mse 7025 magnetic materials (and spintronics)cfpai/mse7025/mse7025_lecture12_halleffect.pdf · (and...
TRANSCRIPT
![Page 1: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/1.jpg)
MSE 7025 Magnetic Materials
(and Spintronics)
Chi-Feng Pai [email protected]
Lecture 12: Transport measurements Episode I: Family of the Hall effect
![Page 2: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/2.jpg)
Course Outline • Time Table
Week Date Lecture
1 Feb 24 Introduction
2 March 2 Magnetic units and basic E&M
3 March 9 Magnetization: From classical to quantum
4 March 16 No class (APS March Meeting, Baltimore)
5 March 23 Category of magnetism
6 March 30 From atom to atoms: Interactions I (oxides)
7 April 6 From atom to atoms: Interactions II (metals)
8 April 13 Magnetic anisotropy
9 April 20 Mid-term exam
10 April 27 Domain and domain walls
![Page 3: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/3.jpg)
Course Outline • Time Table
Week Date Lecture
11 May 4 Magnetization process (SW or Kondorsky)
12 May 11 Characterization: VSM, MOKE
13 May 18 Characterization: FMR
14 May 25 Transport measurements in materials I: Hall effect
15 June 1 Transport measurements in materials II: MR
16 June 8 MRAM: TMR and spin transfer torque
17 June 15 Guest lecture (TBA)
18 June 22 Final exam
![Page 4: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/4.jpg)
Transport measurement
• In solid state physics and condensed matter physics, one wants to study the “transport properties.”
I
V
![Page 5: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/5.jpg)
Transport measurement
• In solid state physics and condensed matter physics, one wants to study the “transport properties.”
![Page 6: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/6.jpg)
Transport measurement
• In solid state physics and condensed matter physics, one wants to study the “transport properties.”
I
VH
, , , ...T T
![Page 7: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/7.jpg)
Transport measurement
• Out-of-plane field
– Hall voltage VH
– Hall effect
– Anomalous Hall effect
• In-plane field
– Resistance ~ V/I
– Magnetoresistance
– Anisotropic MR
I
V
H I
V
H
x xx xJ E y yx xJ E
![Page 8: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/8.jpg)
Transport measurement
• Out-of-plane field
• In-plane field
I
V
H I
V
H
![Page 9: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/9.jpg)
The Hall effect
• Family of the Hall effect
– Ordinary Hall effect (metals, 1879)
– Anomalous Hall effect (magnetic metals, 1880)
– (Extraordinary Hall effect)
• Modern family of the Hall effect
– Quantum Hall effect (2DEG, 1985 Nobel prize in physics)
– Fractional quantum Hall effect (2DEG, 1998 Nobel prize in physics)
– Quantum anomalous Hall effect (topological insulators, 2010s)
– Spin Hall effect (metals, 2000s)
– Quantum spin Hall effect (topological insulators, 2010s)
![Page 10: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/10.jpg)
The Hall effect
• The Hall effects
Weng et. al., From the Anomalous Hall Effect to the Quantum Anomalous Hall Effect, arXiv (2015)
![Page 11: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/11.jpg)
The Hall effect
• The Hall effects
Cui-Zu Chang and Mingda Li, Journal of Physics: Condensed Matter, 28, 12 (2016)
![Page 12: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/12.jpg)
The Hall effect
• Edwin Hall, Johns Hopkins University, 1879 – PhD student under Henry Rowland
– Read Maxwell’s Electricity and Magnetism and had doubts
– Carried out experiments
– Published “On a new action of the magnet on electric currents” at 24
• Experimental
1y HH
x z
E V tR
j B IB ne
![Page 13: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/13.jpg)
The Hall effect
• Edwin Hall, Johns Hopkins University, 1879 – PhD student under Henry Rowland
– Read Maxwell’s Electricity and Magnetism and had doubts
– Carried out experiments
– Published “On a new action of the magnet on electric currents” at 24
• Experimental
1y HH
x z
E V tR
j B IB ne
0.0 0.5 1.0 1.5 2.0
0
20
40
60
RH=0.510
-11m
3C
-1
VH (
V)
V
H (V
)
W(4nm)
Bext
(T)
RH=10.10
-11m
3C
-1
0
2
4
6
8
10
W(10nm)
![Page 14: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/14.jpg)
The Hall effect
• Edwin Hall, Johns Hopkins University, 1879 – PhD student under Henry Rowland
– Read Maxwell’s Electricity and Magnetism and had doubts
– Carried out experiments
– Published “On a new action of the magnet on electric currents” at 24
• Experimental
0.0 0.5 1.0 1.5 2.0
0
20
40
60
RH=0.510
-11m
3C
-1
VH (
V)
V
H (V
)
W(4nm)
Bext
(T)
RH=10.10
-11m
3C
-1
0
2
4
6
8
10
W(10nm)
![Page 15: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/15.jpg)
The Hall effect
• The Hall conductivity
Schultz et. al., PRB 45, 10886 (1992)
2 32
0 33 2
kdfe d kk v k
d
2 32 3
3
1
6 2
k
H
dfe d kk v k
k d
2
0
1/ 0H HR
ne
2
0 *
Fne k
m
Free-electron approximation F
![Page 16: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/16.jpg)
The Hall effect
• The Hall conductivity – Cannot be directly calculated from free electron model
– Related to the details of Fermi surface
http://www.phys.ufl.edu/fermisurface/
![Page 17: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/17.jpg)
Anomalous Hall effect
• Anomalous Hall effect – Also observed by Edwin Hall
– The Hall effect in (ferro) magnetic materials
– Or the Hall effect in materials with intrinsic magnetic moments
0.0 0.5 1.0 1.5 2.0
0
20
40
60
RH=0.510
-11m
3C
-1
VH (
V)
V
H (V
)
W(4nm)
Bext
(T)
RH=10.10
-11m
3C
-1
0
2
4
6
8
10
W(10nm)
0.0 0.5 1.0 1.5 2.0 2.5
0
200
400
600
VH (
V)
Bext
(T)
VH (V
)
CFB(1.7nm)/W(4nm)
0
20
40
60
80
100
CFB(10nm)/W(10nm)
W thin films W/CoFeB bilayer films
![Page 18: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/18.jpg)
Anomalous Hall effect
• Anomalous Hall effect – Also observed by Edwin Hall
– The Hall effect in (ferro) magnetic materials
– Or the Hall effect in materials with intrinsic magnetic moments
xy O z A zR H R M
Co thin films CoFeB PMA thin films
A OR R
![Page 19: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/19.jpg)
Anomalous Hall effect
• Anomalous Hall effect – Also observed by Edwin Hall
– The Hall effect in (ferro) magnetic materials
– Or the Hall effect in materials with intrinsic magnetic moments
xy O z A zR H R M
2 2/xy xy xx xy xx xy xy Weng et. al., From the Anomalous Hall Effect to the Quantum Anomalous Hall Effect
A OR R
AR M
0xy O z A zR H R M
![Page 20: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/20.jpg)
Anomalous Hall effect
• From spin-orbit interaction
• Possible mechanisms – Intrinsic
– Side-jump (Extrinsic)
– Skew-scattering (Extrinsic)
N. Nagaosa et al., ROMP 82 1539 (2010)
S. Onoda et al., PRL 97 126602 (2006)
(Berry curvature)
![Page 21: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/21.jpg)
Anomalous Hall effect
• From spin-orbit interaction
• Possible mechanisms – Intrinsic
– Karplus-Luttinger (1954)
– “Anomalous velocity” or “Berry phase curvature”
N. Nagaosa et al., ROMP 82 1539 (2010)
(Berry curvature)
![Page 22: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/22.jpg)
Anomalous Hall effect
• From spin-orbit interaction
• Possible mechanisms – Intrinsic
– Spin-dependent Hall “angle”
(Berry curvature)
Ferromagnetic material
Paramagnetic material
Non-zero
![Page 23: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/23.jpg)
Anomalous Hall effect
• Calculations
N. Nagaosa et al., ROMP 82 1539 (2010)
Tons of Green’s function calculations…
![Page 24: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/24.jpg)
But wait, what is a spin current?
• (charge) Current
• Spin-polarized current
• Spin current
e
e
e e
e
e
e
e
e
e
e
e
ˆ ˆsJ s v
![Page 25: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/25.jpg)
But wait, what is a spin current?
• Anomalous Hall effect
• Spin Hall effect
e
e
e
e
e
e
e e
e
xJ
e
xJ
0
0
e
y
s
y
J
J
0
0
e
y
s
y
J
J
![Page 26: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/26.jpg)
How to measure, anyway?
• Which of the following is the recommended way to measure Hall effect?
![Page 27: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/27.jpg)
How to measure, anyway?
• Van der Pauw method
– Proposed by L. J. van der Pauw in 1958 (Philips)
– If you have an extended film or a uniform sample with no holes on it
– If you want to measure both resistivity and Hall coefficient
The ideal bridge-type sample Arbitrary-shaped sample
![Page 28: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/28.jpg)
How to measure, anyway?
• Van der Pauw method
• Resistivity Relative errors if P is not ideal
![Page 29: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/29.jpg)
How to measure, anyway?
• Van der Pauw method
• Hall effect (coefficient) Relative errors if P is not ideal
![Page 30: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/30.jpg)
How to measure, anyway?
• Van der Pauw method
, ,exp exp 1MN OP NO PM
d dR R
,
1H MO NP
dR R
ne B
ne
1
Get (Resistivity)
Get (major carrier density)n
Get (mobility)
![Page 31: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/31.jpg)
How to measure, anyway?
• But of course, Hall-bars are always better (if you have time and money!)
![Page 32: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/32.jpg)
How to measure, anyway?
• In mesoscopic regime, one has to be careful…
Quasi-ballistic transport
G. Mihajlovic et. al., PRL 103, 166601 (2009)
(But experimentally not the case)
![Page 33: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/33.jpg)
What can we extract (from AHE signals)?
• Many useful information
cH
anH
Out-of-plane field AHE voltage
In-plane field AHE voltage
In-plane field 2nd harmonic AHE voltage
SOT
DLHSOT
FLH
![Page 34: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/34.jpg)
The spin Hall effect
e-
e-
e-
e-
Js Je
J. E. Hirsch, Phys. Rev. Lett. 83 1834 (1999)
ˆS SH eJ J
M. I. Dyakonov and V. I. Perel, JETP 13 467 (1971)
Spin-orbit interaction
The spin Hall angle
/SH s eJ J
![Page 35: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/35.jpg)
Possible mechanisms
• Intrinsic
• Side jump
• Skew scattering
( )1( )n k e
r E kk
extrinsic
Berry curvature
N. Nagaosa et al., Rev. Mod. Phys. 82 1539 (2010) T. Fujita et al., J. Appl. Phys. 110 121301 (2011)
![Page 36: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/36.jpg)
Demonstration of the SHE
Spin Hall Effect in semi conductor (GaAs) - Optical detection Y.K. Kato et al., Science 306 1910 (2004)
Spin Hall Effect in metallic system (Al) -Transport measurement -Inverse SHE voltage S.O. Valenzuela et al., Nature 442 176 (2006)
4~10Al
SH
![Page 37: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/37.jpg)
The SHE in Pt
• Pt is a heavy element large spin-orbit interaction possible large intrinsic spin Hall effect1
• Experiments were carried out
by several groups with different
techniques2
1Guo et al., Phys. Rev. Lett. 100 096401 (2008) 2Kimura, T., et al, Phys. Rev. Lett. 98, 156601 (2007) Ando, K. et al. Phys. Rev. Lett. 101, 036601 (2008) Mosendz, O. et al., Phys. Rev. Lett. 104, 046601 (2010)
θSH = 0.003 ~ 0.08 (?)
![Page 38: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/38.jpg)
The spin Hall conductivity (intrinsic)
• If due to intrinsic mechanism
• Spin current operator
![Page 39: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/39.jpg)
The calculated SHC of transition metals
• The spin Hall conductivity calculated for 4d 5d elements
• ab initio calculation: θSH(Ta)<0 and θSH(Pt)>0
for highly resistive case, θSH(Ta) can be large
Tanaka, T. et al, Phys. Rev. B 77, 165117 (2008)
![Page 40: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/40.jpg)
Demonstration of the GSHE in beta-Ta
DC current induced SHE-ST switching
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
60
80
100 B
ext = -3.5 mT
dV
/dI
(k
)
IDC
(mA)
Schematics of a SHE-3T device
-Ta 0.12 0.04SH
Pt 0.06SH
![Page 41: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/41.jpg)
e-
Ta
e-
e- Je
Js
CoFeB
CoFeB
MgO
V
![Page 42: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/42.jpg)
QHE and QSHE
• Next semester: Contemporary Solid State Materials in a Nutshell
(Regular insulators)
(High field effect, Landau level)
(Topological insulators)
0sJ
0sJ
![Page 43: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/43.jpg)
QHE and QAHE
• Next semester: Contemporary Solid State Materials in a Nutshell
![Page 44: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/44.jpg)
QHE and QAHE
• Next semester: Contemporary Solid State Materials in a Nutshell
http://www.sp.phy.cam.ac.uk/
![Page 45: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/45.jpg)
QHE and QAHE
• Next semester: Contemporary Solid State Materials in a Nutshell
Y. Tokura group (2014)
topological insulator Crx(Bi1 − ySby)2 − xTe3
Qi-Kun Xue group, Science (2013)
![Page 46: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/46.jpg)
QHE and QAHE
• Next semester: Contemporary Solid State Materials in a Nutshell
![Page 47: MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture12_HallEffect.pdf · (and Spintronics) Chi-Feng Pai cfpai@ntu.edu.tw Lecture 12: Transport measurements Episode](https://reader033.vdocuments.site/reader033/viewer/2022042622/5fa28cc51276a009eb40cec9/html5/thumbnails/47.jpg)
Topological (skyrmion) Hall effect
• In skyrmion lattice
• In a magnetic heterostructure