Temperature dependence of the effective spin-mixing conductance probed with lateral non-local spin valves
TTemperature dependence of the effective spin-mixing conductance probedwith lateral non-local spin valves
K. S. Das, a) F. K. Dejene, B. J. van Wees, and I. J. Vera-Marun b) Physics of Nanodevices, Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen,The Netherlands Department of Physics, Loughborough University, Loughborough LE11 3TU,United Kingdom School of Physics and Astronomy, University of Manchester, Manchester M13 9PL,United Kingdom
We report the temperature dependence of the effective spin-mixing conductance between a normal metal(aluminium, Al) and a magnetic insulator (Y Fe O , YIG). Non-local spin valve devices, using Al as thespin transport channel, were fabricated on top of YIG and SiO substrates. By comparing the spin relaxationlengths in the Al channel on the two different substrates, we calculate the effective spin-mixing conductance( G s ) to be 3 . × Ω − m − at 293 K for the Al/YIG interface. A decrease of up to 84% in G s is observedwhen the temperature ( T ) is decreased from 293 K to 4.2 K, with G s scaling with ( T /T c ) / . The real partof the spin-mixing conductance ( G r ≈ . × Ω − m − ), calculated from the experimentally obtained G s , is found to be approximately independent of the temperature. We evidence a hitherto unrecognizedunderestimation of G r extracted from the modulation of the spin signal by rotating the magnetization directionof YIG with respect to the spin accumulation direction in the Al channel, which is found to be 50 times smallerthan the calculated value.The transfer of spin information between a normalmetal (NM) and a magnetic insulator (MI) is the cruxof electrical injection and detection of spins in therapidly emerging fields of magnon spintronics and an-tiferromagnetic spintronics . The spin current flow-ing through the NM/MI interface is governed by thespin-mixing conductance , G ↑↓ , which plays a cru-cial role in spin transfer torque , spin pumping ,spin Hall magnetoresistance (SMR) and spin See-beck experiments . In these experiments, the spin-mixing conductance ( G ↑↓ = G r + iG i ), composed of areal ( G r ) and an imaginary part ( G i ), determines thetransfer of spin angular momentum between the spin ac-cumulation ( (cid:126)µ s ) in the NM and the magnetization ( (cid:126)M ) ofthe MI in the non-collinear case. However, recent experi-ments on the spin Peltier effect , spin sinking and non-local magnon transport in magnetic insulators neces-sitate the transfer of spin angular momentum throughthe NM/MI interface also in the collinear case ( (cid:126)µ s (cid:107) (cid:126)M ).This is taken into account by the effective spin-mixingconductance ( G s ) concept, according to which the trans-fer of spin angular momentum across the NM/MI inter-face can occur, irrespective of the mutual orientation be-tween (cid:126)µ s and (cid:126)M , via local thermal fluctuations of theequilibrium magnetization (thermal magnons ) in theMI. The spin current density ( (cid:126)j s ) through the NM/MIinterface can, therefore, be expressed as : (cid:126)j s = G r ˆ m × ( (cid:126)µ s × ˆ m ) + G i ( (cid:126)µ s × ˆ m ) + G s (cid:126)µ s , (1)where, ˆ m is a unit vector pointing along the directionof (cid:126)M . While G r and G i have been extensively studied a) e-mail: [email protected] b) e-mail: [email protected] in spin torque and SMR experiments , direct experi-mental studies on the temperature dependence of G s arelacking.In this letter, we report the first systematic study of G s versus temperature ( T ) for a NM/MI interface. Forthis, we utilize the lateral non-local spin valve (NLSV)geometry, which provides an alternative way to studythe spin-mixing conductance using pure spin currents ina NM with low spin-orbit coupling (SOC) . A lowSOC of the NM in the NLSV technique also ensures thatthe spin-mixing conductance is not overestimated dueto spurious proximity effects in NMs with high SOC orclose to the Stoner criterion, such as Pt . We exclu-sively address the temperature dependence of G s for thealuminium (Al)/Y Fe O (YIG) interface, which is ob-tained by comparing the spin relaxation length ( λ N ) insimilar Al channels on a magnetic YIG substrate and anon-magnetic SiO substrate, as a function of tempera-ture. G s decreases by about 84% when the temperature isdecreased from 293 K to 4.2 K and scales with ( T /T c ) / ,where T c = 560 K is the Curie temperature of YIG, con-sistent with theoretical predictions . The real partof the spin-mixing conductance ( G r ) is then calculatedfrom the experimentally obtained values of G s and com-pared with the modulation of the spin signal in rotationexperiments, where the magnetization direction of YIG( (cid:126)M ) is rotated with respect to (cid:126)µ s .The NLSVs with Al spin transport channel were fab-ricated on top of YIG and SiO thin films in multiplesteps using electron beam lithography (EBL), electronbeam evaporation of the metallic layers and resist lift-offtechnique, following the procedure described in Ref. 34.The 210 nm thick YIG film on Gd Ga O substrate andthe 300 nm thick SiO film on Si substrate were obtainedcommercially from Matesy GmbH and Silicon Quest In-ternational, respectively. Permalloy (Ni Fe , Py) has a r X i v : . [ c ond - m a t . m e s - h a ll ] D ec (b)(a) (c) Al I L Py YIG M xzy Py V + _ (cid:80) S M agnon s
500 nm I Py V + _ AlPy xy B θ L FIG. 1. (a)
Schematic illustration of the experimental geometry. The spin accumulation ( (cid:126)µ s ), injected into the Al channelby the Py injector, has an additional relaxation pathway into the (insulating) magnetic YIG substrate due to local thermalfluctuations of the equilibrium YIG magnetization ( (cid:126)M ) or thermal magnons. (b) SEM image of a representative NLSV devicealong with the illustration of the electrical connections for the NLSV measurements. An alternating current ( I ) was sourcedfrom the left Py strip (injector) to the left end of the Al channel and the non-local voltage ( V NL ) was measured across theright Py strip (detector) with reference to the right end of the Al channel. An external magnetic field ( B ) was swept along the y -axis in the non-local spin valve (NLSV) measurements. In the rotation measurements, B was applied at different angles ( θ )with respect to the y -axis in the xy -plane. (c) NLSV measurements at T = 293 K for an Al channel length ( L ) of 300 nm onthe YIG substrate (red) and on the SiO substrate (black). been used as the ferromagnetic electrodes for injectingand detecting a non-equilibrium spin accumulation in theAl channel. A 3 nm thick Ti underlayer was depositedprior to the evaporation of the 20 nm thick Py electrodes.The Ti underlayer prevents direct injection and detectionof spins in the YIG substrate via the anomalous spin Halleffect in Py . In-situ Ar + ion milling for 20 secondsat an Ar gas pressure of 4 × − Torr was performed,prior to the evaporation of the 55 nm thick Al chan-nel, ensuring a transparent and clean Py/Al interface. Aschematic of the device geometry is depicted in Fig. 1(a)and a scanning electron microscope (SEM) image of arepresentative device is shown in Fig. 1(b). A low fre-quency (13 Hz) alternating current source ( I ) with anr.m.s. amplitude of 400 µ A was connected between theleft Py strip (injector) and the left end of the Al channel.The non-local voltage ( V NL ) due to the non-equilibriumspin accumulation in the Al channel was measured be-tween the right Py strip (detector) and the right end ofthe Al channel using a standard lock-in technique. Themeasurements were carried out under a low vacuum at-mosphere in a variable temperature insert, placed withina superconducting magnet.In the NLSV measurements, an external magnetic field( B ) was swept along the y -axis and the correspondingnon-local resistance ( R NL = V NL /I ) was measured. InFig. 1(c), NLSV measurements for an Al channel length( L ) of 300 nm at T = 293 K are shown for two devices,one on YIG (red) and another on SiO (black). Thespin signal, R s = R PNL − R APNL , is defined as the differencein the two distinct states corresponding to the parallel( R PNL ) and the anti-parallel ( R APNL ) alignment of the Pyelectrodes’ magnetizations. The R s was measured as afunction of the separation ( L ) between the injector and the detector electrodes for several devices fabricated onYIG and SiO substrates, as shown in Fig. 2(a). To de-termine the spin relaxation length ( λ N ) in the Al chan-nels on YIG ( λ N, YIG ) and SiO ( λ N, SiO ) substrates, theexperimental data in Fig. 2(a) were fitted with the spindiffusion model for transparent contacts: R s = 4 α (1 − α ) R N (cid:18) R F R N (cid:19) e − L/λ N − e − L/λ N , (2)where, α F is the bulk spin polarization of Py, R N = ρ N λ N /w N t N and R F = ρ F λ F /w N w F are the spin resis-tances of Al and Py, respectively. λ N(F) , ρ N(F) , w N(F) and t N are the spin relaxation length, electrical re-sistivity, width and thickness of Al (Py), respectively.At room temperature, λ N, YIG = (276 ±
30) nm and λ N, SiO = (468 ±
20) nm were extracted, with α F λ F =(0 . ± .
05) nm.The NLSV measurements were carried out at differ-ent temperatures, enabling the extraction of λ N, YIG and λ N, SiO , as shown in Fig. 2(b). From this tempera-ture dependence, it is obvious that λ N, YIG is lower than λ N, SiO throughout the temperature range of 4.2 K to293 K. The corresponding electrical conductivities of theAl channel ( σ N ) on the two different substrates were alsomeasured by the four-probe technique as a function of T ,as shown in Fig. 2(c). The similar values of σ N for the Alchannels on both YIG and the SiO substrates suggeststhat there is no significant difference in the structure andquality of the Al films between the two substrates. There-fore, considering the dominant Elliott-Yafet spin relax-ation mechanism in Al , differences in the spin relax-ation rate within the Al channels cannot account for thedifference in the effective spin relaxation lengths betweenthe two substrates. (a) (b) (c) FIG. 2. (a)
The spin signal ( R s ) plotted as a function of the Al channel length ( L ) for NLSV devices on YIG (red circles) andSiO (black square) substrates at 293 K. The solid lines represent the fits to the spin diffusion model (Eq. 2). (b) The effectivespin relaxation length in the Al channel ( λ N ) extracted at different temperatures ( T ). λ N is smaller on the YIG substrate ascompared to the SiO substrate. (c) The electrical conductivity ( σ N ) of the Al channels on the YIG and the SiO substratesas a function of temperature. The close match between the two conductivities suggests similar quality of the Al film grown onboth substrates. The smaller values of λ N, YIG as compared to λ N, SiO suggest that there is an additional spin relaxation mech-anism for the spin accumulation in the Al channel on themagnetic YIG substrate. This is expected via additionalspin-flip scattering at the Al/YIG interface, mediated bythermal magnons in YIG and governed by the effectivespin-mixing conductance ( G s ). As described in Ref. 17, λ N, YIG and λ N, SiO are related to G s as1 λ = 1 λ + 1 λ , (3)where, λ r = 2 G s / ( t Al σ N ). Using the extracted valuesof λ N from Fig. 2(b) and the measured values of σ N forthe devices on YIG from Fig. 2(c), we calculate G s =3 . × Ω − m − at 293 K. At 4.2 K, G s decreases byabout 84% to 5 . × Ω − m − .The temperature dependence of G s is shown inFig. 3(a). Since the concept of the effective spin-mixingconductance is based on the thermal fluctuation of themagnetization (thermal magnons), G s is expected toscale as ( T /T c ) / , where T c is the Curie temperatureof the magnetic insulator . Using T c = 560 Kfor YIG, we fit the experimental data to C ( T /T c ) / ,which is depicted as the solid line in Fig. 3(a). Thetemperature independent prefactor, C , was found to be8 . × Ω − m − . The agreement with the experimentaldata confirms the expected scaling of G s with tempera-ture. Note that the deviation from the ( T /T c ) / scalingat lower temperatures could be in part due to slightlydifferent quality of the Al film on the YIG substrate.Nevertheless, the small difference of ≈
10% in the elec-trical conductivities of the Al channel on the two differentsubstrates at
T <
100 K in Fig. 2(c) cannot account forthe differences in λ N . On the other hand, we note thatquantum magnetization fluctuations in YIG can alsoplay a role at low T , leading to an enhanced G s .Next, we investigate the temperature dependence ofthe real part of the spin-mixing conductance ( G r ). For this, we first calculate G r from the experimentally ob-tained G s , using the following expression : G s = 3 ζ (3 / πs Λ G r , (4)where ζ (3 /
2) = 2 . / s = S/a is the spin density with totalspin S = 10 in a unit cell of volume a = 1 .
896 nm , andΛ = (cid:112) πD s /k B T is the thermal de Broglie wavelengthfor magnons, with D s = 8 . × − Jm being the spinwave stiffness constant for YIG . The temperaturedependence of the calculated G r is shown in Fig. 3(b).Keeping in mind that Eq. 4 is not valid in the limits of T → T c and T →
0, we ignore the data points below100 K. Above this temperature, G r is almost constant at ≈ . × Ω − m − , represented by the dashed line inFig. 3(b). This is consistent with Ref. 25, where G r wasfound to be T -independent. Moreover, the magnitudeof G r is comparable with previously reported values for (a) (b) FIG. 3. (a)
Temperature dependence of the effectivespin-mixing conductance (black symbols). G s scales withthe temperature as ( T /T c ) / (solid line). (b) The realpart of the spin-mixing conductance ( G r ) is calculated fromEq. 4 by using the experimentally obtained values of G s . G r ( ≈ . × Ω − m − ) is essentially found to be constant(dashed line) for T > K . (a) (b) (c) FIG. 4. (a)
NLSV measurement for a device on the YIG substrate with L = 300 nm at 150 K. (b) Rotation measurementfor the same device with B = 20 mT applied at different angles ( θ ) with respect to the y -axis. The black and the red symbolscorrespond to the average of ten rotation measurements carried out with the magnetization of the Py electrodes in the parallel(P) and the anti-parallel (AP) configurations, respectively. (c) The spin signal ( R s = R PNL − R APNL ) exhibits a periodic modulationof magnitude ∆ R s when the angle θ between the magnetization direction in YIG ( (cid:126)M ) and the spin accumulation direction inAl ( (cid:126)µ s ) is changed. The black symbols represent the experimental data at 150 K, while the red line is the numerical modellingresult corresponding to G r = 1 × Ω − m − . Al/YIG and Pt/YIG interfaces.An alternative approach for extracting G r from theNLSVs fabricated on the YIG substrate, is by the rota-tion of the sample with respect to a low magnetic fieldin the xy -plane. We have also followed this method, de-scribed in Refs. 17 and 26. In the rotation experiments,the angle θ between the magnetization direction in YIG( (cid:126)M ) and the spin accumulation direction in Al ( (cid:126)µ s ) ischanged, which results in the modulation of the spin sig-nal in the Al channel due to the transfer of spin angu-lar momentum across the Al/YIG interface, as describedin Eq. 1, dominated by the G r term. First, the NLSVmeasurement for a device with L = 300 nm was carriedout at 150 K, as shown in Fig. 4(a). In the next step, B = 20 mT was applied in the xy -plane and the samplewas rotated, with the magnetization orientations of thePy electrodes set in the parallel (P) or the anti-parallel(AP) configuration. For improving the signal-to-noiseratio, ten measurements were performed for each of theconfigurations (P and AP). The average of these measure-ments is shown in Fig. 4(b). The spin signal is extractedfrom Fig. 4(b) and plotted as a function of θ in Fig. 4(c). R s exhibits a periodic modulation with the maxima at θ = 0 ◦ and minima at θ = ± ◦ , consistent with thebehaviour predicted in Eq. 1. The modulation in the R s ,defined as ( R ◦ s − R ± ◦ s ) R ◦ s = ∆ R s R ◦ s , was found to be 2 . .
9% was reported in Ref 26 for anNLSV with a Cu channel on YIG with L = 570 nm atthe same temperature. G r is estimated from the rotation measurements us-ing 3D finite element modelling, as described in Ref. 17.From the modelled curve for the spin signal modula-tion, shown as the red line in Fig. 4(c), we extract G r = 1 × Ω − m − . This value is comparable to thatreported in Ref. 26, within a factor of 2, for an evaporatedCu channel on YIG. However, this value is more than 50times smaller than our estimated value from Eq. 4, and also that reported in Ref. 17 for a sputtered Al chan-nel on YIG. One reason behind the small magnitude of G r extracted from the rotation measurements can be at-tributed to the thin film deposition technique used. InRef. 14, it was shown that the SMR signal for a sputteredPt film on YIG is about an order of magnitude largerthan that for an evaporated Pt film. Moreover, duringthe fabrication of our NLSVs, an Ar + ion milling stepis carried out prior to the evaporation of the NM chan-nel for ensuring a clean interface between the NM andthe ferromagnetic injector and detector electrodes .Consequently, this also leads to the milling of the YIGsurface on which the NM is deposited, resulting in theformation of an ≈ . Since an external magnetic field of 20 mTis not sufficient to completely align the magnetization di-rection within this amorphous layer parallel to the fielddirection , the resulting modulation in the spin signalwill be smaller. This might lead to the underestima-tion of G r . Note that since the effect of G s does notdepend on the magnetization orientation of YIG (Eq. 1),the milling does not affect the estimation of G s . Ourobservations are consistent with a similarly small valueof G r ≈ × Ω − m − reported in Ref. 26 for theCu/YIG interface, where the Cu channel was evaporatedfollowing a similar Ar + ion milling step. Using the re-ported values of λ N = 522 nm (680 nm) on YIG (SiO )substrate for the 100 nm thick Cu channel at 150 K inRef. 26, we extract G s = 2 × Ω − m − , which is 5times larger than their reported G r extracted from rota-tion measurements.In summary, we have studied the temperature depen-dence of G s and G r using the non-local spin valve tech-nique for the Al/YIG interface. From NLSV measure-ments, we extracted G s to be 3 . × Ω − m − at 293 K,which decreases by about 84% at 4.2 K, approximatelyobeying the ( T /T c ) / law. While G r remains almostconstant with the temperature, the value extracted fromthe modulation of the spin signal (1 × Ω − m − )was around 50 times smaller than the calculated value(5 . × Ω − m − ). The lower estimate of G r from therotation experiment can be attributed to the formationof an amorphous YIG layer at the interface due to Ar + ion milling prior to the evaporation of the Al channel, aconsideration missing in the literature so far. ACKNOWLEDGMENTS
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