Spin Hall Angle Quantification from Spin Pumping and Microwave Photoresistance

Abstract

We present a method to quantify the spin Hall angle (SHA) with spin pumping
and microwave photoresistance measurements. With this method, we separate the
inverse spin Hall effect (ISHE) from other unwanted effects for permalloy/Pt
bilayers using out-of-plane microwave excitation. Through microwave
photoresistance measurements, the in- and out-of-plane precessing angles of the
magnetization are determined and enabled for the exact determination of the
injected pure spin current. This method is demonstrated with an almost perfect
Lorentz line-shape for the obtained ISHE signal and the frequency independent
SHA value as predicted by theory. By varying the Pt thickness, the SHA and
spin-diffusion length of Pt is quantified as 0.012 (0.001) and 8.3 (0.9) nm,
respectively.

Full text

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PHYSICAL REVIEW B 85, 214423 (2012)
Spin Hall angle quantification from spin pumping and microwave photoresistance
Z. Feng,1J. Hu,1L. Sun,1B. You,1,*D. Wu,1J. Du,1W. Zhang,1A. Hu,1Y. Yang,2D. M. Tang,2B. S. Zhang,2and H. F. Ding1,*
1National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road,
Nanjing 210093, P. R. China
2School of Electronic Science and Engineering, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
(Received 21 March 2012; published 20 June 2012)
We present a method to quantify the spin Hall angle (SHA) with spin pumping and microwave photoresistance
measurements. With this method we separate the inverse spin Hall effect (ISHE) from other unwanted
effects for permalloy/Pt bilayers using out-of-plane microwave excitation. Through microwave photoresistance
measurements, the in- and out-of-plane precessing angles of the magnetization are determined and enabled for
the exact determination of the injected pure spin current. This method is demonstrated with an almost perfect
Lorentz line shape for the obtained ISHE signal and the frequency independent SHA value as predicted by
theory. By varying the Pt thickness, the SHA and spin-diffusion length of Pt is quantified as 0.012 ± 0.002 and
8.3 ± 0.9 nm, respectively.
DOI: 10.1103/PhysRevB.85.214423PACS number(s): 75.76.+j, 85.75.−d, 72.25.Pn, 73.50.Jt
I. INTRODUCTION
Electrons have two fundamental properties: the charge and
the spin. Over the past, information technology has made
tremendous progress, even though primarily only the charge
property of the electrons was used. One can image that adding
the usage of the spin property will enrich the functionalities of
the devices. More importantly, pure spin devices may provide
apotentialsolutionforthepowerconsumptionproblem,which
becomes increasingly serious with the speed acceleration and
sizereductionofthemicroelectronicdevices.1Thedetectionof
a spin current, however, is not easy. Optical detection has been
successfully used for observation of spin accumulation,2–4but
this method is limited to semiconductor systems that typically
have long spin diffusion lengths. A more general solution is
to convert the spin current to the charge current, which is the
basis for existing technology. Therefore, the conversion of the
spinandchargecurrentsisoneofthekeyissuesforspintronics
technology.
The spin Hall effect (SHE) refers to the generation of
a spin current transverse to an applied charge current in
a paramagnetic metal or a doped semiconductor.5,6Con-
currently, a spin current can also give rise to a transverse
charge current, which is called the inverse spin Hall effect
(ISHE). The efficiency of the spin-charge conversion can be
quantifiedbyasinglematerial-specificparameter,i.e.,thespin
Hall angle (SHA), θSH. It is defined as the ratio of the spin
Hall and charge conductivities.7The SHA can be measured
through the nonlocal magnetotransport measurements8–12or
the method based on spin pumping due to ferromagnetic
resonance (FMR).13–20Because of the complexity of the
interface effect, it is typically difficult to estimate the exact
amplitude of the injected pure spin current with the first
method. The second method is of more advantage as the above
difficultycanberemovedwithadditionalFMRmeasurements.
Surprisingly, the experimentally reported values are quite
different for nominally identical materials, even for similar
methods utilizing spin pumping. For instance, the measured
SHA value for Pt varied between 0.0067 and 0.08.15–18,21
With a literature value of the spin diffusion length, λsd =
10 nm, Mosendz et al., reported the SHA for Pt to be 0.006715
and later refined it to 0.013 after correcting for the elliptical
magnetization precessing trajectory.16Using the same spin
diffusion length, the measurements of Ando et al., however,
show a value of 0.04.18With the Pt thickness-dependent
measurements,Azevedoetal.obtainedaSHAvalueof0.04(in
their original paper the value is 0.08, however, their definition
is a factor 2 larger than the one that commonly used) and
a spin diffusion length of 3.7 ± 0.2 nm.17The discrepancy
may be related to the fact that the ISHE signal is typically
mixed with the unwanted effects related to the anisotropic
magnetoresistance (AMR) effect.15–17Therefore, the correct
separation of the ISHE signal from the other effects is crucial
for the SHA estimation. In addition, the measured ISHE
voltage is closely related to the SHA and the amplitude of the
injected pure spin current as well as the spin diffusion length.
In such a case, the correct measurements of the amplitude of
the injected pure spin current and the spin diffusion length are
also very essential. This, however, is not easy. For example,
the effective microwave magnetic field hrf acting on the
magnetic layer can be different even with the same microwave
power input, as it also depends on the thicknesses of both the
ferromagnetic (FM) and nonmagnetic (NM) layers.
In this paper we present a method to separate the ISHE
from other effects for permalloy (Py)/Pt bilayers with an
out-of-plane microwave excitation. The successful separation
is demonstrated with an almost perfect Lorentz line shape
for the obtained signal and the frequency independent SHA
value. Instead of using the microwave magnetic field hrf
to calculate the in- and out-of-plane precessing angles of
the magnetization, we directly measure them through the
microwave photoresistance measurements.22–24This allows
for the exact estimation of the injected pure spin current for
individual samples. With varying the Pt thickness, the SHA
and spin-diffusion length of Pt are quantified.
II. THEORY
The basic theory of utilizing the spin pumping effect for
measuring the SHA has been described in Refs. 15 and 16.
For the reader’s convenience, we briefly summarize it below.
Spin pumping during the excitation of FMR occurs when
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Z. FENG et al.
PHYSICAL REVIEW B 85, 214423 (2012)
FIG. 1. (Color) (a) Schematic illustration of the inverse spin
Hall effect induced by spin pumping in a FM/NM bilayer system.
(b) Experimental setup for spin pumping-induced inverse spin Hall
effect and microwave photoresistance measurements.
the precession of the magnetization in a FM layer injects a
pure spin current into an adjacent NM layer, as shown in
the schematic picture in Fig. 1(a).25–27Due to the ISHE, the
injected pure spin current creates a transverse voltage, i.e., the
inverse spin Hall voltage induced by spin pumping VSP
Taking into account the spin relaxation and diffusion in the
NM layer, the dc part of pure spin current density along the
y direction can be written as
ISHE.13–18
js(y) = j0
s
sinh[(tN− y)/λsd]
sinh(tN/λsd)
,
(1)
wheretNandλsdarethethicknessandthespin-diffusionlength
of NM layer, respectively. j0
FM/NM interface (y = 0), and it is related to the effective spin
mixing conductance g↑↓
precessing angle of the FM. Following the basic theory of
FMR, its magnetic field (H) dependence can be written as
sis the spin-current density at the
eff, the microwave frequency f, and the
j0
s(H) =¯ h
2g↑↓
efffα1β1
?H2
(H − H0)2+ ?H2,
(2)
where H0is the resonance magnetic field, ?H is the half-
width of the FMR linewidth, and α1and β1are the maximum
amplitudes of the in- and out-of-plane precessing angles of
the magnetization, respectively. Due to the ISHE, the pure
spin current js(y) gives rise to a transverse charge current
?jc(y) = θSH(2e
¯ h)js(y)[? n × ? σ], where ? n is the direction of the
purespincurrent,and ? σ isthepolarizationvectorofthedcspin
current. The charge current flowing along the NM layer (with
length L, width w, and resistance RN) generates a voltage,
i.e., VSP
direction, the field dependence can be written as
?
× tanh
2λsd
ISHEalong the z direction. By integrating along the y
VSP
ISHE(H) = RN
(?jc(y) • ˆ z)ds = θSHλsdg↑↓
?tN
efffewRN
?
α1β1sinα0
?H2
(H − H0)2+ ?H2,
(3)
where α0is the angle between H and the z axis, as shown in
Fig. 1(a). From the previous equation, we see that VSP
Lorentz line-shape signal as a function of H.
In any real measurements, VSP
another voltage (VAMR) due to AMR. VAMRis the spin rectifi-
cation voltage caused by the induction current I1cos(ωt) and
the oscillating resistance R(t) = R0− RAsin2[α0+ α1(ωt)]
caused by the AMR effect in the FM stripe.15–17,22,24For
out-of plane hrf (corresponding to our experimental setup),
the voltage can be written as22,24
ISHEhas a
ISHEis often accompanied by
VAMR(H) = −I1RAα1sin2α0
2
?
?H2
(H − H0)2+ ?H2cosφ
?
−
(H − H0)?H
(H − H0)2+ ?H2sinφ,
(4)
where RAis the resistance difference when magnetization is
parallel and perpendicular to the stripe, and φ is the phase
difference between the rf current and the magnetization at
resonance.
Fromthepreviousdiscussion,wecanfindthatthemeasured
voltage signal can have two components, V = VSP
VSP
respect to resonance field H0, while VAMR contains both
symmetric and asymmetric contributions. These characters
make it difficult to separate both effects from the symmetry
point of view. To quantify θSH, we however need to distinguish
VSP
obtain other unknown parameters described in Eq. (3), such as
g↑↓
WithcarefulanalysisonecanfindthatVSP
a different dependency with respect to α0. More specifically,
VSP
onsin2α0.Therefore,onecaneliminatetheVAMRcontribution
bychoosingtwospecificgeometries,α0= 90◦andα0= 270◦,
where VAMR= 0 and VSP
In our measurements discussed below, we use this method to
separate VSP
The effective spin-mixing conductance g↑↓
mined by the enhanced Gilbert damping factor due to the
losing spin momentum during spin pumping:13–18
ISHE+ VAMR.
ISHEhas a Lorentz line shape, i.e., it is symmetrical with
ISHEfrom VAMR first. In addition, one needs to correctly
eff, α1, β1, λsd, etc.
ISHEandVAMRhave
ISHEis proportional to sinα0, and VAMRis linearly dependent
ISHEreaches its maximum amplitude.
ISHEfrom the unwanted signals.
effcan be deter-
g↑↓
eff=4πM0tF
gμB
(αF/N− αF).
(5)
The damping factor of FM/NM layer αF/N, and FM layer αF
canbecalculatedfromthelinearfitofthefrequency-dependent
FMR half linewidth ?H through ?H = ?H0+ α2πf
γ is the gyromagnetic ratio and ?H0is the fitting parameter.
γ, where
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SPIN HALL ANGLE QUANTIFICATION FROM SPIN ...
PHYSICAL REVIEW B 85, 214423 (2012)
The maximum amplitudes of in- and out-of-plane angles
α1and β1can be determined by microwave photoresistance
effect.22–24Microwave photoresistance is the dc resistance
change in the FMR. The magnetization precession alters the
angle of the magnetization withrespect todc current, resulting
in a change of the time-averaged AMR. For a single FM layer,
the field-dependent microwave photoresistance is given as22
?RF
MW(H) = −RA
2
?α2
1cos2α0+ β2
?H2
(H − H0)2+ ?H2.
1cos2α0
?
×
(6)
When α0= 90◦or α0= 270◦, it can be simplified as
MW(H) =RA
Therefore, α1 can be calculated with Eq. (7) after we take
measurements of ?RF
according to FMR theory,
?
?RF
2α2
1
?H2
(H − H0)2+ ?H2.
(7)
MW. Besides, β1can also be determined
α1
β1
=
1 +Meff
H0
,
(8)
where Meff is the effective magnetization of FM and it can
be obtained through the frequency-dependent resonance field
measurements according to Kittle equation. The real sample
is a double layer which consists of both FM and NM layers.
For this, one needs to make a correction with the assumption
of parallel resistance configuration. At last, the spin diffusion
lengthλsd,togetherwiththeSHAθSH,needtobeobtainedwith
the NM thickness-dependent measurements and the fitting
according to Eq. (3), as we will discuss below.
III. EXPERIMENTS
As shown in Fig. 1(b), the Py/Pt bilayer stripes (in light
gray) are integrated into the slots between the signal and
ground lines (in brown) of a coplanar waveguide (CPW).
In this configuration the magnetic dynamics are excited
with an out-of-plane microwave magnetic field hrf. This
experimentalsetupallowsfortheFMRexcitationforα0= 90◦
and α0= 270◦and the frequency-dependent measurements.
We note that our experimental configuration is similar to the
spin dynamo described by Gui et al.28The stripes’ lateral
dimensions are 2.5 mm × 20 μm, and the thickness of Py
layer is fixed at 20 nm while the thickness of Pt layer varies
from 2 nm to 65 nm. The bilayer stripes are prepared by
photolithography,magnetronsputteringdeposition,andlift-off
onsemi-insulatingGaAssubstrates.ThePtandPythicknesses
are calibrated with x-ray diffraction. Subsequently, a copper
CPW with a 50-? characteristic impendence and the electrical
contacts are fabricated. The measurements are performed at
room temperature (RT). In order to achieve high sensitivity, a
lock-in technique is used. A vector network analyzer (VNA)
supplies to the CPW a CW microwave, which is modulated
with a 51.73 kHz signal. The lock-in amplifier picks up the
voltage signal as a function of external magnetic field H.
The magnetic field H with controllable field strength can be
rotated within the film plane. The angular-dependent FMR
measurements show that the Py/Pt samples typically have an
in-plane magnetic anisotropy of about 0.5 mT. The external
field we used for the ISHE detection is typically two orders of
magnitudelargerthantheanisotropyfield,andthesamplesare
saturated. For the microwave photoresistance measurements,
a constant dc current is applied to the stripe through Keithley
2400 SourceMeter. A 50-k? resistor is used in series with the
SourceMeter to minimize the flowing of the ac voltage signal
into the source branch.
IV. RESULTS AND DISCUSSIONS
Before showing the experimental results, we will first
discuss the criteria for the pure ISHE measurements. As
discussed in the section of theory, the measured voltage
typically contains two parts: VSP
voltagesbeardifferentcharactersduetotheirdifferentphysical
origins. From Eqs. (3) and (4) we learn that VSP
Lorentz line shape and that its magnetic field dependence
shouldbesymmetricwithrespectstotheresonancefield,while
VAMRcontains both symmetric and asymmetric parts. Second,
VSP
on sin2α0. Therefore, we performed the measurements for
α0= 90◦and α0= 270◦, where VSP
amplitude and VAMR= 0. The measured signal for these
two configurations should bear the same magnitude but with
an opposite sign with the same excitation. Third, VSP
generatedbythedccomponentoftheinjectedpurespincurrent
while VAMRis proportional to the induction current and it is
frequency dependent. Therefore, we set up four criteria to
determine the pure ISHE signal: (i) the field dependence of
measured voltage should have a Lorentz line shape; (ii) it has
the opposite sign for α0= 90◦and α0= 270◦; (iii) it has the
same amplitude for α0= 90◦and α0= 270◦with the same
injected pure spin current; and (iv) most importantly, as θSHis
a material specific parameter, it should be independent on the
microwave frequency used for the measurements. Particularly,
theISHEsignalwemeasuredisgeneratedbythedccomponent
of the injected pure spin current.
Figure 2(a) shows a typical result of the measured dc
voltages V as a function of H for α0= 90◦and α0= 270◦
with the same microwave power input. The symbols are the
experimental data, while the lines are the Lorentz fit. The
sample isPy/Pt(15 nm),and thefrequency of themicrowave is
fixedto8GHz.WefindthatbothcurvesareclosetotheLorentz
line shape, and they have opposite sign for α0= 90◦and
α0= 270◦. Therefore, the previously discussed criterion (i)
and(ii)aresatisfied,suggestingtheobtainedsignalsaremainly
caused by the ISHE. One, however, can also find that the
curves have different amplitudes for α0= 90◦and α0= 270◦.
This is, at first glance, in contrast with (iii) even though the
difference between them is not big. As discussed previously,
the criterion (iii) requires a precondition that the injected
pure spin currents are the same for these two configurations.
Even with the same microwave power input, this precondition
may not be necessary fulfilled, as will be discussed below.
From Eq. (2) we can find that the injected pure spin current
is proportional to the product of the effective spin-mixing
conductance, the microwave frequency, and in- and out-of-
plane precessing angles, i.e., g↑↓
the spin-mixing conductance and the microwave frequency
ISHEand VAMR. These two
ISHEhas a
ISHEis proportional to sinα0, and VAMRis linearly dependent
ISHEreaches its maximum
ISHEis
efffα1β1. For a given sample
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Z. FENG et al.
PHYSICAL REVIEW B 85, 214423 (2012)
FIG. 2. (a)Themeasuredmagneticfield-dependentdcvoltagesV
(f =8GHz)forthesampleofPy/Pt(15nm)atα0= 90◦(solidsquare)
and α0= 270◦(open circle). (b) The magnetic field-dependent
microwave photoresistance for the same sample at α0= 90◦(solid
square)andα0= 270◦(opencircle)underthesamemicrowavepower
input.
are fixed; the precessing angles, α1and β1, can be determined
by the microwave photoresistance measurements,22,23as also
discussed in Eqs. (6)–(8).
The microwave photoresistance measurements are per-
formed for the same Py/Pt sample at α0= 90◦and α0= 270◦
with the same input microwave power used for the above
measurements. To eliminate the influence of VSP
positive/negative dc currents I0 (=2.5 mA) are used, and
microwave photoresistance of Py/Pt bilayers is obtained by
their difference: ?RF/N
Rb, the background resistance which can be determined
experimentally. In addition, the modulation frequency 51.73
kHz is high enough to exclude the bolometric effect at
resonance.23Figure 2(b) shows the results of ?RF/N
function of the applied magnetic field H. The symbols are the
experimental data while the lines are the Lorentz fit. They
also have a Lorentz line shape, corresponding to Eq. (7),
and more importantly, they are different for α0= 90◦and
α0= 270◦, suggesting that the precessing angles for these two
configurations are different even though the same microwave
power is used. We can find that ?RF/N
which is consistent with the relationship for the magnitude
of the measured voltages for these two configurations. To
ISHE, additional
MW= [V(I0) − V(−I0)]/2I0− Rb,with
MWas a
MW|270◦ > ?RF/N
MW|90◦,
be more quantitative, we need to calculate α1 and β1. For
this, one needs to obtain the microwave photoresistance of the
single FM stripe, ?RF
MW. This can be calculated from ?RF/N
MW
by through the shunt relationship ?RF
assuming a parallel connection. (Through comparing the
angular-dependent resistance measurements for both pure
Py and Py/Pt film, we find this assumption only gives an
uncertainty of 5% for samples with the Pt thickness above
2nm.)RFistheresistanceofFMlayerwhenitsmagnetization
is perpendicular to the stripe, and RN can be calculated
from RF and RF/N (resistance of FM/NM bilayer) through
the shunt relationship. RF, RF/N, and RA are obtained
by four probe static magnetoresistance measurements. For
this particular sample we obtain that RA= 36.3 ?, RF=
2700 ?, and RF/N= 1179 ?. With the shunt relationship
discussed previously, we can calculate RN= 2093 ?. From
the Lorentz fit of the two curves in Fig. 2(b), we obtain
?RF/N
the resonance field H0= 705 Oe and the effective magnetiza-
tionμ0Meff= 0.967T,wecanfurthercalculatetheprecessing
angle according to Eqs. (6)–(8). We find that α1= 0.52◦,
β1= 0.14◦for α0= 90◦and α1= 0.59◦, β1= 0.15◦for
α0= 270◦. Therefore, we further normalized the measured
voltage to the precessing angle. Interestingly, we find that
V
α1β1|90◦ ≈ −
FollowingthemethodgiveninRef.22,wecanalsoestimate
the effective microwave magnetic field hrf acting on FM
layer from α1=
α = 0.011, we obtain hrf≈ 1.11 Oe for α0= 90◦and hrf≈
1.26 Oe for α0= 270◦. The exact reason for the different hrf
for these two configurations is unclear at the present stage. We
find this difference also exists for the single Py film, and it is
independentonI0thatisusedfortheresistancemeasurements,
suggesting it is not caused by the current induced heating.
We note that similar effects have also been shown in other
systems.29,30
To eliminate the residual AMR effects caused by the
small experimental misalignment and the contact rectification
effect,31we redefine a normalized ISHE caused by spin
pumping:
?
When H is not perfectly applied perpendicular to the strip, the
VAMRsignal will be mixed in the measurements. With˜VSP
the mixing effect can be minimized because of VAMR(α0) =
VAMR(α0+ 180◦). In addition, there exists a small voltage
due to the contact rectification effect.31This additional small
voltage bears similar symmetry as VAMR, and it can also be
eliminated by ˜VSP
˜VSP
experimental data, and the line is the Lorentz fit. We can
find that it shows an almost perfect Lorentz line shape. This
strongly supports its spin-pumping origin.
Previously, we discussed the criteria (i)–(iii). In the fol-
lowing we will continue to discuss the criterion (iv), i.e.,
the frequency independence of θSH. For this, we further
performed the measurements for the same sample but with
MW≈
?RF/N
MW(RF+RN)2
R2
N
MW|270◦ = 0.366 m? and ?RF/N
MW|90◦ = 0.286 m?. With
V
α1β1|270◦, and the criterion (iii) is fulfilled.
hrf
α(2H0+Meff). With the Gilbert damping factor
˜VSP
ISHE=
V
α1β1
????
90◦−
V
α1β1
????
270◦
??
2.
(9)
ISHE,
ISHEas well. A typical field dependence of
ISHEis presented in Fig. 3(a). The solid symbols are the
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SPIN HALL ANGLE QUANTIFICATION FROM SPIN ...
PHYSICAL REVIEW B 85, 214423 (2012)
FIG. 3. (a) Normalized inverse spin Hall voltage induced by
spin pumping corresponding to Fig. 2(a). Solid squares are the
experimental data, and the line is the Lorentz fit. (b) Microwave
frequency-dependent
eRNw
for Py/Pt(15 nm) (solid square) and
Py/Pt(6 nm) (open circle), respectively.
˜VSP
ISHE(H0)
differentfrequencies.AsθSHisfrequencyindependent,wecan
find, from Eq. (3), that VSP
parameters for a given sample:f, α1, and β1. The normalized
ISHE caused by the spin pumping, however, only has a
simplelineardependencewiththefrequency,i.e.,˜VSP
θSHλsdtanh(tN
dence of the measured
eRNw
for two samples: Py/Pt(15 nm) and Py/Pt(6 nm), respectively.
We can find that both curves show almost perfect linear
dependence, strongly supporting the frequency independence
of θSH. Therefore, the four criteria mentioned previously are
all fulfilled. The satisfaction of these four criteria also proves
that our measurements for VSP
the NM thickness-dependent measurements discussed below,
these four criteria are examined for all samples.
The effective spin-mixing conductance g↑↓
minedbytheenhancedGilbertdampingfactorduetothelosing
spinmomentumduringspinpumping.13–18Typically,g↑↓
dependent, and it reaches a saturation value for large tN.32,33
Figure 4(a) shows the tNdependence of g↑↓
Eq. (5). To exclude the extrinsic effect, we measure the FMR
ISHEhas three frequency-dependent
ISHE(H0) =
2λsd)g↑↓
effewRNf. Figure 3(b) shows the depen-
˜VSP
as a function of the frequency
ISHE(H0)
ISHE, α1, and β1are correct. For
effcan be deter-
effistN
effcalculated with
FIG. 4. (a) Pt thickness-dependent g↑↓
the guide for eyes. The value is saturated at tN≈ 2 nm. The inserts
show the frequency-dependent FMR half linewidth measurements
used for deriving g↑↓
dependent
eRNwg↑↓
square). The lines are the fitting curves according to the formula,
˜VSP
ISHE(H0)
eRNwg↑↓
efffor Py/Pt(tN). The line is
eff. (b) Experimental determined Pt thickness-
efffatf =8GHz(solidcircles)andf =9GHz(open
˜VSP
ISHE(H0)
efff= θSHλsdtanh(
tN
2λsd).
halflinewidthfordifferentfrequenciesandtakethelinearslope
for the calculation, as shown in the insert in Fig. 4(a). We can
findthatg↑↓
tent with the results of Ref. 34 where g↑↓
∼1.5 nm for samples Cu/Py(3 nm)/Cu(10 nm)/Pt(tN)/Cu. The
low saturation thickness shows that Pt is an effective spin-sink
material, as pointed out by Tserkovnyak et al.27The obtained
g↑↓
is similar to the results from other groups.15–18We note that
the saturation distance for g↑↓
λsdas it describes the thickness of the NM layer, which is
necessary to sink the spin accumulation at the interface.27,34
Up to now, the only parameters left unknown are θSHand
λsd.TheycanbeobtainedthroughtheNMthickness-dependent
measurements as we can easily derive that θSHλsdtanh(tN
˜VSP
eRNwg↑↓
experimentally. The results are shown in Fig. 4(b) for two
frequencies. The solid circles and open squares are the
experimental measured
eRNwg↑↓
effissaturatedwhentN≈ 2nmforPt.Thisisconsis-
effreaches saturation at
eff= 2.5(±0.2) × 1019m−2for the Pt thickness above 2 nm
effis not the spin-diffusion length
2λsd) =
ISHE(H0)
efff,wheretherightsideoftheequationcanbemeasured
˜VSP
ISHE(H0)
effffor the frequency of 8 GHz
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Z. FENG et al.
PHYSICAL REVIEW B 85, 214423 (2012)
and 9 GHz, respectively. We fit the data with θSHand λsd,
which are the only two parameters using the aforementioned
relationship. The results are plotted as the solid (8 GHz)
and the dash (9 GHz) line, respectively. The fitting yields
θSH= 0.0120 ± 0.0006 and λsd= 8.3 ± 0.5 nm for f =
8 GHz, and θSH= 0.0118 ± 0.0005 and λsd= 8.2 ± 0.5 nm
for f = 9 GHz. We can find that their differences are within
2%, strongly supporting the frequency independence of the
SHA. With the overall experimental error margin analysis,
we obtain θSH= 0.012 ± 0.002 and λsd= 8.3 ± 0.9 nm,
respectively. The obtained spin-diffusion constant is in good
agreement with the nonlocal spin valve measurements12
and the theoretical calculation.35Interestingly, we find the
measured spin-diffusion length is considerably larger than the
saturation distance of the effective spin-mixing conductance
for Pt (∼2 nm). The origin of this difference remains an
open question and requires further investigation. We further
calculate the spin Hall conductivity with the obtained SHA,
and the experimentally determined the conductivity of Pt:
σPt= (4.3 ± 0.2) × 106(?m)−1according to σSH
σPt. The value is 516 ± 30 (?cm)−1, and it is larger than the
theoretical value of 330 (?cm)−1,36suggesting the existence
of the extrinsic effect in this particular system. This can
be understood as the calculation is made for single crystalline
sample while our samples are polycrystalline films.
In the following we will make a brief comparison of our
resultswiththosefromothergroups.15–18References15and16
successfully demonstrated the applicability of using spin
pumpingforSHAmeasurements.TheydisentangledVSP
VAMRbyassumingthat VAMRhas onlyasymmetriccomponent
in their particular geometry. The SHA value obtained by them
is very close to our result, suggesting the assumption may be
valid. The measured magnetic field-dependent ISHE voltage
in Ref. 18 shows a Lorentz line shape by placing the sample
near the center of a TE011 cavity. The authors calculated
θSH to be 0.04 from a single NM thickness measurement
and utilizing a literature value of λsd= 10 nm. Reference 17
separatedVSP
and performed the NM thickness-dependent measurements.
The authors, however, did not measure the NM thickness-
dependent g↑↓
dampingparameterwiththeformulamainlyvalidfordiffusive
material [Eq. (6) in the original paper]. Pt, however, is an
effective spin sink material,27and g↑↓
at about 2 nm, as discussed previously. Moreover, Ref. 17
and Ref. 18 used the input microwave power to calculate
the effective hrf and further estimated the precessing angles
Pt= θSH•
ISHEand
ISHEandVAMRwiththeangular-dependentanalysis
eff. Instead, they fitted the data for the additional
effis already saturated
and the injected pure spin current. Our measurements show
that hrf can be different even though the same microwave
power is used. Therefore, we measured the precessing angles
directly utilizing the microwave photoresistance effect for
all the samples, which should give better estimation for the
injectedpurespincurrent.Duringthesubmission,weareaware
that the same group with Ref. 18 refined their results, and both
theSHAvalueandspin-diffusionlengthareingoodagreement
with our data.20
We note that, in literature, there is a debate whether it is
necessary to consider the backflow of electric current into Py
layer.15–17,20If this effect is considered, the resistance RNin
Eq. (3) needs to be replaced by RF/N. Our experimental data
suggeststhatthebackflowisnotsignificantinthePy/Ptsystem.
We speculate it is related to the fact that the charge current
generated by the pure spin current is not an ordinary charge
current, as their spin orientations are either parallel or antipar-
allelwiththespindirectionofthepurespincurrent.Inastrong
spin-orbit interaction system like Pt, the flow direction of such
specialchargecurrentisprotectedbythespin-orbitinteraction.
Therefore, it would not flow through the Pt/Py interface as the
direction has to be changed for penetrating the interface.
V. SUMMARY
In summary, we find that the ISHE induced by spin
pumping is typically mixed with signals due to AMR, and the
injected pure spin current is geometry and sample thickness-
dependent even for the same microwave power input. We
develop a method to separate the ISHE signal from other
unwantedsignalsusingout-of-planemicrowaveexcitationand
determine the in- and out-of-plane precessing angles through
the microwave photoresistance measurements. This method
enables the exact quantification of the SHA. It is demonstrated
for the Py/Pt bilayer system with an almost perfect Lorentz
line shape for the obtained ISHE signal and a frequency-
independent SHA value, as expected from theory. By varying
the Pt thickness, the SHA and spin-diffusion length of Pt is
quantified as 0.012 ± 0.002 and 8.3 ± 0.9 nm, respectively.
ACKNOWLEDGMENTS
The authors acknowledge Q. Y. Zhao and T. Jia for wire-
bondinghelp.ThisworkissupportedbytheStateKeyProgram
for Basic Research of China (Grant No. 2010CB923401),
NSFC (Grants No. 10834001, No. 10974087, No. 11023002,
and No. 11174131), and PAPD.
*Corresponding authors: youbiao@nju.edu.cn and hfding@nju.
edu.cn
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