Spin-injection Hall Effectpeople.physics.tamu.edu/sinova/Talks/SPIE_August_2010.pdf · SPIE...
Transcript of Spin-injection Hall Effectpeople.physics.tamu.edu/sinova/Talks/SPIE_August_2010.pdf · SPIE...
Research fueled by:
JAIRO SINOVATexas A&M University
Institute of Physics ASCR
Hitachi CambridgeJörg Wunderlich, A. Irvine, et al
Institute of Physics ASCRTomas Jungwirth, Vít Novák, et al
Spin-injection Hall Effect:a new paradigm in using spin-orbit coupling to
create a spin FET with pure spin-currents
University of UtrechtUtrecht, January 8th 2010SPIE conference
Spintronics IIIAugust 1st 2010Sand Diego, CA
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 2
I. Technology motivation
II. Spin injection Hall effect•Making the device•Basic observation; analogy to AHE•The effective Hamiltonian•Spin-charge Dynamics
III. iSHE FET•Gating action of iSHE•iSHE AND-gate with pure spin current
Spin-injection Hall Effect:a new paradigm in using spin-orbit coupling to
create a spin FET with pure spin-currents
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Circuit heat generation is one key limiting factor for scaling device speed
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Industry has been successful in doubling of transistor numbers on a chip approximately every 18 months (Moore’s law). Although expected to continue for several decades several major challenges will need to be faced.
The need for basic research in technology development
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 4
International Technology Roadmap for Semiconductors
Basic Research Inc.
1D systems
Single electron systems (FETs)
Spin dependent physics
Ferromagnetic transport
Molecular systems
New materials
Strongly correlated
systems
Nanoelectronics
The need for basic research in technology development
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-orbit coupling interaction
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(one of the few echoes of relativistic physics in the solid state)
HSO = −µB · Beff
This gives an effective interaction with the electron’s magnetic moment
Consequences•Effective quantization axis of the spin depends on the momentum of the electron. Band structure (group velocities, scattering rates, etc.) mixed strongly in multi-band systems
•If treated as scattering the electron gets asymmetrically scattered to the left or to the right depending on its “spin”
Classical explanation (in reality it is quantum mechanics + relativity )
E = −1e∇V (r)• “Impurity” potential V(r) Produces
an electric field
∇V
Beff
ps
Beff = − kcm
× EIn the rest frame of an electronthe electric field generates and effective magnetic field
• Motion of an electron
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 6
Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system?
Long standing paradigm: Datta-Das FET
Unfortunately it has not worked :•no reliable detection of spin-polarization in a diagonal transport configuration •No long spin-coherence in a Rashba spin-orbit coupled system (Dyakonov-Perel mechanism)
Towards a realistic spin-based non-magnetic FET device
Beff = − kcm
× E
E
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 7
Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism).
New paradigm using SO coupling: SO not so bad for dephasing
Beff = − kcm
× E
E
1) Can we use SO coupling to manipulate spin AND increase spin-coherence?
2) Can we detect the spin in a non-destructive way electrically?
3) Can this effect be exploited to create a realistic spin-FET?
Use the persistent spin-Helix state and control of SO coupling strength(Bernevig et al 06, Weber et al 07, Wünderlich et al 09)
Use AHE to measure injected current polarization at the nano-scale electrically (Wünderlich, et al 09, 04)
YES (Wünderlich, Irvin, JS, Jungwirth et al 2010)
Vd
VH
2DHG
2DEG
Vs
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Device schematic – Hall measurement
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 9
2DHG
2DEG
e
h
e eee
e
hhh
h h
Vs
Vd
VH
Spin-injection Hall effect device schematics
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-injection Hall device measurements
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trans. signal
σoσ+σ- σo
VL
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-injection Hall device measurements
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trans. signal
σoσ+σ- σo
VL
SIHE ↔ Anomalous Hall
Local Hall voltage changes sign and magnitude along a channel of 6 µm
H2DEG =2
k2
2m+ α(kyσx − kxσy) + β(kxσx − kyσy) + λ
∗σ × (k ×∇Vdis(r))
λ∗ =P 2
3
1
E2g
− 1(Eg + ∆so)2
≈ 5.3A
2for GaAs β = −Bk2
z B = 10 eV A3 α = λ∗Ez
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 12
Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling
a 2DEG is well described by the effective Hamiltonian:
Something interesting occurs when
H2DEG ≈2
k2
2m+ α(ky − kx)(σx + σy)
• spin along the [110] direction is conserved• long lived precessing spin wave for spin perpendicular to [110]
E↓(k) = E↑(k + Q) Q =4mα
2
The nesting property of the Fermi surface:
Bernevig et al PRL 06, Weber et al. PRL 07
Schliemann et al PRL 04
H2DEG =2
k2
2m+ α(kyσx − kxσy) + β(kxσx − kyσy)
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 13
Effects of Rashba and Dresselhaus SO couplingα = -β
[110]
[110]_
ky [010]
kx [100]
α > 0, β = 0[110]
[110]_
ky [010]
kx [100]
α = 0, β < 0[110]
[110]_
ky [010]
kx [100]
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 14
Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling
For the same distance traveled along [1-10], the spin precesses by exactly the same angle.[110]
[110]_
[110]_
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 33
Persistent state spin helix verified by pump-probe experiments
Similar wafer parameters to ours
Sz/x−(x[110]) = S0z/x− exp[qx[110]]
L1/2 = 2m|α ± β|/2|q| =L2
1L22 + L4
2
1/4and θ =
12
arctan
2L2
1L22 − L4
1/4
L22 − L2
1/2
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 16
Spatial variation scale consistent with the one observed in SIHE
Spin-helix state when α ≠ β
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
ρxy = − σxy
σ2xx + σ2
xy
≈ −σxy
σ2xx
≈ −σxyρ2xx ≈ −Aρxx − Bρ2
xx
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Simple electrical measurement of out of plane magnetization
InMnAs
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Spin dependent “force” deflects like-spin particles
ρH=R0B +4π RsM
Understanding AHE in SIHE: AHE basics
I
_ FSO
FSO
_ __majority
minority
V
σAH
xy ≈ B + Aσxx
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 18
Cartoon of the mechanisms contributing to AHE σAH
xy ≈ B + Aσxx
independent of impurity density
xc =∂ε(k)∂k
+e
E × Ω
Ωz(k, n) = 2Im
∂
∂ynk
∂
∂xnk
Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling.
Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure)
E
SO coupled quasiparticles
Intrinsic deflection B
Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.
independent of impurity density
Side jump scatteringVimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ)
B
Skew scattering
Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering.
~σ~1/niVimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ) A
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Contributions understood in simple metallic 2D models
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Semi-classical approach:Gauge invariant formulation
Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07
Kubo microscopic approach:in agreement with semiclassical
Borunda, Sinova, et al PRL 07, Nunner, JS, et al PRB 08
Non-Equilibrium Green’s Function (NEGF) microscopic approach
Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08
σAH
xy ≈ B + Aσxx
Nanoelectronics, spintronics, and materials control by spin-orbit coupling 20
Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii)
Crepieux et al PRB 01Nozier et al J. Phys. 79
Two types of contributions: i)S.O. from band structure interacting with the field (external and internal)ii)Bloch electrons interacting with S.O. part of the disorder
Lower bound estimate of skew scatt. contribution
AHE contribution to Spin-injection Hall effect
H2DEG =2
k2
2m+ α(kyσx − kxσy) + β(kxσx − kyσy) + λ
∗σ × (k ×∇Vdis(r))
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Local spin-polarization → calculation of AHE signal Weak SO coupling regime → extrinsic skew-scattering term is dominant
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Lower bound estimate
Spin-injection Hall effect: theoretical expectations
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
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SiHE: continuous shift of spin injection
VH2I
VbVH1
σ+σ-σ+σ- σ+
σ-
R[Ω
]
I ph[n
A]
Spin polarized charge current
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
iSHE with spin-helix state
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B
spin polarizedcharge current
pure spin diffusive current:no particle current, no Joule heating
generalized Boltzmann MC simulation
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin Hall Transistor
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Manipulation2µm long gate: reverse biased pn-junction
Spin injectorreverse biased pn-junction+ light spotof 2µm diameter
DetectionHall crosses 1 2
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
iSHE transistor: GATING
Channel closed
Channel opened
Gating action of iSHE
Spin polarized charge current
Pure spin diffusive current
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
2 Detectors and 1 Gate
σ-
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
2 Detectors and 2 Gates
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σ-
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
SiHE AND spin logic gatecharge currentpure spin current:
no particle current
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Summary of spin-injection Hall effect
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• Basic studies of spin-charge dynamics and Hall effect in non-magnetic systems with SO coupling • Spin-photovoltaic cell: solid state polarimeter on a semiconductor chip requiring no magnetic elements, external magnetic field, or bias
• SIHE-FET with pure spin currents in the active region
•SiHE-AND gate
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Next step ....
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Electrical injec,on through barrier from Fe
Electrical detec,on by SIHE Scho:ky barrier: Kamil Olejnik (HCL, IOP Prague)MgO barrier: Sankara Rutala (CNRS, Thales, UPSUD, Orsay, France)
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Allan MacDonald U of Texas
Tomas JungwirthTexas A&M U.
Inst. of Phys. ASCRU. of Nottingham
Joerg WunderlichCambridge-Hitachi
Laurens MolenkampWürzburg
Xiong-Jun LiuTexas A&M U.
Mario BorundaTexas A&M Univ.
Harvard Univ.
Nikolai SinitsynTexas A&M U.
U. of TexasLANL
Alexey KovalevTexas A&M U.
UCLA
Liviu ZarboTexas A&M Univ.
Xin LiuTexas A&M U.
Ewelina Hankiewicz(Texas A&M Univ.)
Würzburg University
Principal Collaborators
Gerrit BauerTU Delft
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Bryan GallagherU. of Nottingham
and many others
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
The Spin-Charge Drift-Diffusion Transport EquationsFor arbitrary α,β spin-charge transport equation is obtained for diffusive regime
For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling Sx+ and Sz:
For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004); Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004)
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