spin transport in topological insulators
TRANSCRIPT
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Spin transport in topological insulators
Yu-Ting Fanchiang
Department of Physics,
National Taiwan University
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Outline
• Introduction to spin current and spin transfer torques
• Measuring spin Hall angle and IEE length
- Spin pumping
- Spin-torque ferromagnetic resonance (ST-FMR)
- Modulation of magnetization damping (MOD)
• Spin transport in TIs: paper review
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Spin transfer torques Ferromagnetic resonance (FMR) Spin pumping
Field-like torque: Damp-like torque:
LLG equation with torque terms:
effy Ht t
m mm m τ
2
s
s
IeM V
m m
2s
s
IeM V
m
A. Brataas, et al., Nat. Mater. 11, 372 (2012)
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Spin current Q v s
2
*Im2m
σ
For a spinor plane-wave wavefunction in x direction:
Imikxe
a b
2*
2*
22 2
2Re2
2Im2
2Re2
xx
xy
xz
kQ ab
m
kQ ab
m
kQ a b
m
Conservation of angular momentum Spin transfer torque:
2 ˆst
pillboxd R N n Q
3
pillboxd r Q
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cos / 2 sin / 2ikx
in
e
cos / 2 sin / 2
cos / 2 sin / 2
ikx
trans
ikx
refl
et t
er r
2
2 2* *
22 22 2
2 2* *
22 22 2
ˆ ˆsin cos2
ˆ ˆsin Re sin Im2 2
ˆcos / 2 sin / 22
ˆ ˆsin Re sin Im2 2
cos / 2 sin2
in
trans
refl
k
m
k kt t t t
m m
kt t
m
k kr r r r
m m
kr r
m
Q x z
Q x y
z
Q x y
ˆ/ 2 z
D. C. Ralph, J. Magn. Magn. Mat. 320, 1190 (2008)
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2* *
2* *
ˆ
ˆsin 1 Re2
ˆsin Im2
st in refl transA
A kt t r r
m
A kt t r r
m
N x Q Q Q
x
y
2 2
2 2
( 1
1)
t r
t r
Damp-like torque
Field-like torque
Spin mixing conductance
*
'
'
G Ga a
G Gb b
Re ImG G
for metals
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Spin current projected along Hext:
Spin pumping
K. Ando, J. Appl. Phys. 109, 103913 (2011)
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/
2 3 s Fr F N F
B
M dg W W
g
/
4 s Fr F N F
B
M dg
g
or
20
2 22 2
0 0
2ISHE AHE
H HV V V
H H H H
A phenomenological model
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Antisymmetric lineshape from AHE or AMR
Phase shift between the microwave and magnetization determine the polarity.
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2
2 2
2, where powerrf
r r c rf
hg fP g fP h
Small cone angle (linear) regime Linear power dependence
Hext
M(t)
θc
22 2 2 2
0 22 2 2
4 4 4
8 4 4
r rf s s
s
g h M M
jM
j0(t)
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The P factor
2 2 2
2 2 2
2 4 4 4
4 4
s s
s
M M
PM
can be viewed as a correction factor.
The pumped spin current is proportional to the trajectory area. Spin pumping is an adiabatic process. (think about the Carnot engine.)
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Spin distribution in normal metals
Spin Hall effect acts as a charge current source.
Solving the spin diffusion equation…
0
sinh /
sinh /
N N
s s
N N
d zj z j
d
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Thickness dependence
Spin backflow depends on the spin diffusion length.
0
0
1
2tanh
2
Nd
c c
N
N NSH s
N N
j j y dyd
dej
d
Need to get the thickness dependence data to calculate the spin Hall angle
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Spin Hall angles strongly depend on the d-electron count.
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1. The larger spin Hall angles, the shorter spin diffusion lengths. 2. Depending on techniques, materials preparation and geometry,
the calculated spin Hall angle can vary by 1 order of magnitude. 3. Rashba effect (broken inversion symmetry) at the interface adds
complexity to analyses.
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Spurious effects • Microwave induced Seebeck effect in semiconductor.
• Spin rectification effect. (can be prevented by YIG)
- the boundary conditions, phase shift between E and B field can strongly affect voltage signals.
• Self-induced ISHE and spin backflow. (can be prevented by YIG)
H. Hung et al., Appl. Phys. Lett. 105, 152413 (2014)
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Spin-torque ferromagnetic resonance (ST-FMR)
,
0
ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ
2eff S rf rf
S
dm dmm H m J m m m H
dt dt e M t
Anti-damp torques
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0
20
2 22 2
0 0
cos1
4 2 / |ext
rf ext
mix
H H ext ext
I H HdRV S A
d df dH H H H H
Rely on AMR to generate voltage signals. Not suitable for magnetic insulator. Special case: Pt/YIG, Ta/YIG…
1/2
, 0
,rf
1 4 /S rf S
eff ext
C
J e M tdSM H
J A
The spin Hall angle can be determined from the relative magnitude of the two components.
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Modulation of magnetization damping (MOD)
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Thermal effects on FMR spectra can be serious. Need to change the in-plane field angle to separate the spin-transfer effect from the thermal effect.
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Controlled sample Py/Cu: Cu has small spin Hall angle.
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Spin pumping to topological insulators
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Application: data storage
Goal: Find a material that can generate maximum spin torques from a given charge current.
Non-volatility: KV > 50-60 kBT K: magnetic anisotropy constant V: volume of nano-particle kB: Boltzmann constant
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Topological insulators ARPES spectra
Nearly 100 % spin polarization.
Spin-momentum locking: the direction of electron motion determines the spin direction.
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Challenges
• Bulk conduction of TIs obscures the effect of topological surface states
• Large variation of reported effective spin Hall angle θSH (or conversion efficiency)
- 0.022 in Bi2Se3/Py at 15 K (Deorani et al. (2014))
- ~10-4 in bulk insulating Bi1.5Sb0.5Te1.7Se1.3 at 15 K (Shiomi et al. (2014))
- 0.021~0.43 in Bi2Se3/CoFeB at RT (Jamali et al. (2015))
• Current shunting effect by ferromagnetic metals in ST-FMR measurement
Ferrimagnetic insulator YIG with high thermal
stability is an ideal spin source.
27
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Inverse spin Hall effect (ISHE)
Inverse Edelstein effect (IEE)
location bulk surface
condition Spin current normal to the interface
“non-equilibrium” spin density at interface
material Normal metals and semiconductors including 3D TIs
TIs and Rasba materials possessing k-dependent spin-polarized states
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Spin Hall angle and IEE length
tanh ,2
2D charge current from ISHENc SH N s
N
dj j
(definition of IEE length)c IEE sj j
1,
2
,
N N IEE N SH
N N IEE N SH
d d
d
Using spin Hall angle to determine conversion ratio of 3D jc and 2D js can lead to “unphysical” value (> 1). Ex: θSH = 1.6 for α-Sn if compared with W
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Questions
1. Does ferromagnetic metal suppress topological surface states?
2. Can spin pumping distinguish surface and bulk effects (IEE and ISHE) of Bi2Se3?
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Structure Journal method Spin-charge ratio Importance
Nat. Commun. 4, 2944 (2013)
(A. Fert)
Spin pumping 300K: 0.09 ~ 0.2 0.3 nm
First demonstration of RT IEE with Rasba
alloys Ag/Bi
Nature 511, 449 (2014) (D. Ralph)
ST-FMR 300K: 2 ~ 3.5 Giant RT spin torque ratio of Bi2Se3
“Signature” of RT EE
PRB 90, 094403 (2014) (S. Oh)
Spin pumping
300K: 0.009 15K: 0.02
ISHE of Bi2Se3
PRL 113, 196601 (2014) (E. Saitoh)
Spin pumping
15K: ~10-4 Low T IEE of TIs (crystal)
PRL 114, 257202 (2015) (S. Oh)
ST-FMR 300K: 0.047 50K: 0.42
Large Low T spin torque ratio of Bi2Se3
“Signature” of RT EE
Al2O3
Bi2Se3
Py
Bi2Se3, BSTS, and Sn-BTS
Py
Al2O3
Bi2Se3
Co40Fe40B20
Al2O3
Bi2Se3
Py
Si (001)
Bi
Py
Ag
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Structure Journal method Spin-charge ratio Importance
Sci. Rep. 5, 7907 (2015) (University of Oxford)
Spin pumping -- Atypical thickness dependence of mixing
conductance
Nano Lett. 15, 7126 (2015) (Jian-Ping Wang,
University of Minnesota)
Spin pumping 300K: 0.43 Giant RT ISHE of Bi2Se3
PRL 116, 096602 (2016) (A. Fert)
Spin pumping 300K: 0.62 ~ 1.5 2.1 nm
Giant RT IEE of TI Sn
Submitted to PRB (S. F. Lee)
Spin pumping 5 K: 0.003 ~ 0.0062 “Signature” of low T IEE of Bi2Te3
Low T ISHE of Bi2Te3
(our work) Spin pumping
-- “Signature” of RT IEE of Bi2Se3
First study on FI/TI
InP
Bi2Se3
Co20Fe60B20
InSb (001)
Sn
Fe
Ag
Al2O3
Bi2Te3
Py
GGG
Bi2Se3
YIG
Bi2Se3
Co50Fe50
Py
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Structure Journal method Spin-charge ratio Importance
PRB 90, 094403 (2014) (S. Oh)
Spin pumping
300K: 0.009 15K: 0.02
ISHE of Bi2Se3
Al2O3
Bi2Se3
Py
Nothing new.
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In order to distinguish the surface and bulk contributions, they assumed a spin Hall angle θsh1 for TSS, believing that TSS would give far larger spin Hall angle than the bulk. However, the fitting results show that θsh1 ≈ θsh2. That is, no TSS features were revealed in this work.
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Structure Journal method Spin-charge ratio Importance
PRL 113, 196601 (2014) (E. Saitoh)
Spin pumping
15K: ~10-4 Low T IEE of TIs (crystal)
Bi2Se3, BSTS, and Sn-BTS
Py
Obviously, they have realized the difficulties of separating surface and bulk effects. So they choose bulk-insulating BSTS to rule out ISHE. However, the very small spin-charge ratio is very puzzling. (Question 1)
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The data show negative field shifts as T became lower, similar to Faris’ data. However, they did not mention this.
The thing is, are TSS still “robust” in this structure?
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Structure Journal method Spin-charge ratio Importance
Nano Lett. 15, 7126 (2015) (Jian-Ping Wang, University of
Minnesota)
Spin pumping 300K: 0.015 ~ 0.43 Giant RT ISHE of Bi2Se3
InP
Bi2Se3
Co20Fe60B20
Nothing new in physics again.
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The samples had severely degraded. All of the curves should be smooth, so the calculated spin Hall angles are questionable.
(Question 2??)
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Structure Journal method Spin-charge ratio Importance
PRL 116, 096602 (2016) (A. Fert)
Spin pumping 300K: 0.62 ~ 1.5 2.1 nm
Giant RT IEE of TI Sn
InSb (001)
Sn
Fe
Ag
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Fermi level is very closed to the Dirac point of Sn. TSS disappeared when Fe was deposited on top. (Question 1)
Could this explain the small spin-charge ratio from the Japanese group’s work?
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Structure Journal method Spin-charge ratio Importance
Nature 511, 449 (2014) (D. Ralph)
ST-FMR 300K: 2 ~ 3.5 Giant RT spin torque ratio of Bi2Se3
“Signature” of RT EE
Al2O3
Bi2Se3
Py
Signatures of Edelstein effect (EE): 1. Large anti-symmetric component of voltage signals. 2. Resonance field shifts. The two features result from non-equilibrium spin density at TSS.
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Al2O3
Bi2Se3
Py
Py
Pt
Large antisymmetric component for Bi2Se3/Py. In contrast, symmetric signals dominate for Pt/Py (without EE).
The resonance field shifted when applying dc current. From the shifts, magnitude of field-like torques can be determined.
They did not do Bi2Se3 thickness dependence measurement, so it’s still hard to extract the EE.
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Structure Journal method Spin-charge ratio Importance
PRL 114, 257202 (2015) (S. Oh)
ST-FMR 300K: 0.047 50K: 0.42
Large Low T spin torque ratio of Bi2Se3
“Signature” of RT EE
Al2O3
Bi2Se3
Co40Fe40B20
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Large antisymmetric component of voltage.
Spin-charge ratio was greatly enhanced at low T. But the RT values are two order of magnitudes smaller than that from the Cornell group.
They explained the origin of field-like torques with spin texture only qualitatively. They did not resort to the model proposed by the Cornell group.
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Questions
1. Does ferromagnetic metal suppress topological surface states?
Yes. (A. Fert and E. Saitoh)
2. Can spin pumping distinguish surface and bulk effects (IEE and ISHE) of Bi2Se3?
It’s difficult for TI/FM, but how about FI/TI?
3. Now that ST-FMR have shown the signature of EE with large field-like torques, which come from non-equilibrium spin density, is it possible to observe similar effect (IEE) with spin pumping?
Note that in A. Fert’s work they did not deposit Fe directly on Sn. A Ag layer may weaken the effect of non-equilibrium spin density, which is localized, on Fe. That is, the Ag layer separate Fe and Sn out of the range of exchange coupling. Therefore, “signatures (negative field shift)” of IEE were not observed.
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More questions
• How does the ac component of the pumped spin current affect the TSS?
• How does spin canting of TSS affect the spin transport properties?
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Spin texture of Bi2Se3
Large Rashba splitting of 2DEG in Bi2Se3 has been confirmed by ARPES. The interplay between TSS and 2DEG leads to intricate spin texture.
The spin pumping effect strongly depends on the interface electronic structure and spin texture.
The spin transport of topological interface state near a magnetic layer is of further interest to investigate.
King et. al., PRL 107, 096802 (2011) Bahramy et. al., Nat. Commun. 3, 1159 (2012)