Table Of ContentVector spectroscopy for spin pumping
J. Lustikova∗
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
Y. Shiomi
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan and
Spin Quantum Rectification Project, ERATO,
6 Japan Science and Technology Agency, Sendai 980-8577, Japan
1
0
2
E. Saitoh
n
a Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
J
4 Spin Quantum Rectification Project, ERATO,
1
Japan Science and Technology Agency, Sendai 980-8577, Japan
]
l
l
a WPI Advanced Institute for Materials Research,
h
- Tohoku University, Sendai 980-8577, Japan and
s
e
m Advanced Science Research Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan
.
t (Dated: January15,2016)
a
m
We propose a method to separate the inverse spin Hall effect (ISHE) from galvanomag-
-
d
n netic effects in spin pumping experiments on metallic bilayer systems by measuring the dc
o
c
electromotiveforceintwoorthogonaldirections. Calculationsofdcvoltagesinlongitudinal
[
1 and Hall directions induced in Ni Fe and Ni Fe |Pt films at ferromagnetic resonance
81 19 81 19
v
8 in a microwave cavity predict that contributions from ISHE and from the galvanomagnetic
8
5 effects,i.e. theanisotropicmagnetoresistanceandtheanomalousHalleffect,exhibitdistinct
3
0
signalsymmetryaswellasangulardependencewhenchangingthedirectionoftheexternal
.
1
0 field with respect to the film plane. According to measurements on Ni Fe |Pt, only that
81 19
6
1 dc voltage component which includes ISHE is more than five times larger than purely gal-
:
v
Xi vanomagneticcomponents. ThisiscorroboratedbyresultsonLa0.67Sr0.33MnO3|Ptsamples,
r demonstratinguniversalityofthismethod.
a
2
I. INTRODUCTION
Knowledge of the transport properties of ferromagnetic films at ferromagnetic resonance
(FMR) is vital in spin pumping experiments, where spin current (the flow of electronic spin)
is injected into an adjacent paramagnetic metal upon FMR in the ferromagnetic layer.1–3 Spin
pumping in combination with the inverse spin Hall effect (ISHE),3–8 which enables conversion of
spin current into charge current, are powerful tools for exploring spin-charge related phenomena
inbilayersystems. ISHEisarelativisticphenomenonoccurringinthepresenceofspin-orbitcou-
pling, where both up and down electrons with opposite velocity directions are deflected into the
samedirectionresultinginanelectromotiveforcetransversebothtothespincurrentflowdirection
j andtothespinpolarizationσ:
s
E ∝j ×σ. (1)
ISHE s
ToaccuratelyestimatethecontributionofISHEintheobservedelectromotiveforceinsystems
comprising metallic ferromagnet/paramagnet bilayers, it is necessary to separate contributions
from galvanomagnetic effects in the ferromagnetic layer, i.e. the anisotropic magnetoresistance
(AMR)9 and the anomalous Hall effect (AHE).10 The electromotive force E induced by a current
densityJflowingthroughaferromagneticmetalwithmagnetizationMcanbeexpressedas11
ρ −ρ
(cid:107) ⊥
E=ρ J+ (M·J)M−R J×M, (2)
⊥ M2 a
where ρ , ρ , R are the resistivity in a transverse magnetic field, that in a longitudinal magnetic
⊥ (cid:107) a
field, and the anomalous Hall coefficient, respectively. The first term on the right-hand side of
Eq. (2) expresses the Ohm law, the other two terms the contribution from the galvanomagnetic
effects: AMR and AHE, respectively. That component of AMR which is perpendicular to J is
oftenreferredtoastheplanarHalleffect.11
In case of spin pumping setups,3,12–14 both the electric field component and the magnetic field
component of the microwave can induce an rf current in the sample. Coupling of the oscillating
induction current j and of the dynamic magnetization m at FMR excited in thin sheets of fer-
romagnetic conductors by a microwave gives rise to time-independent electromotive forces (the
spinrectificationeffect).15,16 Inmetallicbilayers,theseappearsimultaneouslywithISHEandob-
structtheobservationandestimationofpurespininjectionphenomena. Inrecentyears,significant
amountofresearchhasbeendoneinordertodeviseauniversalmethodforseparatingISHEfrom
3
galvanomagnetic effects in spin pumping experiments.12–14,17–21 The situation is complicated by
the fact that the magnetic field spectrum of a voltage signal induced by AMR or AHE can have
both symmetric (Lorentzian) and anti-symmetric (dispersive) contributions, and can fully overlap
withtheLorentzianspectrumoftheISHEsignal.12–14
In this work, we propose a method to separate ISHE from galvanomagnetic effects by inves-
tigating the angular dependence of the symmetric and anti-symmetric parts of two orthogonal
components of the induced dc electromotive force at FMR in a microwave cavity while chang-
ing the direction of the magnetic field out of the film plane. Comparison of electromotive force
measurements on Ni Fe and Ni Fe |Pt samples shows that only in the bilayer samples is the
81 19 81 19
componentincludingISHEmorethanfivetimeslargerthanpurelygalvanomagneticcomponents,
indicatingdominanceofISHE.
II. THEORETICALFORMULATION
Weconsiderametallicthin-filmsampleconsistingof(i)aferromagneticsinglelayerand(ii)a
ferromagnet-paramagnet bilayer placed close to the centre of a cylindrical TE microwave cav-
011
ity, as illustrated in Fig. 1(a). The z axis is taken along the magnetization vector M. Another
coordinate system x(cid:48)y(cid:48)z(cid:48) is taken with the x(cid:48)(=x) axis along the Hall direction of the sample, and
the z(cid:48) axis fixed along the longitudinal direction of the sample. A static external magnetic field H
is applied in the y(cid:48)z(cid:48) plane at an angle θ to the surface normal y(cid:48). The angle between the surface
H
normal y(cid:48) and the magnetization vector M is defined as θ . The microwave rf magnetic field h
M
is oscillating along the x direction, h=(h,0,0)eiωt, and the rf electric field ε along the z(cid:48) direc-
tion, ε = (0,εcosθ ,−εsinθ )ei(ωt+Φ).22 Electromotive force is measured in the longitudinal
M M
(z(cid:48))directionandtheHall(x=x(cid:48))direction.
The magnetization dynamics in the ferromagnetic layer is phenomenologically described by
theLandau-Lifshitz-Gilbertequation,
dM(t) α dM(t)
=−γM(t)×µ H + M(t)× , (3)
0 eff
dt M dt
where γ is the gyromagnetic ratio and α the damping parameter. The time-dependent magnetiza-
tionvectorM(t)isasumofthestaticmagnetizationvectorMandthetime-dependentcomponent
m(t) oscillating in the xy-plane. The effective field H is a sum of the external field H, the
eff
4
FIG.1. (a)MeasurementgeometryinacylindricalTE microwavecavity. Here,Hdenotestheexternal
011
staticmagneticfield,Mthestaticmagnetization,htherfmagneticfield,ε therfelectricfield,θ theangle
M
betweenthesurfacenormalandthemagnetizationvector,andθ theanglebetweenthesurfacenormaland
H
the external magnetic field. Voltageis measured along the x(cid:48) direction (V ) and thez(cid:48) direction (V ) as the
H L
sampleisrotatedaboutthexaxis. (b)Comparisonofthecalculated(“calc”)andmeasured(“expt”)angular
dependence of the resonance field µ H with ω/γ =0.325 T, µ M =0.884 T, α =0.02. (c) Calculated
0 R 0 z
spectral shapes of the real and imaginary components of the dynamic magnetization components m and
x
m ,aswellasthatoftheISHEvoltage[Eq. (7)]withparametersasin(b).
y
demagnetizing field H induced by the static magnetization vector, the rf field h and the rf de-
M
magnetizing field H induced by the dynamic magnetization.8 Neglecting second order terms of
m
handm,thesolutionofEq. (3)is
m=mxeiωt = 1 γ2Mzh[µ0Hcos(θM−θH)−µ0Mzcos2θM]+iαγωMzheiωt, (4)
Ξ
m −iγωM h
y z
where
Ξ=γ2[µ Hcos(θ −θ )−µ M cos2θ ]
0 M H 0 z M
×(cid:2)µ Hcos(θ −θ )−µ M cos2θ (cid:3)−(1+α2)ω2
0 M H 0 z M
+iαωγ(cid:2)2µ Hcos(θ −θ )−µ M cos2θ −µ M cos2θ (cid:3). (5)
0 M H 0 z M 0 z M
The ISHE electromotive force observed in the x direction is proportional to the z(cid:48) component
5
ofthetimeaverageoftherealpartofM(t)×dM(t)/dt,2,7,8 thatis,
(cid:20) (cid:21)
dM(t)
E ∝Re M(t)× | . (6)
ISHE z(cid:48)
dt
UsingthesolutionoftheLLGequation,onefinds12
E ∝[Im(m )Re(m )−Re(m )Im(m )]sinθ , (7)
ISHE x y x y M
where the real and imaginary parts of the dynamic magnetization are defined as m≡(Re(m )+
x
iIm(m ),Re(m )+iIm(m ))eiωt.
x y y
The expressions for the dc electromotive forces due to AMR and AHE are obtained by finding
thetimeaverageoftherealpartofthecorrespondingelectricfieldsinEq. (2):12,23
E ∝Re[(M·ε)M], (8)
AMR
E ∝Re(ε×M). (9)
AHE
Projections into the x and z(cid:48) axes lead to the following expressions for dc electromotive forces
alongtheHalldirection(E )andthelongitudinaldirection(E ),respectively:
H L
EAMR ∝εM sinθ [Re(m )cosΦ+Im(m )sinΦ], (10)
H z M x x
EAHE ∝εsinθ [Re(m )cosΦ+Im(m )sinΦ], (11)
H M y y
EAMR ∝εM sinθ cosθ [Re(m )cosΦ+Im(m )sinΦ], (12)
L z M M y y
EAHE =0. (13)
L
Equations (10) and (11) were calculated by Chen et al. in Ref. 12 using the same procedure.
UsingtheapproachabovetocalculatethecontributionfromtheordinaryHalleffect,Re(ε×H ),
eff
we find EHE ∝ εsinθ [Re(m )cosΦ+Im(m )sinΦ] and EHE = 0, which has the same angular
H M y y L
dependenceasAHE.
Treatment of the phase shift Φ requires special care. For a microwave confined in a lossless
metallic resonator, the time phase shift between the rf electric field and the rf magnetic field is
Φ = 90◦.22 However, dissipation by currents induced in cavity walls as well as in a conducting
sampleanditswiringmayleadtophaseshiftsotherthan90◦.14 Inaddition,anaccurrentjinduced
6
in the sample may lag behind the rf electric field ε due to capacitive losses. In the calculations
above, we assumed j ∝ ε, where Φ is a general phase which includes the phase shift between h
andε,aswellasthatbetweenε andj.
Todeterminethespectralshapesandangulardependenceoftheelectromotiveforcesinthecase
of Ni Fe as a ferromagnetic layer, we input particular parameter values α = 0.02,8,12ω/γ =
81 19
0.325 T and µ M =0.884 T. The reasonableness of the latter two parameters is demonstrated in
0 z
Fig. 1(b) which shows the angular dependence θ of the ferromagnetic resonance field H . The
H R
red dots are experimental data obtained for a 10-nm-thick Ni Fe film used in the study. The
81 19
blackcurvewasobtainedbynumericallysolvingthecoupledequationsfortheresonancecondition
(cid:2) (cid:3)
(ω/γ)2 =[µ H cos(θ −θ )−µ M cos2θ ]× µ H cos(θ −θ )−µ M cos2θ [Eq. (9)
0 R H M 0 z M 0 R H M 0 z M
in Ref. 8] and for the static equilibrium condition 2µ Hsin(θ −θ )+µ M sin2θ = 0 [Eq.
0 H M 0 z M
(6) in Ref. 8] for H at each θ . The chosen parameter values give a good agreement between
R H
calculationandexperiment.
Figure 1(c) shows the calculated magnetic field spectra of Re(m ), Im(m ), Re(m ), and
x x y
Im(m ), as well as that of V at θ = 90◦. The components Re(m ) and Im(m ) have a
y ISHE M x y
dispersive (anti-symmetric) spectral shape, while Im(m ) and Re(m ) exhibit an absorption-like
x y
(symmetric) spectrum.12 As a consequence, the contributions from AHE and AMR in Eqs. (10)-
(12) can have both symmetric and anti-symmetric components, depending on the value of the
phaseshiftΦ. Bycontrast,thespectralshapeoftheelectromotiveforceduetoISHEissymmetric
(absorption-like). In order to determine the angular dependence of each contribution we calculate
theθ dependenceoftheamplitudesAasdefinedinFig. 1(c).
H
The θ angular dependence of the calculated amplitudes A of the symmetric and anti-
H
symmetric components of ISHE, AHE and AMR in the Hall and longitudinal directions are sum-
marizedinFig. 2. ThecontributionfromISHE[Eq. (7)]appearsonlyinthesymmetriccomponent
intheHalldirection. ItsangulardependenceisgivenbyEs ∝A[Im(m )Re(m )−Re(m )Im(m )]sinθ
H x y x y M
and is shown in Fig. 2(a) (red curve). It has several features: (i) The signal amplitude is maximal
for in-plane magnetic field (θ =±90◦), (ii) it is zero for perpendicular magnetic field (θ =0◦,
H H
180◦), (iii) it changes sign by reversing the direction of the magnetic field, (iv) the amplitude
change is abrupt around θ = 0◦, 180◦, and (v) the signal soon saturates at its θ = 90◦ value
H H
whentiltingthedirectionofthemagneticfieldintothefilmplane.
AHE (blue curve) appears in the symmetric and anti-symmetric components of the electromo-
tiveforceintheHalldirection[Eq. (11)]. Theangulardependenceoftheamplitudeofthesymmet-
7
FIG. 2. Calculated angular dependence of the dc-voltage amplitudes induced by the inverse spin Hall
effect(ISHE),anisotropicmagnetoresistance(AMR),andtheanomalousHalleffect(AHE):(a)Symmetric
componentintheHalldirectionEs,(b)anti-symmetriccomponentintheHalldirectionEa,(c)symmetric
H H
componentinthelongitudinaldirectionEs,and(d)anti-symmetriccomponentinthelongitudinaldirection
L
Ea. Insetsillustratethemeasurementsetupandsignalsymmetryineachcase.
L
ric component, Es ∝sinθ A[Re(m )]cosΦ, is shown in Fig. 2(a) and that of the anti-symmetric
H M y
component, Ea ∝sinθ A[Im(m )]sinΦ, is plotted in Fig. 2(b). All of the characteristics (i)-(v)
H M y
of the angular dependence of ISHE are shared by the symmetric as well as the anti-symmetric
components of the AHE signal. However, here the angular dependence exhibits a cusp before
saturationintotheθ =90◦ valuewhentiltingthemagneticfieldfromtheperpendiculardirection
H
(θ =0◦)intothefilmplane. Thesecuspsappearatθ ≈±12◦ and180◦±12◦.
H H
Finally, contributions from AMR (black curves), are present in all four components: Es, Ea,
H H
Es, and Ea [Figs. 2(a)-(d)]. The angular dependences of the amplitudes of the symmetric and
L L
anti-symmetric components in the Hall direction are given by Es ∝ sinθ A[Im(m )]sinΦ and
H M x
Ea ∝sinθ A[Re(m )]cosΦ, respectively [Eq. (10)]. The angular dependence of Es [Fig. 2(a)]
H M x H
showsagainallofthefeatures(i)-(v)ofISHE.However,thechangeofthesignalamplitudewhen
tilting the magnetic field from the perpendicular direction to the in-plane direction is slower than
forISHEandthemaximalamplitudeisreachedataθ higherthaninthecaseofISHE.Thesame
H
is true for Ea [Fig. 2(b)]. In the longitudinal direction, AMR is the only contribution [Figs. 2(c)
H
and (d)]. The angular dependences of the symmetric and anti-symmetric components are given
8
by Es ∝sinθ cosθ A[Re(m )]cosΦ and Ea ∝sinθ cosθ A[Im(m )]sinΦ, respectively [Eq.
L M M y L M M y
(12)]. Here,theangulardependencesaredistinctlydifferentfromthoseintheHalldirectionwitha
periodof180◦ andzerosignalforbothperpendicularandin-planefields. Theangulardependence
exhibitssharppeaksofoppositepolarityatθ =±8.0◦ andagainatθ =180±8.0◦. Thisistrue
H H
both for the symmetric and the anti-symmetric components and is caused by the presence of the
sinθ cosθ factor. We also note that due to the cosΦ factor, the symmetric component in the
M M
longitudinaldirection(Es)isexpectedtobezeroifΦ=90◦.
L
The symmetric component of the dc voltage in the Hall direction [Es, Fig. 2(a)] in general
H
includes not only a contribution from ISHE, but also from AHE and AMR. Similarly, the anti-
symmetric component in the Hall direction Ea is a sum of the contributions from AMR and AHE
H
[Fig. 2(b)]. The ratio of AMR and AHE in each case depends on the value of the phase shift Φ
[Eqs. (10), (11)]. Therefore, knowledge of the amplitudes of Es and Ea alone is not sufficient
H H
to estimate the galvanomagnetic contribution in Es. However, voltage signal in the longitudinal
H
direction provides the missing pieces of information [Eqs. (12), (13)]. The ratio of the anti-
symmetricand symmetriccomponentsin thelongitudinaldirection,Ea/Es,which arepurely due
L L
to AMR, uniquely determines the phase shift Φ. By contrast, the sum of the second squares,
(cid:0)Ea(cid:1)2+(cid:0)Es(cid:1)2, determines the AMR coefficient. This information can be used to reconstruct
L L
the angular dependence of the anti-symmetric AMR signal in the Hall direction [Eq. (10)], and
consequently to attribute the remaining Ea signal to AHE [Eq. (11)], finding the anomalous Hall
H
coefficient. In this way, the AMR and AHE contributions to Es can be in principle determined,
H
makingitpossibletoquantifythesizeoftheISHEsignal.
III. EXPERIMENTALRESULTSANDDISCUSSION
Experiments were performed on Ni Fe (10 nm) single layers and Ni Fe (10 nm)|Pt (10
81 19 81 19
nm) bilayers. The Ni Fe films were prepared by electron beam evaporation on a thermally
81 19
oxidized Si substrate. In case of bilayer samples, Pt was deposited on the Si substrate by rf
sputtering before Ni Fe deposition. The samples were of 1×1.6 mm2 rectangular shapes.
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For spin pumping measurements, four voltage electrodes were made by wire bonding with an
aluminium wire at the midpoints of the sample edges, as suggested in Fig. 1(a). The sample
on a quartz rod was then placed close to the centre of a cylindrical cavity in TE mode with
011
a resonance frequency of 9.45 GHz. The Q-values in case of a wired Ni Fe sample and a
81 19
9
wired Ni Fe |Pt sample were 8700 and 9500, respectively. Electromotive force measurements
81 19
were performed at a microwave power P =200 mW (rf field µ h=0.16 mT) in the Hall and
MW 0
longitudinaldirectionswhilerotatingthesampleabouttheHalldirection[Fig. 1(a)].
A typical voltage signal from a Ni Fe |Pt sample measured in the Hall direction is shown in
81 19
Fig. 3(a). The size of the voltage signalV is normalized by the electrode distance l, E ≡V/l. A
voltagesignalappearsaroundtheferromagneticresonancefieldwhensweepingthemagneticfield,
containing both a symmetric (Lorentzian) component and an anti-symmetric (dispersive) compo-
nent. The amplitudes of the symmetric and anti-symmetric components, Es and Ea, respectively,
aredeterminedbyfittingthevoltagesignalwiththefollowingfunction.
∆2 −2∆(H−H )
E =Es +Ea R (14)
(H−H )2+∆2 (H−H )2+∆2
R R
Figures 3 (b) and (c) show the voltage signals in Ni Fe and Ni Fe |Pt, respectively, for
81 19 81 19
FIG.3. (a)VoltagesignalinaNi Fe |PtsampleintheHalldirectionatθ =90◦ (greydots)fittedwith
81 19 H
Eq. (14) (black curve). The red and blue curves indicate the symmetric and anti-symmetric components,
respectively. Es and Ea denote the amplitude of the symmetric and the anti-symmetric components. (b),
(c)Normalizedvoltagesignalsfordifferentvaluesofθ measuredonaNi Fe (10nm)sample[(b)],and
H 81 19
a Ni Fe (10 nm) | Pt (10 nm) sample [(c)] in the Hall direction (E , black circles) and the longitudinal
81 19 H
direction(E ,violettriangles)fittedwithEq. (14)(redcurves).
L
10
selected values of θ in both the Hall direction (E , black circles) as well as the longitudinal
H H
direction(E ,violettriangles). Asignalconsistingofasymmetricandananti-symmetriccompo-
L
nent is observed in all cases. The signal vanishes when the magnetic field is perpendicular to the
surface plane. A sign reversal is observed when reversing the direction of the magnetic field. In
allcases,goodagreementisobtainedbyfittingthedatawithEq. (14)(redcurves). Theamplitude
of the signal in Ni Fe is three times larger than that in Ni Fe |Pt. This is due to shunting of
81 19 81 19
galvanomagnetic effects in Ni Fe when measuring the electromotive force in a bilayer sample,
81 19
aswellasduetoadecreaseinthemicrowaveabsorptionintensityintheNi Fe |Ptsample.
81 19
The angular dependences of Es, Ea, Es, and Ea extracted from fitting are shown in Figs. 4
L L H H
(a)-(h). The symmetric and anti-symmetric components in the longitudinal direction, Es and Ea,
L L
foraNi Fe sampleareshowninFigs. 4(a)and(b),respectively. Bothareplottedalongwiththe
81 19
calculated dependence (black curve, not to scale) which predicts that the only contribution comes
fromAMR.IncaseoftheexperimentaldataforEs,theappearanceoftwosharppeaksofopposite
L
polarity at θ = ±8◦ and again at θ = 180±8◦ agrees well with the prediction. However, the
H H
θ dependence does not fully overlap with the predicted curve. The experimental result includes
H
a contribution which changes sign by reversing the direction of H, similar to the predicted AMR
or AHE contributions to Es. In the case of Ea in Fig. 4(b), the angular dependence also includes
H L
a signal which matches the predicted AMR dependence, and a contribution from a signal which
changessignbyreversingthedirectionofH. Es andEa haveoppositepolarity.
L L
Thesymmetricandanti-symmetriccomponentsintheHalldirection,Es andEa foraNi Fe
H H 81 19
sample are shown in Figs. 4(c) and (d), respectively. Both are plotted along with the predicted
dependence of AMR and AHE (black and blue curves, respectively). The experimental plot for
both components qualitatively agrees with the predicted dependence: the signal changes sign by
reversing the direction of H and is zero for θ =90◦. Both Es and Ea are of the same polarity.
H H H
Ineachcase,thereisaslightdiscrepancybetweentheexperimentaldataandthecalculatedcurves
for AMR and/or AHE. The difference between the calculated curves for AHE and AMR is too
minutetodeterminetheirratiowithintheaccuracyofthisexperiment.
The results for a Ni Fe |Pt sample are shown in Figs. 4(e)-(h). The symmetric component
81 19
of the voltage signal in the longitudinal direction Es in Fig. 4(e) changes sign by reversing the
L
direction of H and has an angular dependence rather similar to that of AMR in the Hall direction.
This is in disagreement with the predicted AMR behaviour in the longitudinal direction (black
curve). The anti-symmetric component Ea in Fig. 4(f) contains a contribution similar to the
L
