970
Smit 1955
From 1990’s numerics based on relativistic ab initio band strucrure & Kubo formula
Scattering considered essential for both AMR and AHE
alloys like FeNi (treated in CPA)
AMR
AHE
Numerically successful but difficult to connect with
microscopic models due to complex bands in metals
Banhart&Ebert EPL‘95
Khmelevskyi ‘PRB 03
AMR sensors: dawn of spintronics in early 1990’s
Magnetoresistive read element
Inductive read/write element
In mid 1990’s replaced in HDD by GMR or TMR
but still extensively used in e.g. automotive industry
From late 1990’s AMR and AHE studied in novel ferromagnets
Ferromagnetic DMS GaMnAs with much simpler 3D band structure than metals
Ga
As-p-like holes
As
Bso
Mn
Mn-d-like local
moments
Bex + Bso
Jungwirth et al. RMP’06
Dietl et al. Semicond. and Semimet. ‘08
Semiquantitative numerical description of
AMR and AHE in GaMnAs
Jungwirth et al. RMP’06
Dietl et al. Semicond. and Semimet. ‘08
AMR in GaMnAs DMS: from full numerics to microscopic mechanism
Anisotropic scattering rate:
non-crystalline and crystalline AMR
Spherical model:
non-crystalline AMR only
M
current
M
[110]
Rushforth et al. PRL‘07
current
AMR in GaMnAs DMS: from full numerics to microscopic mechanism
Non-crystalline AMR mechanisms:
1) Polarized SO bands
2) Polarized impurities & SO bands
M
MGa
current
current
Leading AMR mechanism in DMSs
Rushforth et al. PRL‘07
Microscopic mechanism of AHE in GaMnAs DMS
Jungwirth et al PRL‘02
AHE explained by the revived intrinsic mechanism
Note: Inspired to explain AHE in pure Fe,etc by intrinsic AHE
Experiment
sAH 1000 (W cm)-1
Theroy
sAH 750 (W cm)-1
Yao et al PRL‘04
2D SO-coupled systems simplest band-structures offer
most 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
Nagaosa et al RMP ‘to be published (arXiv:0904.4154)
We will discuss 2D AHE related experiment:
Spin-injection Hall effect in a planar photo-diode
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
Rashba
current
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
Negative AMR in (Ga,Mn)As due to electro-magnetic MnGa impiruties
Rashba
Kohn-Luttinger
current
AMR in 2D Rashba system from exact solution to integral Boltzmann eq.
= const. for
or
independent of
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.
contains only cos and sin harmonics
analytical solution to the integral Boltzmann eq.
Spintronic Hall effects in magnetic and non-magnetic (2D) systems
AHE
++++++++++
jqs
–––––––––––
SHE
Ferromagnetic
(polarized charge current)
jq
nonmagnetic
(unpolarized charge current)
Co/Pt
p-AlGaAs
etched
2DHG
i-GaAs
2DEG
n--doped AlGaAs
Wunderlich et al. IEEE 01, PRL‘05
Spin-injection Hall effect: Hall measurement of spin-polarized electrical current
injected into non-magnetic system
++++ ––––
––––
++++
Spin-polarizer
(e.g. ferromagnet, s light)
jqs
nonmagnetic
Wunderlich et al. Nature Phys. in press, arXives:0811.3486
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
ni
p
2DHG
29
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
-
ni
p
2DHG
30
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
p
i
n
2DHG
2DEG
31
Optical injection of spin-polarized charge currents into Hall bars
GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell
h
h
h h h
h
e
VH
e
e
e
e
e
2DHG
2DEG
32
Optical spin-generation area near the p-n junction
Simulated band-profile
Vb
h
h
h h h
h
e
e
e
e
e
VL
e
VH2
2DHG
2DEG
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
Spin transport in a 2DEG with Rashba+Dresselhaus SO
H 2DEG
2k 2
*
k ys x k xs y k xs x k ys y s (k Vdis (r ))
2m
o2
P 2 1
1
5.3 A for GaAs,
2
2
3 E g ( E g so )
*
weak spin orbit coupling regime:
0
B k with B 10 eV A 3 for GaAs,
2
z
* Ez
, ( 5meV)
System can be described by a set of spin-charge diff. Equation:
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)
Spin dynamics in a 2DEG with Rashba Dresselhaus SO
Steady state solution for the out of plane spin-polarization component
pZ ( x[1 1 0] ) exp[ q x[1 1 0] ]
~2~ 2 ~4
L
~2~ 2 ~ 4 14
1 L2 L1 4
1
q | q | exp( i ) , | q | ( L1 L2 L2 ) , 2 arctan
L~ 2 L~ 2 2
2
1
Spin-diffusion along the channel
of injected spin- electrons
~
L1/ 2 2m | | 2
SO-length ~1m
SO-length (~1m) >> mean-free-path (~10 nm)
Spin-diffusion along the channel
of injected spin- electrons
see also Bernevig
et al., PRL‘06
Local spin-dependent transverse deflection
due to skew scattering
Skew-scattering Hall effect
H 2DEG
2k 2
*
k ys x k xs y k xs x k ys y s (k Vdis (r ))
2m
o2
P 2 1
1
5.3 A for GaAs,
2
2
3 E g ( E g so )
*
0
B k with B 10 eV A 3 for GaAs,
2
z
* Ez
Spin injection Hall effect: theoretical estimate
Local spin polarization calculation of the Hall signal
Weak SO coupling regime extrinsic skew-scattering term is dominant
A. Crepieux and P. Buno, PRB ’01
e
H ( x[1 1 0] ) 2
n pz ( x[1 1 0] )
ni
*
Large Hall angles – comparable to
AHE in metals
Vb
h
SIHE device realization
h
h h h
h
e
e
e
e
e
VL
e
VH2
n3,n2,n1: local SIHE
2DHG
2DEG
3
2
1 0
n0: averaged-SIHE / AHE
Spin-generation
area
Unmasked and masked SIHE devices
5.5m
50
25
0
-25
Vb= 0V
Measured SIHE phenomenology
RH2 [W]
-50
50
25
0
Vb
Vb= -10V
-25
-50
h
h h h
h
e
2DHG
2DEG
e
e
e
e
VL
e
VH2
20
R L [k W ]
h
s-
10
s0
s+
0
0
25
50
tm [s]
75
2
SIHE: spatially dependent, linear, strong
H1
Skew scattering
H [ 10
-3
]
1
+
-
-
+
Bso
+
0
-1
-
-
-2
+
-1.0
-0.5
0.0
0.5
1.0
0.5
1.0
s s
10
H0 (x3)
10
H2
]
5
5
0
H [ 10
-3
-3
H [ 10 ]
H2
H1 (x3)
H3 (x3)
-5
s-
-10
0
10
-5
s+
20
30
tm [s]
40
0
-10
50
-1.0
-0.5
0.0
s s
SIHE vs AHE
(a)
s-
s-
0
H2
H3
-10
-20
I [ A]
20
s0
-10
2
2
-2
-4
0
20
Vb=+5V
40
tm [s]
60
80
H2
H3
-20
4
Vb=-5V
s- s0
0
4
0
s-
s0
10
I [ A]
V H [ V]
10
s0
V H [ V]
20
0
-2
-4
Vb=-0.5V
0
20
Vb=+0.5V
40
tm [s]
60
80
SIHE survives to high temperatures
-3
H [10 ]
5
s-
100K
160K (x2)
220K (x3)
0
-5
s+
0
30
60
90
120 150 180
tm [s]
Spin-detection in semiconductors
Datta-Das transistor
Magneto-optical imaging
non-destructive
lacks nano-scale resolution
and only an optical lab tool
MR Ferromagnet
electrical
requires semiconductor/magnet
Ohno et al. Nature’99, others
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
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
Ohno et al. Nature’99, others
hybrid design & B-field to orient
the FM
spin-LED
all-semiconductor
requires further conversion of
emitted light to electrical
signal
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
Application of SIHE
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