Supplementary Material
Determination of intrinsic spin Hall angle in Pt
Yi Wang, Praveen Deorani, Xuepeng Qiu, Jae Hyun Kwon, and Hyunsoo Yang
Department of Electrical and Computer Engineering, National University of
Singapore, 117576, Singapore
S1- Analysis of the symmetric part in ST-FMR signals
We carried out the microwave-network analysis measurement to calibrate the RF
current (Irf) in our samples by a Vector Network Analyzer (VNA, Agilent PNX-X
Network Analyzer, N5245A). The calibration schematic diagram is presented in Fig.
S1. We connected two same length RF cables, two nominally same Bias-Tees, and
two GSG probes and make GSG probes contacted on a “through” on a standard
calibration kit. Here we assume each half of the circuit is the same and no power loss
or reflection in the “through”. Hence, we identified the power loss in the Bias-Tee, 1
meter long RF cable, and GSG probe during the transmission by moving the
calibration surface outside the measured circuit (denoted by the black dashed line).
From the measured S11 and S21 parameters, the total power loss in the cables
and connectors in our ST-FMR measurement was found to be 75% of the total input
power. Thus, using 25% of power (13 dBm = 19.95 mW) in the equation
P  I rf 2 Z m 2 , we can calculate the Irf in different Pt (6 nm)/Ni81Fe19 (Py, 2 ‒ 10 nm)
devices, respectively.
We then used the following equations [S1] to obtain the spin Hall angle from the
symmetric part of ST-FMR signal separately,
Sym(Vmix )  
I rf  cos  H dR 0 1
0
M st /E , and  m   s /
 ST Fsym (H ext ) ,  s  J s /E   ST
4
d H

where Sym (Vmix) is the symmetric component of the ST-FMR signal, Irf is the RF
1
current flowing through the device, R is the anisotropic magnetoresistance as a
function of angle  between Irf and magnetic field Hext,  is the linewidth of
0
ST-FMR signal, Fsym (Hext) is a symmetric Lorentzian,  ST
is the spin torque on unit
Ni81Fe19 (Py) moment by spin currents at  H = 0o,  s is the spin Hall conductivity,
 is the conductivity, t is the thickness of Py, E is the microwave field, and  m is
the measured spin Hall angle, respectively.
Vector Network Analyzer (VNA)
Calibration
Surface
Bias-Tee
Bias-Tee
RF cable
GSG probe
“Through” on calibration kit
Figure S1: The calibration schematic diagram to calibrate the RF current (Irf) in our
samples by a Vector Network Analyzer (VNA).
We have plotted together the Py thickness dependent spin Hall angle from both
methods (by taking the ratio of the symmetric (S) and antisymmetric components (A)
of the ST-FMR signals, and separate calibration) in Fig. S2. The error bars are from
the slight uncertainty of the measurement angle in dR /d H . We find that there is not
a significant difference between the results from the two measurement techniques.
Results from both methods show that the measured spin Hall angle increases as the Py
thickness increases in thin Py thickness range. This confirms that the thickness
dependent spin Hall angle does not originate from the in-plane effective-field
component of current-induced spin torque when the Py layer is thin.
2
Ratio S/A
T = 300 K
Separate calibration
0.12
m
0.09
0.06
0.03
0
2
4
6
tNiFe (nm)
8
10
Figure S2: The Py thickness dependent spin Hall angle obtained by taking the ratio of
the symmetric (S) and antisymmetric components (A) of the ST-FMR signals, and
separate calibration method only by symmetric components (S).
S2- The magnetic field angle  for the largest ST-FMR signals
The
Vmix 
spin
torque
ferromagnetic
resonance
(ST-FMR)
signal
is
dR
cos ( H ) , where  H is the angle between the magnetic field and applied
d H
RF current Irf [S2]. The resistance of the Pt/Py microstrip can be written as
R  R0  R cos 2 ( H ) due to the anisotropic magnetoresistance (AMR) effect.
Consequently,
dR
 2R sin ( H ) cos ( H )  sin ( H ) cos ( H ) [maximum value is
d H
occurred at  H = 45o], and Vmix  cos 2 ( H ) sin ( H ) [maximum value is achieved at
 H ~ 35]. Thus, although the change of AMR is maximum at  H = 45, the largest
ST-FMR signals is achieved at  H ~ 35.
S3- Possible sources of measurement artifact
Heating effect due to input RF Power (P)
Figure S3(a) shows the measured ST-FMR signals on Pt (6 nm)/Py (5 nm) device
at a nominal input RF power (P) spanning from 9 to 16 dBm (i.e. 7.95 – 39.8 mW ) at
f = 8 GHz and T = 300 K. The extracted peaks of ST-FMR signals (open symbols) as
3
a function of P are plotted in Fig. S3(b) with a linear fit (solid line). From this
observation, we find that the response of our device is in the linear regime up to P =
16 dBm (39.8 mW). As shown in Fig. S3(c), the measured spin Hall angle  m
remains constant as a function of P at T = 300 K. This indicates that there is no
significant heating effect in our ST-FMR measurements.
Device impedance (Zm)
As shown in Fig. S3(d), we confirm that  m determined from a Pt (6 nm)/Py (5
nm) device is independent of device impedances (Zm) ranging from 33 to 60 Ω at f = 8
GHz, with an input RF power P = 13 dBm and T = 300 K.
50
(a)
9 dBm
10 dBm
11 dBm
12 dBm
13 dBm
T = 300 K
f = 8 GHz
0
-50
90
Vmix (V)
Vmix (V)
100
14 dBm
15 dBm
16 dBm
500
1000
1500
(b)
60
30
0
10
Hext (Oe)
(c)
20
30
40
P (mW)
T = 300 K
f = 8 GHz
0.09
m
m
0.09
Data
Fitting
0.06
(d)
T = 300 K
f = 8 GHz
0.06
0.03
0.03
9
10
11
12
13
14
15
32
16
36
40
44
48
52
56
60
Zm ()
P (dBm)
Figure S3: (a) The measured ST-FMR signals on a Pt (6 nm)/Py (5 nm) device at
different nominal input RF power P (dBm) at f = 8 GHz and 300 K. (b) The extracted
peaks of ST-FMR signals (open symbols) as a function of P (mW) with a fit (solid
line). (c) Measured spin Hall angle m determined from a Pt (6 nm)/Py (5 nm) device
as a function of P. (d) m as a function of impedance Zm at f = 8 GHz. The red dashed
lines are guides to the eye.
4
Magnetic field component (Hem) of electromagnetic wave
As shown in Fig. S4(a), in addition to the RF-current induced Oersted field (Hrf)
and spin current Js, the Oersted field (Hem) due to RF signals transmitting along the
coplanar waveguide (CPW) may exist and exert torque (  m̂  H em ) on the Py layer.
The out-of-plane component of Hem also yields symmetric Lorentzian peaks with the
same signals for both directions of Hext [S3, S4], which could lead to a slight
overestimation or underestimation of S/A depending on the Hext direction, and thus the
spin Hall angle sh . In our work, as shown in Fig. S4(b), the effect caused by Hem
was eliminated by locating the microwave GSG probe at a proper position around the
center of CPW, yielding the same amplitude of S/A and sh with both directions of
Hext. Furthermore, we have made a control ST-FMR device Pt (6 nm)/Py (5 nm) with
symmetric CPW as shown in Fig. S4(c). The measured spin Hall angle is ~ 0.063 at 8
GHz and room temperature. This value is consistent with what we obtained in our
manuscript (0.063) by using the Pt (6 nm)/Py (5 nm) device as shown in Fig. 3S(b).
z
(a)
x
W
y
Hem
Jc
Js
L
Pt
NiFe
Hrf
Pt/Py strip
(b)
(c)
ST-FMR device
G
S
G
GSG Probe
G
S
G
Figure S4: (a) The Pt/Py microstrip with the charge current Jc, spin current Js, RF
Oersted field (Hrf), and the Oersted field (Hem) due to RF signals transmitting along
the coplanar waveguide (CPW). (b) The layout of CPW for the ST-FMR devices used
in our ST-FMR measurements. (c) The layout of the CPW for the control ST-FMR
device.
5
S4- Meff vs. Ms at different Py thicknesses
As shown in Fig. S5(a), the 4πMeff (from the Kittel fitting) decreases
dramatically as the Py thickness decreases from 10 to 2 nm. The saturation
magnetization Ms of Py at different thicknesses were independently measured by
vibrating sample magnetometer (VSM). As shown in Fig. S5(b), it is found that there
is a discrepancy (～33% for 2 nm Py and ～11.6 % for 3 nm Py) between Meff and
measured Ms, which indicates a weak perpendicular anisotropy at the Pt/Py interface,
calculated from 4 M eff  4 M s  2 Ks /(M st ) , where Ks is the perpendicular interface
anisotropy, and t is the thickness of the Py layer. When t > 4 nm, the discrepancy
almost disappears.
4Meff (T)
1.0
(a)
4Meff
0.8
T = 300 K
0.6
0.4
(Ms-Meff)/Ms (%)
30
(b)
T = 300 K
20
10
0
1
2
3
4
5
6
tNiFe (nm)
7
8
9 10
Figure S5: The 4πMeff (a) and the difference (b) between Ms and Meff as a function of
Py thickness at 300 K.
S5- Damping constant  eff for different Py thicknesses
The linewidth (∆H) was extracted from the fitting of ST-FMR signal. Accordingly,
the effective damping constant  eff was determined by  eff   (H )/2 f [S2, S5]
and was found to increase from 0.0123 (Py = 10 nm) to 0.063 ± 0.003 (Py = 2 nm), as
seen in Fig. S6. This could be possibly attributed to the spin pumping effect [S6, S7],
6
film inhomogeneous broadening, and/or two-magnon scattering [S8].
Damping Constant
0.07
T = 300 K
0.06
0.05
0.04
0.03
0.02
0.01
1
2
3
4
5
6
7
tNiFe (nm)
8
9 10
Figure S6: The effective damping constant  eff as a function of Py thickness at 300
K.
S6- Estimation of spin pumping contributions in ST-FMR signals
The possible existence of spin pumping contribution to the symmetric
components of the ST-FMR signals might also cause the Py thickness dependent spin
Hall angle. In order to clarify this and confirm our claim in the main text, we have
estimated the spin pumping contribution for samples covering the full range of
different Py thicknesses by the following equations [S1].
VSP   m
eW S R
t
eff
tanh ( Pt )Re(g
)P2 sin ( H ) H ext /(H ext  4 M eff ) ,
2
2S
P 
1
2
dR /d H I rf
S 2  A2 ,
where VSP is the spin pumping signal in our ST-FMR measurements, W is the
microstrip width, R is the device resistance, λS is the spin diffusion length in Pt, m is
eff
the measured spin Hall angle, tPt is the Pt thickness, Re( g
) is the real part of the
effective spin mixing conductance ( 2×1019 m-2), H is the angle between Irf and
magnetic field Hext, Irf is the RF current flowing through the device, P is the
maximum precession angle in the device plane, S and A are the symmetric and
antisymmetric components of the ST-FMR signal, respectively. The estimated spin
pumping contribution VSP together with S as a function of Py thickness are shown in
Fig. S7. We have found that the estimated spin pumping signals for all the devices in
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the full range of different Py thicknesses are extremely small (all less than 0.75 V) as
compared to the measured symmetric component S (tens of V) in our ST-FMR
measurements. The ratios of VSP/S are less than 4%. Hence, we confirm that the spin
pumping contributions in our ST-FMR measurements are negligible and will not
cause the Py thickness dependent spin Hall angle shown in Fig. 3(a) in the main text.
30
V (uV)
25
20
15
Measured S
Estimated VSP
10
5
0
0
2
4
6
tNiFe (nm)
8
10
Figure S7: The estimated spin pumping contribution VSP together with symmetric
component S as a function of Py thickness.
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