Origin of the spin Seebeck effect probed by temperature dependent measurements in Gd 3 Fe 5 O 12
Stephan Geprägs, Andreas Kehlberger, Tomek Schulz, Christian Mix, Francesco Della Coletta, Sibylle Meyer, Akashdeep Kamra, Matthias Althammer, Gerhard Jakob, Hans Huebl, Rudolf Gross, Sebastian T.B. Goennenwein, Mathias Kläui
OOrigin of the spin Seebeck effect probed by temperature dependent measurements inGd Fe O Stephan Gepr¨ags, ∗ Andreas Kehlberger,
2, 3, † Tomek Schulz, Christian Mix,
2, 3
Francesco Della Coletta, Sibylle Meyer, Akashdeep Kamra,
1, 4
Matthias Althammer, Gerhard Jakob,
2, 3
HansHuebl,
1, 5
Rudolf Gross,
1, 5, 6
Sebastian T.B. Goennenwein,
1, 5 and Mathias Kl¨aui
2, 3, ‡ Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany Institute of Physics, University of Mainz, 55099 Mainz, Germany Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 M¨unchen, Germany Physik-Department, Technische Universit¨at M¨unchen, 85748 Garching, Germany (Dated: October 8, 2018)We probe the spin Seebeck effect in Gd Fe O /Pt hybrid structures as a function of temperatureand observe two sign changes of the spin Seebeck signal with decreasing temperature. A first signchange occurs at a temperature close to the Gd Fe O magnetic compensation point at around280 K. There the spin Seebeck signal changes sign abruptly with unaltered amplitude, indicating thatthe spin current is mainly caused by the magnetic Fe sub-lattices, which reorient their directions atthis temperature. A second, more gradual sign change takes place around the ordering temperatureof the Gd sub-lattice in the range of 65-85 K, showing that the Gd magnetic sub-lattice dominatesthe thermally driven spin current at lower temperatures. These sign changes together with thenon-monotonous dependence of the spin Seebeck signal on the temperature demonstrate that themagnonic spin current is not simply replicating the effective magnetization of Gd Fe O . Rather,the thermally generated net spin current results from a complex interplay of the three magneticsub-lattices involved. PACS numbers: 75.76.+j, 75.30.Ds, 85.75.-d, 85.80.-b
Magnons are the fundamental excitations in a magnet-ically ordered system. Their dispersion relations, propa-gation properties, etc., have been extensively investigatedtheoretically and experimentally.[1–3] In the presence of atemperature gradient, the magnon population at the hotend of a magnetic material is larger than at the cold end,resulting in an effective magnon flow along the thermalgradient.[4–8] Since magnons carry spin angular momen-tum, a thermal gradient thus will drive a (pure) magnonicspin current in a magnetic material, a phenomenon re-ferred to as the spin Seebeck effect (SSE).[4, 7]Lately, the SSE has attracted much attention, due toopen fundamental physics questions regarding its originon the one hand,[5, 9–18] and due to its application po-tential on the other hand.[19] It is now widely acceptedthat the thermopower signals measured in magnetic in-sulator/normal metal hybrids in the so-called longitu-dinal SSE geometry are indeed a consequence of themagnonic spin currents generated by the temperaturegradient.[5, 9–12] However, the exact mechanism behindthe excitation of the individual magnon modes, and thecontribution of different magnon modes to the spin cur-rent are still under discussion.[13–18] So far most SSEexperiments were performed in electrically insulating gar-net materials, which are ferrimagnetic, with several inter-acting magnetic sub-lattices.[1, 20–22] For yttrium irongarnet (Y Fe O , YIG) it was shown that the two Fesub-lattices with 20 magnetic atoms per unit cell lead toa complex spin wave dispersion relation.[1] Even more complex magnon spectra are expected for iron garnets RE Fe O where the rare earth RE carries a magneticmoment (e.g., RE =Gd, Tb, Dy, etc.), such that one cananticipate more complex and rich SSE physics in thesematerials (cf. Fig. 1). In particular, Ohnuma et al. the-oretically calculated the SSE voltage amplitude and signdepending on the magnetization in a ferrimagnet.[9] Us-ing a two-sub-lattice model, these authors predict thatthe SSE signal should reverse sign at the magnetizationcompensation point, due to the different, non-degeneratemagnons that contribute to the spin current. Since realgarnets exhibit a rather complex magnon dispersion re-lation with a large number of magnon branches,[1] how-ever, such a two-sub-lattice model might not be sufficientto fully describe the real material. Moreover, the detec-tion of the magnonic spin currents is usually realized viathe inverse spin Hall effect (ISHE) in an adjacent nor-mal metal, and the spin current transfer (spin mixingconductance) of magnons carried by different magneticsub-lattices or atomic species across the interface, fromthe magnetic insulator to the normal metal, might alsobe different. Thus, there is a clear need to study the SSEin complex ferrimagnetic garnets and magnetic systemswith complex magnetic structure.In this paper, we experimentally investigate the evo-lution of the magneto-thermopower (i.e., the longitudi-nal SSE) as a function of temperature in Gd Fe O /Pt(GdIG/Pt) hybrids. We observe a rather abrupt SSEsign change close to the magnetic compensation point, a r X i v : . [ c ond - m a t . m e s - h a ll ] M a y followed by yet another, more gradual SSE sign changeat lower temperatures. We interpret our experimentalobservations in terms of the different relative contribu-tions of the Fe and Gd magnons to the SSE, which havequalitatively different temperature dependences.Two sets of samples were fabricated and investi-gated. At Mainz, GdIG films were deposited on singlecrystalline, [100]-oriented Gadolinium Gallium Garnet(Gd Ga O , GGG) substrates by pulsed laser deposi-tion (PLD) using a KrF excimer laser with a laser fluenceof 1 . / cm . We here focus on a 100 nm thick GdIG film(sample A) grown with optimized parameters, i.e., in anoxygen atmosphere at 2 × − mbar and at a substratetemperature of 650 ◦ C. No parasitic phases were detectedusing x-ray diffraction [cf. Fig. 2(a)]. Furthermore, anout-of-plane lattice constant of (1 . ± . .
247 nm,[23] is cal-culated using the GdIG (400) film reflection. Moreover,the rocking curve around the GdIG (400) reflection hasa full width at half maximum (FWHM) of 0 . ◦ in-dicating a high crystalline quality and low mosaicity.The 8 nm thick Pt layer, used for the ISHE measure-ments, was deposited by DC-magnetron sputtering af-ter in-situ cleaning of the interface. At Garching, theGdIG films were deposited onto single crystalline, [111]-oriented Yttrium Aluminum Garnet (Y Al O , YAG)substrates via PLD. Best structural and magnetic prop-erties of the GdIG films were obtained by using a sub-strate temperature of 500 ◦ C, an oxygen atmosphere of1 . × − mbar, and an energy fluence of the KrF ex-cimer laser of 2 . / cm at the target surface.[24] Thecrystalline quality of the GdIG films demonstrated bythe FWHM of the rocking curves around the GdIG (444)reflection of around 0 . ◦ is comparable to the GdIG thinfilms fabricated at Mainz. We here discuss a 26 nm thickGdIG film with a lattice constant of (1 . ± . in-situ , without breaking the vac-uum, with 4 nm of Pt deposited via electron beam evap-oration [cf. Fig. 2(a)].The longitudinal SSE was recorded as a function oftemperature, using two complementary methods. AtMainz, the sample is sandwiched between two copperblocks,[10] which are cooled by the Helium exchange gasin a magnet cryostat [cf. Fig. 2(b)]. A resistive heaterwithin each block allows to independently set and stabi-lize its temperature. In particular, it thus is possible toinvert the temperature difference between the two copperblocks, allowing to exclude spurious effects due to asym-metric sample mounting. The temperature of the copperblocks is controlled by Pt-100 elements, which are alsoused to define the temperature difference applied acrossthe sample. Thin single crystalline sapphire plates com-bined with thermo-conductive foil ensure good thermalcontact as well as electric insulation between the copperblocks and the sample. To determine the longitudinalSSE signal, the transverse voltage V t , perpendicular to Gd Fe Fe ad c O M H Gd Fe Fe ad c O MH T T>T comp (a) (b) FIG. 1. (color online) (a), (b) The three different mag-netic sub-lattices of GdIG shown for temperatures below( T < T comp ) and above ( T > T comp ) the magnetic compen-sation temperature T comp . [25] Due to the strong temperaturedependence of the magnetic Gd sub-lattice ( c sites), the Gdsub-lattice dominates the magnetic behavior for T < T comp ,while for T > T comp the magnetic behavior is mainly causedby the antiferromagnetically coupled Fe sub-lattices ( d and a sites). In the presence of a finite magnetic field, the net mag-netization M points along the external magnetic field H . Thedirection and length of the colored arrows mark the directionand magnitude of the magnetization for the three magneticsub-lattices. an external magnetic field, is measured while modifyingthe magnetic field magnitude at a fixed magnetic fieldorientation ( H (cid:107) x ). In Garching, the GdIG/Pt bilayeris micropatterned into a Hall bar structure using opticallithography and Argon ion beam milling [cf. Fig. 2(c)].The sample is then inserted into a 3D vector magnetcryostat, in which He exchange gas in a variable tem-perature insert allows us to adjust the sample base tem-perature. We generate the temperature gradient acrossthe GdIG/Pt interface required for SSE experiments bysourcing a large current I d along the Pt microstructure it-self, and exploit the temperature-dependent resistance ofthe Pt for on-chip thermometry.[26] Here, V t is recordedas a function of the in-plane external magnetic field di-rection α using a fixed magnetic field magnitude. Asdetailed below, both experimental methods yield quali-tatively and quantitatively similar results, demonstratingthe validity of the approaches used.First, we investigate the magnetic properties of theGdIG films as a function of temperature, recorded usingSQUID magnetometry. As evident from Figs. 3(d) and(f), sample A and sample B show the characteristics ex-pected for a ferrimagnet with a compensation point:[25]The magnetization first decreases with decreasing tem-perature, reaches a minimum, and then increases again.As sketched in Figs. 1(a) and (b), GdIG is a ferrimag-net with three magnetic sub-lattices. Each unit cell con-sists of 12 trivalent Fe atoms that are tetrahedrally co-ordinated with oxygen atoms ( d sites, point group S ),8 Fe atoms that are octahedrally coordinated ( a sites,point group S ), and 12 dodecahedrally coordinated Gdatoms ( c sites). The two Fe sub-lattices are stronglycoupled via antiferromagnetic superexchange (exchangeconstant J ad (cid:39) 32 cm − ),[27] with a N´eel temperature (b) G d I G c u rr en t s ou r c e v o l t m e t e r YA G ( ) P t I d PtGdIG I d / YAG T V t V t G d I G v o l t m e t e r GGG ( ) P t PtGdIGT T GGG T c oppe r b l o ck V t V t (c) H H x y z sample A sample B 27° 28° 29° 30°10 I ( a . u . ) θ GGG (400)GdIG (400) θ 50° 51° 52° 53° 50 51 52 53 GdIG (444)YAG (444) (a) sample A sample B FIG. 2. (color online) (a) High resolution x-ray diffraction(HR-XRD) measurements of sample A and sample B. (b)-(c) Sketches of the experimental setups used to record thelongitudinal spin Seebeck effect (SSE). of about T N = 550 K. Since the Gd moments aremore weakly exchange coupled to the Fe a sub-lattices( J ac (cid:39) − )[27] leading to an ordering temperatureof the Gd spins at around 69 K,[28] they experience aneffective magnetic field below T N and can be treated asan ‘exchange-enhanced’ paramagnetic moment.[29] As aconsequence the Gd magnetization can be described bya strongly temperature-dependent Brillouin function forspin 7/2. At high temperatures, the d site Fe ions dom-inate the net magnetization of GdIG. As the tempera-ture is reduced, the magnetization of the Gd sub-latticestrongly increases, and together with the Fe magnetiza-tion at the a site eventually overwhelms the Fe magneti-zation at the d site. At the so-called magnetic compensa-tion temperature T comp ≈ 288 K (bulk value),[20, 30] themagnetization of the a site of Fe and the c site of Gd isequal in magnitude but antiparallel to the magnetizationof the d site of Fe (cf. Fig. 1), such that the remanentmagnetization of GdIG becomes zero. Since our magne-tometry experiments were performed in a finite externalmagnetic field of magnitude 0.1-1 T (comparable to theexperimental situation in the SSE experiments below),the net GdIG magnetization does not vanish, but rathergoes through a minimum at T comp , owing to the para-magnetic response of the Gd moments. Figure 3(d) re-veals that the compensation temperature of sample A isaround 285 K, in line with literature.[20, 30] For sample B, T comp ≈ 260 K is somewhat lower [cf. Fig. 3(f)], mostlikely due to the smaller GdIG film thickness resulting ina finite strain state, which reduces the magnetic exchangestrength.We now turn to the SSE experiments shown inFigs. 3(a)-(c). The data was taken on sample A at fourdifferent sample base temperatures, with a temperaturedifference of +10 K applied across the sample. Posi-tive temperature difference hereby means that the Pt iswarmer than the GdIG and the GGG substrate. As afunction of the external magnetic field, the voltage sig-nal V t shows a hysteresis behavior, which is characteristicfor the SSE.[5] Interestingly, however, the V t hysteresisloop flips sign two times with decreasing temperature:while V t ( H ) is ‘regular’ for T = 280 K (i.e., the V t ( H )recorded in GdIG/Pt hybrids has the same sign as theestablished SSE signal of YIG/Pt),[31] the V t ( H ) looprecorded for T = 232 . T = 35 K again is ‘regular’.In order to characterize the temperature-dependentevolution of the SSE signal in more detail, we de-fine the SSE amplitude V SSE as the difference V SSE =( V t (+ H sat ) − V t ( − H sat )) / 2, recorded at external mag-netic field strengths µ H sat large enough to saturate theGdIG magnetization. Taking the temperature depen-dence of the Pt resistance R ( T ) into account, Figure 3(e)shows the I SSE ( T ) = V SSE ( T ) /R ( T ) curve from sampleA. The SSE signal first is negative at high tempera-tures, then becomes positive in a temperature interval T sign2 (cid:46) T (cid:46) T sign1 with T sign2 ≈ 80 K, and is negativeagain for T (cid:46) T sign2 . Note also that the sign changearound T sign1 ≈ . T sign2 is much smoother. Asevident from Figure 3(g) the SSE signal I SSE of sampleB derived from angular dependent measurements con-firms the described temperature dependence of sampleA. The I SSE signal was obtained by recording the trans-verse voltage V t with I d = 6 mA applied across the Hallbar structure as a function of the in-plane orientation α of the external magnetic field at constant magnitudeof 1 T. The SSE signal I SSE = V SSE ( T ) /R ( T ) was thencalculated from V SSE = [ V t (+ I d ) + V t ( − I d )].[26]We start the discussion by comparing our experimen-tal observations with the theoretical model by Ohnuma etal. .[9] For the compensated ferrimagnet Er Fe O , theseauthors predict a temperature-independent SSE magni-tude, which abruptly changes sign once at the magne-tization compensation temperature. Ohnuma et al. at-tribute this SSE sign change to the inversion of the sub-lattice magnetization orientations at the compensationpoint [cf. Figs. 1(a),(b)] corresponding to a reversal ofthe spin current polarization, while the contributions ofthe two non-degenerate magnon branches do not changeas a function of temperature. This model is based ontwo non-degenerate magnon branches corresponding totwo magnetic sub-lattices, namely a ferric and a rare- T (K) I SSE ( n A ) M ( k A / m ) (d)(e) µ H=0.1T sample A ∆ T=+10K T sign2 T sign1 T comp -50 0 50-0.40.00.4 µ H (mT) V t ( µ V ) µ H (mT) -100 0 100 -100 0 100 µ H (mT) (a) (b) (c) ∆ T=+10K ∆ T=+10K ∆ T=+10K T=35K T=232.5K T=290Ksample A T (K) I SSE ( n A ) M ( k A / m ) (f)(g) µ H=1T sample B µ H=1T T sign1 T comp T sign2 FIG. 3. (color online) (a)-(c) Measured transverse voltage V t of sample A for selected temperatures showing two signchanges as a function of temperature. (d) Temperature-dependent magnetization of sample A recorded at a magneticfield of 0.1 T. (e) SSE signal I SSE as a function of tempera-ture obtained from the difference in V t at positive and nega-tive saturation taking the temperature dependence of the Ptresistance R ( T ) into account. (f) Magnetization as a func-tion of temperature of sample B measured at µ H = 1 T. (g) I SSE signal of sample B derived from angular dependent mea-surements. Here, the V t is recorded under different in-planeorientations α of the magnetic field at constant magnitudeof 1 T. The SSE signal I SSE = V SSE /R ( T ) is calculated from V SSE = [ V t (+ I d ) + V t ( − I d )]. The blue dashed lines markthe zero-crossings of the I SSE signal. The temperature of themagnetic compensation points T comp for sample A and B areindicated by the black dashed lines. earth sub-lattice.[9, 32] While the model by Ohnuma etal. thus accounts for the rather abrupt sign change in I SSE around T sign1 , it fails to reproduce the second SSEsign change at T sign2 .Based on these findings, we extend the theory ofOhnuma et al. , using a mean field description of the three magnetic sub-lattices in GdIG as shown in Fig. 1(cf. Ref. 25). We assume that all thermal magnetic exci-tations in the different magnetic sub-lattices contributeequally to the SSE – however only if the correspond-ing sub-lattice is sufficiently ordered. In other words,the magnons in the Fe sub-lattices will substantially con-tribute to the SSE for T < T C ≈ 550 K, while the Gdsub-lattice exhibits a qualitatively different thermomag-netic behavior and significantly contributes to the SSEonly for T (cid:46) T Gd ≈ − 85 K. As mentioned above,the latter temperature is often also referred to as the Gdordering temperature in the literature.[28] This assump-tion is motivated by the existing literature investigatingfinite temperature effects on ferromagnets via the selfconsistent renormalization of magnon dispersions.[33] Inparticular, it has been shown that the magnons ceaseto be the admissible eigenstates above a temperaturearound the ordering temperature. In this scenario, onlythe magnons from the Fe sub-lattices contribute to theSSE for T Gd < T (cid:46) T Fe . The net Fe magnetizationthereby determines the spin current spin polarization,such that the inversion of the sub-lattice magnetizationorientation at the magnetization compensation point re-sults in a sharp inversion of the SSE sign at this temper-ature. For T (cid:46) T Gd , however, the Gd magnons becomegradually more important. Since the Gd sub-lattice mag-netization is oriented along the external magnetic fieldat these temperatures, the corresponding spin current iscarrying angular momentum with an opposite directioncompared to the spin current from the Fe magnons. Withdecreasing T , the Gd magnons eventually dominate, re-sulting in a second, more gradual SSE sign change backto the high temperature sign of the signal, as observed inexperiment. This means that the difference in abruptnessof the transitions at T sign1 and T sign2 directly reflects thedifferent nature of the transitions ( T sign1 related to theabrupt Fe sublattice reorientation at the magnetic com-pensation point while T sign2 comes from the graduallyincrease of the influence of the magnetic Gd sub-lattice).Note also that the Gd is weakly exchange-coupled to theFe sub-lattice, such that magnetic excitations caused bythe Gd sub-lattice could arise already for T > T Gd .Clearly, the above model is too simplistic to quantita-tively describe the observed behavior. For a consistentand robust analysis, the full spin wave spectrum needsto be calculated by taking into account all 32 magneticatoms in the unit cell (8 Fe atoms in the octahedral sites,12 Fe atoms in the tetrahedral sites and 12 Gd atoms),which is beyond the scope of this paper. Nevertheless,our results clearly show that the magnon spectrum andthe temperature dependences of the individual magnonbranches are more complex than assumed in Ref. 9, whichcan also contribute to the observed fact that the transi-tion temperature T sign1 is lower than the compensationtemperature T comp . Finally we note that a quantitativeanalysis might also need to consider possibly differentspin mixing conductances for the interface between Gdand Pt as compared to Fe and Pt.[34]In summary, we have experimentally investigated thetemperature dependence of the longitudinal spin Seebeckeffect in GdIG/Pt hybrids with different crystallographicorientations of the GdIG thin films grown on differentsubstrate materials. Using two complementary experi-mental approaches to record the SSE, two consecutivesign changes of the SSE signal were found with decreasingtemperature, which we attribute to different temperaturedependences of magnonic spin currents of the Fe and Gdmagnetic sub-lattices involved. The first sign change oc-curs around the magnetic compensation point of GdIGindicating the dominant role of the Fe sub-lattices in thistemperature range. The more gradual sign change of theSSE signal at around the ordering temperature of Gd(65-85 K) demonstrates that the magnetic Gd sub-latticedominates the spin current at lower temperatures. Ourresults thus show that magnons from different magneticsub-lattices can quantitatively alter the SSE and that thethermal magnonic spin currents do not simply replicatethe total magnetization. This opens intriguing perspec-tives for spin caloritronics in ferri- and antiferromagnetsand shows that current theoretical models are not suffi-cient to describe the experimental observations, callingfor more elaborate theoretical work.The authors would like to thank the DeutscheForschungsgemeinschaft (DFG) for financial support viaSPP 1538 “Spin Caloric Transport” (Project No. GO944/4-1 and KL 1811/7-1) and the Graduate School ofExcellence Materials Science in Mainz (MAINZ) GSC266, the EU (IFOX, NMP3-LA-2012 246102; MASPIC,ERC-2007-StG 208162; InSpin FP7-ICT-2013-X 612759)and the Research Center of Innovative and Emerging Ma-terials. At Garching, we thank T. Brenninger for techni-cal support, A. Habel and K. Helm–Knapp for the fabri-cation of the stoichiometric GdIG target, and M. Schreieras well as J. 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