Temperature dependent relaxation of dipole-exchange magnons in yttrium iron garnet films
Laura Mihalceanu, Vitaliy I. Vasyuchka, Dmytro A. Bozhko, Thomas Langner, Alexey Yu. Nechiporuk, Vladyslav F. Romanyuk, Burkard Hillebrands, Alexander A. Serga
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov Temperature dependent relaxation of dipole-exchange magnonsin yttrium iron garnet films
Laura Mihalceanu, ∗ Vitaliy I. Vasyuchka, Dmytro A. Bozhko, Thomas Langner, Alexey Yu. Nechiporuk, Vladyslav F. Romanyuk, Burkard Hillebrands, and Alexander A. Serga Fachbereich Physik and Landesforschungszentrum OPTIMAS,Technische Universit¨at Kaiserslautern, 67663 Kaiserslautern, Germany Faculty of Radiophysics, Electronics and Computer Systems,Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine (Dated: November 22, 2017)Low energy consumption enabled by charge-free information transport, which is free from ohmicheating, and the ability to process phase-encoded data by nanometer-sized interference devices atGHz and THz frequencies are just a few benefits of spin-wave-based technologies. Moreover, whenapproaching cryogenic temperatures, quantum phenomena in spin-wave systems pave the pathtowards quantum information processing. In view of these applications, the lifetime of magnons—spin-wave quanta—is of high relevance for the fields of magnonics, magnon spintronics and quantumcomputing. Here, the relaxation behavior of parametrically excited magnons having wavenumbersfrom zero up to 6 · rad cm − was experimentally investigated in the temperature range from 20 Kto 340 K in single crystal yttrium iron garnet (YIG) films epitaxially grown on gallium gadoliniumgarnet (GGG) substrates as well as in a bulk YIG crystal—the magnonic materials featuring thelowest magnetic damping known so far. As opposed to the bulk YIG crystal in YIG films we havefound a significant increase in the magnon relaxation rate below 150 K—up to 10.5 times the refer-ence value at 340 K—in the entire range of probed wavenumbers. This increase is associated withrare-earth impurities contaminating the YIG samples with a slight contribution caused by couplingof spin waves to the spin system of the paramagnetic GGG substrate at the lowest temperatures. The fields of spintronics and magnonics promote therealization of faster data processing technologies withlower energy dissipation by complementing or evenreplacing electron charge-based technologies with spindegree of freedom based devices [1–3]. Simultaneously,novel fascinating magnetic phenomena—such as, e.g.,room-temperature Bose-Einstein magnon condensates[4–6], magnon vortices [7] and supercurrents [8–11]—open a whole new range of research areas [3, 12] both forbasic and applied spin physics. For these purposes manynovel materials have been designed and investigated[13–15] whereupon one of the most outstanding onesso far is the insulating ferrimagnet yttrium iron garnet(Y Fe O , YIG).Since its discovery in 1956, YIG has served as a primeexample material for its microwave, optical, acoustic,and magneto-optical properties [16] in a wide range ofexperiments and applications. Nowadays, single crystalYIG films epitaxially grown on gadolinium galliumgarnet (Gd Ga O , GGG) substrates [17–19] dominatein theoretical and experimental studies [5–8, 20–24].Their pertinence ranges from building of devices likemicrowave YIG oscillators, filters, delay lines, phaseshifters, etc. [25] up to the latest high-profile research asin magnonics [26, 27], spintronics [1, 28] and quantumcomputing [29, 30]. Consequently it has become clearthat a deep understanding of the magnetic dampingproperties, determining the magnon lifetimes, is ofcrucial importance throughout these fields. Given itshigh Curie temperature at 560 K, YIG is applicable atambient temperatures, where its exceptional low Gilbert damping parameter of down to 10 − [31] enables along spin precession lifetime. Furthermore, in quantumcomputing YIG is used at very low temperatures for thecoupling of single magnons to superconductive qubits inmicrowave cavities for the storage of information [32–36].All of this in connection with arising demands on minia-turization of magnonic devices motivates our studies ofthe damping behavior in YIG films towards cryogenictemperatures in a wide range of spin-wave wavelengths.Up to now the temperature dependence of magneticdamping in YIG has been examined only for long-wavelength dipolar magnons with wavenumbers q → q ≤ rad cm − [48, 49]. For example, the parametricpumping process of the first order, as described bySuhl [50] and Schl¨omann et al. [51], resembles a formof spin-wave excitation when either a magnon of anexternally driven magnetization precession or a photon Magnetic field H (Oe) ( a r b . un i t s )
0 1 2 3 -3 -2 -1 h ~ ǁ ω p P (cid:0) q ⊥ H q (cid:1) H F requency (2 π GHz) ω p ω FMR H c y z x h ~ ⊥ H Y I G q ω p q ⊥ H (a)(c) (b) FIG. 1. (a) Sketch of the experimental setup. The spin sys-tem of a YIG sample, which is placed on top of a microstripresonator, is driven by a microwave Oersted field with com-ponents oriented perpendicular ( h ⊥∼ ) and parallel ( h k∼ ) to thebias magnetic field H . (b) Schematic illustration of the para-metric pumping process in an in-plane magnetized YIG film.The transversal (red curve) and longitudinal (blue curve)lowest magnon branches are calculated for H = 1600 Oe. Thepurple area contains the magnon branches with wavevectorslying in the film plane in the angle range between 0 and 90 ◦ relative to the field H . Two arrows show the splitting of amicrowave photon in two magnons at half of the pumping fre-quency ω p /
2. For the given bias magnetic field the magnonsare excited on the transversal dispersion branch. (c) Depen-dence of the threshold power P thr of parametric instabilityon the bias magnetic field H measured in a 53 µ m-thick YIGfilm at 60 K. The minima of the threshold curve at H = H c corresponds to the excitation of magnons with wavenumbers q → H < H c dipolar-exchange magnons corresponding to thetransversal dispersion branch are directly excited by theparallel component h k∼ of the pumping Oersted field. For H > H c the magnons from the purple spectral area (panel(b)) are excited by the precessing magnetization driven by theperpendicular component h ⊥∼ of the pumping Oersted field. of a pumping microwave magnetic field with wavenum-bers q p ≈ q and − q at half of the pumping frequency ω p /
2. Thus, a rather spatially uniform microwavemagnetic field can generate short-wavelength magnons,whose wavenumbers are determined by the applied biasmagnetic field H and are bounded above only by thechosen pumping frequency ω p .In our experiments, we investigated parametrically ex-cited magnons in in-plane magnetized YIG films of thick-nesses of 5.6 µ m, 6.7 µ m and 53 µ m, which were epitax-ially grown in the (111) crystallographic plane on GGGsubstrates of 500 µ m thickness. In addition, the GGGsubstrate was mechanically polished away from the orig-inally 53 µ m-thick sample down to a 30 µ m-thick YIGfilm. This sample was used to reveal a possible contribu- tion of the interaction between the ferrimagnetic YIG andparamagnetic GGG spin systems to the magnon damp-ing. The YIG samples with lateral sizes of 1 × prepared by chemical etching on the 5 × largeGGG substrates were magnetized along their long axisto avoid undesirable influence of static demagnetizing onthe value of the internal magnetic field.The experimental realization is provided by the mi-crowave setup shown in Fig. 1(a). The setup is attachedon a highly heat-conducting AlN substrate at the bot-tom and is allocated inside a closed cycle refrigeratorsystem. A microwave pumping pulse of 10 µ s durationat a frequency ω p of 2 π ·
14 GHz with a 10 ms repetitionrate and a maximal pumping power P p of 12 W feeds a50 µ m-wide microstrip resonator capacitively coupled toa microwave transmission line. The microwave Oerstedfield h p induced by the resonator drives the magnetiza-tion of a YIG-film sample placed on top of the microstrip.Subsequently the signal reflected by the resonator is for-warded to an oscilloscope.When the threshold field condition h p = h thr is ful-filled, the action of the microwave Oersted field com-pensates the spin-wave damping and gives rise to theparametric instability process, where a selected magnonmode, which has the lowest damping and the strongestcoupling to the pumping, grows exponentially in time.The arising mode increasingly absorbs the microwave en-ergy accumulated in the pump resonator. This processdetunes the resonator and, thus, changes the level of thereflected signal passed to the oscilloscope. As a result,a kink appearing at the end of the reflected pump pulseindicates the threshold microwave power P p = P thr re-quired for the parametric excitation process [52]. P thr canbe determined for magnon modes over the wide q -spectralrange by changing the magnetic field H , which leads toa vertical shift of the dispersion curve (Fig. 1 (b)) alongfrequency axis and results in a characteristic thresholdcurve shown in Fig. 1 (c).In order to understand the shape of this curve oneneeds to consider that the overall threshold power P thr is determined by instabilities of magnons excited by thecomponents of the microwave Oersted field oriented bothperpendicular h ⊥∼ (blue arrow in Fig. 1 (a)) and parallel h k∼ (red arrow in Fig. 1 (a)) to the bias magnetic field H [52]. At the critical field H = H c spin waves with q → ω p / ≈ ω FMR . In Fig. 1 (c) this situ-ation corresponds to the minima of the threshold curve P thr ( H ). The threshold power at H ≤ H c is dominatedby direct parametric interaction of the parallel field com-ponent h k∼ with the lowest thickness mode correspondingto the transversal magnon dispersion branch (red curvein Fig. 1 (b)) [53]. As this mode is characterized by thelargest precession ellipticity, the longitudinal component m z of the precessing magnetic moment strongly oscillatesalong the direction of the magnetic field H with frequency T h r e s ho l d po w e r P t h r ( W ) W a v enu m be r q T h r e s ho l d po w e r P t h r ( W ) ( r ad c m - ) FIG. 2. Threshold curves P thr ( H ) at different temperatures in the range 340 −
180 K (a) and 180 −
20 K (c). (b) Wavenumberin the wide temperature range. All present data is recorded and calculated for a 53 µ m-thick YIG film grown on top of a GGGsubstrate. ω p and thus effectively couples with the parallel compo-nent h k∼ of the pumping field. With decreasing externalmagnetic field, the threshold power slowly increases dueto an increase in wavenumbers of the excited magnonsand a related decrease in the precession ellipticity [53].The strong increase in P thr at the magnetic field H be-low 100 Oe is caused by transition of the homogeneouslymagnetized YIG film to a multi-domain state.Above H c no magnons with wavevectors q ⊥ H exist at ω p / θ q < ◦ relative to the field H . Thesemagnons escape the narrow pumping area above the mi-crostrip resonator (Fig. 1 (a)) and the related energy leak-age results in the sharp jump up in the threshold powerjust above H c . This confinement effect together with gen-eral reduction in the precession ellipticity caused by thedecrease of θ q leads to a further transition from the par-allel to the perpendicular pumping regimes for H > H c [52]. Finally, the threshold power P thr → ∞ when thebottom of the magnon spectrum is shifted above ω p / H ≤ H c is of main interest in this re-port as the wavenumbers of the parametrically excitedmagnons can be unambiguously calculated in this case. Henceforth we approximate h p ≃ h k∼ .Figure 2 presents the dependencies P thr ( H ) recordedfor a number of temperatures in the range from 340 Kto 180 K (Fig. 2 (a)) and from 180 K to 20 K (Fig. 2 (c))for the 53 µ m-thick film. The dotted arrows indicate theshift of both the critical threshold power P thr ( H c ) and H c with temperature. One can see that Fig. 2 (a) showsa decrease in the threshold power with decreasing tem-perature from 340 K to 180 K. On the contrary, Fig. 2 (c)reveals a strong increase in the threshold power with fur-ther temperature decrease from 180 K to 20 K. At thesame time, the experimentally determined critical field H c monotonically decreases towards lower temperaturesalong the whole temperature range.This decrease of H c relates to an upward frequencyshift of the magnon spectrum caused by a temperaturedependent increase in the saturation magnetization 4 πM s as well as by changes of the cubic H ca and uniaxial H ua anisotropy fields of the YIG film [54, 55]. The field de-pendence of the wavevector spectral range for the perpen-dicular spin-wave branch can be calculated using Eq. 7.9from Ref. [55]: ω = γ p ( H + Dq )( H + Dq + 4 πM s − H ca − H ua ) , (1)where ω = ω p / γ = 1 . · Oe − s − the gyro-magnetic ratio, and the nonuniform exchange constant D = 5 . · − Oe cm are considered to be not varyingwith temperature [56]. The difference 4 πM s − H ca − H ua is defined from the measured values of H c ( T, q = 0). Anexpected demagnetizing effect caused by a stray mag-netic field induced at low temperatures in YIG films bythe paramagnetic GGG substrate can be neglected in ourcase of laterally extended samples [57].The calculated dependencies of the magnon wavenum-ber q = q ( H ) for different temperatures are shown inFig. 2 (b). The vertical dashed lines in Fig. 2 correlatethe threshold curves with the corresponding wavenum-ber at H c . As is shown, in our experiment spin waves areprobed by parametric pumping in the wavenumber rangefrom zero to 6 · rad cm − .The variation of the saturation magnetization directlyaffects the coupling between the microwave pumping field ~h k∼ and the longitudinal component m z of the precess-ing magnetic moment M . As a result, the threshold field h thr is influenced by two temperature dependent phys-ical quantities: the spin-wave relaxation rate and theparametric coupling strength. These influences can beestimated using the relation for the threshold field [55]: h thr = min (cid:26) ω p ∆ H q ω M sin θ q (cid:27) , (2)where ω M = γ πM s , and θ q is the angle between themagnon wavevector q and the magnetization direction.For the parametric excitation near and above the FMRfrequency ( H ≤ H c ), we can approximate θ q ≈ ◦ . ∆ H q is the width of a linear resonance curve of the parametri-cally excited magnon mode with the wavenumber q . It isdefined as ∆ H q = 1 / ( γT q ) = Γ q /γ , where T q and Γ q arethe magnon lifetime and the spin-wave relaxation rate.It is known that the saturation magnetization 4 πM s for bulk YIG crystals demonstrates a rather non-linearchange with temperature [58], which can be calculatedusing the two-sublattice model described in Ref. [59] asit is shown by the red solid line in Fig. 3 (a). By-turn, thetemperature behavior of the cubic anisotropy field can beapproximated [57] as H ca = H ca (0) + αT , (3)with H ca (0) = −
147 Oe and α = 2 . · − Oe K − . .The slopes of the 4 πM s ( T ) − H ca ( T ) − H ua ( T ) curvesdetermined for all films at room temperatures are ingood agreement with previously reported results [49, 60].However, due to the unknown contribution of the uni-axial anisotropy [61], which is caused by a tempera-ture dependent mismatch between YIG and GGG crys-tal lattices, the calculated temperature dependencies forboth 4 πM s and for 4 πM s − H ca (dashed blue line inFig. 3 (a)) significantly diverge from the experimental dif-ference 4 πM s − H ca − H ua (see, e.g., the data for the 53 µ m-thick YIG film shown by red circles in Fig. 3 (a)).At the same time, the substrate-free YIG sample of30 µ m thickness prepared from the 53 µ m-thick YIG filmdemonstrates good agreement between experimentallymeasured (empty blue circles) and theoretically calcu-lated values of 4 πM s − H ca . In the case of the thinner YIGfilms the experimental data for 4 πM s − H ca − H ua followthe general trend of the calculated saturation magnetiza-tion 4 πM s (see Fig. 3 (a)). This agreement evidences theapplicability of the chosen model for our YIG films andallows us to use the theoretical magnetization values forthe calculation of the temperature dependent parametriccoupling strength.By assuming initially the value of ∆ H q in Eq. 2 tobe constant over the entire temperature range and tak-ing into account the theoretical values of 4 πM s ( T ) wehave calculated the normalized (with respect to 340 K)temperature dependence of the threshold field, which issolely determined by the change in the parametric cou-pling strength. This dependence is shown by the circlesin Fig. 3 (b).The experimental threshold field h expthr , which containsinformation about the relaxation of parametrically ex-cited magnons, can be found from the measured thresh-old powers using the relation h expthr = C √ P thr . The valueof C depends on the pumping frequency ω p , the geom-etry and the quality factor of the pumping resonator.As the resonance frequency and the quality factor of ourmicrostrip resonator do almost not change with temper-ature we assume C to be constant.The experimental values of the dimensionless thresholdfield normalized to the reference value at the temperatureof 340 K are plotted in Fig. 3 (b) (squares) for magnonsexcited near the FMR frequency ( H = H c ). Its behav-ior is visibly non-monotonic: down to 180 K the thresh-old field h expthr slightly decreases, while below 180 K it in-creases up to 6.5 times compared to the reference value.The comparison of the calculated ( h thr ( T ), circles) andexperimental ( h expthr ( T ), squares) threshold dependenciesclearly evidences that at high temperatures ( T ≥
180 K)the experimental dependencies are mostly determined bythe variation in the parametric coupling strength. Onthe contrary, the strong increase of h expthr in the low-temperature range ( T <
180 K) is caused by the spin-wave relaxation.Figure 3 (c) shows the normalized relaxation rate Γ q calculated at H c with help of Eq. 2 using h expthr ( T ) andtheoretically calculated 4 πM s ( T ). It becomes evidentthat for the temperature decrease from 180 K to 20 Kthe relaxation rate Γ q increases up to about 10.5 timesfor the 53 µ m-thick YIG film while the thinner films ex-hibit the same trend. The same relaxation behavior, asit is clear from the nearly wavenumber-independent ver-tical shift of all threshold curves (see, e.g., Fig. 2), is ob-served in all range of probed magnon wavenumbers upto 6 · rad cm − . The strong increase of the relaxation M (T )(cid:2) (cid:3) M (T (cid:4)(cid:5) (cid:6) M (T (cid:7)(cid:8) (cid:9) (cid:10) (cid:11) (cid:12)(cid:13) ) u (cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)1(cid:20)(cid:21) YIG(5.6)/GGG(500)YIG(6.7)/GGG(500) YIG(53)/GGG(500)YIG(30) M M (T) YIG(53)/GGG(500) R e l a x a t i on r a t e R e l a x a t i on r a t e YIG(bulk) ultrapure
FIG. 3. (a) Saturation magnetization plotted as a function of temperature compared to theoretical calculations. (b) Tem-perature dependence of the threshold pumping field for magnons parametrically excited near the FMR frequency at H = H c .Squares – the h expthr values are determined using the measured threshold powers P thr . Circles – the h thr values are calculatedusing Eq. 2 for the experimentally determined values of 4 πM S ( T ) on the assumption that ∆ H q = const . (a) and (b) aredetermined for the 53 µ m-thick sample. (c) Normalized relaxation rate obtained for YIG films of the thicknesses of 5.6 µ m,6.7 µ m and 53 µ m epitaxially grown on a GGG substrate of 500 µ m thickness. (d) Comparison of the normalized relaxationrates of 53 µ m-thick YIG on GGG, 30 µ m-thick substrate-free YIG and an ultrapure bulk YIG sample measured at H = H c .The number in brackets corresponds to the material layer thickness in micrometers. rate is considered to be atypical for pure YIG, for whicha monotonic decrease of Γ q is expected with decreasingtemperature [62].The revealed relaxation behavior at low temperaturescan be related either to the contribution of fast-relaxingrare-earth ions contaminating the chemical compositionof YIG [63, 64] or to the magnetic losses caused by thedipolar coupling of magnons with the spin-system of theparamagnetic GGG substrate [65, 66]. In order to clar-ify the origin of the increased relaxation we replicate ourmeasurements on the 53 µ m-thick YIG sample after pol-ishing the GGG side down to a 30 µ m substrate-free YIGfilm. The comparison of the relaxation rate is shown inFig. 3 (d). Both YIG film samples demonstrate a strongincrease in the magnon relaxation rate for decreasingtemperatures, starting from approximately 150 K. Thisfortifies the assumption of the prevailing contribution offast-relaxing rare-earth ion impurities in epitaxial YIGfilms at low temperatures. Below approximately 80 K therelaxation rate of the 53 µ m-thick YIG sample increasesfaster in comparison with the polished substrate-free YIGfilm. This difference can be attributed to coupling ofYIG’s ferrimagnetic spin system with the electron spinsof Gd ions of paramagnetic GGG. The coupling is sup-posed to be proportional to 1 /T [65] and leads to addi- tional low-temperature energy losses for all YIG filmsplaced on GGG substrates.For comparison, we measured the temperature-dependent magnon damping in an impurity- and GGG-free bulk YIG sample. Similar to the experiments withYIG films, these measurements, which were performed bymeans of the parallel parametric pumping technique in anultrapure YIG crystal of the size of (1 × ×
3) mm , showthe same damping behavior in a wide range of magnonwavenumbers. However, in contrast to the experimentwith YIG films the relaxation rate Γ q monotonically de-creases with decreasing temperature. It is clearly shownby the line denoted by semi-filled circles in Fig. 3 (d). Itfurther supports our assumption about the significant in-fluence of chemical contaminations on magnon dampingin epitaxial YIG films at cryogenic temperatures.In conclusion, in the temperature range from 20 K to340 K we have investigated the relaxation of parametri-cally excited dipole-exchange magnons in YIG films of5.6 µ m, 6.7 µ m, and 53 µ m thickness grown on a GGGsubstrate by liquid phase epitaxy. We have found thatat cryogenic temperatures the magnon lifetime stronglydecreases for all film thicknesses. By comparing thesubstrate-free YIG with the YIG/GGG samples the ob-served relaxation behavior could be related to the mag-netic damping caused by the coupling of magnons to fast-relaxing rare-earth ions inside the YIG film ( T < ∼
150 K)and to the paramagnetic spin system of GGG substrates(
T < ∼
80 K). Comparison of these results with the dataobtained from the ultrapure bulk YIG crystal showsthat in order to sustain a long magnon lifetime low-temperature magnetic experiments in YIG must be per-formed in chemically-pure and substrate-free samples.Financial support from the Deutsche Forschungsge-meinschaft (project INST 161/544-3 within SFB/TR 49,projects VA 735/1-2 and SE 1771/4-2 within SPP 1538“Spin Caloric Transport”, and project INST 248/178-1)is gratefully acknowledged. ∗ [email protected][1] K. Sato and E. Saitoh, Spintronics for Next GenerationInnovative Devices (Wiley, Chichester, 2015).[2] V.V. Kruglyak, S.O. Demokritov, and D. Grundler,
Magnonics , J. Phys. D: Appl. Phys. , 264001 (2010).[3] A.V. Chumak, V.I. Vasyuchka, A.A. Serga, and B. Hille-brands, Magnon spintronics , Nat. Phys., , 453 (2015).[4] S.O. Demokritov, V.E. Demidov, O. Dzyapko,G.A. Melkov, A.A. Serga, B. Hillebrands, andA.N. Slavin, Bose-Einstein condensation of quasi-equilibrium magnons at room temperature underpumping , Nature , 430 (2006).[5] A.A. Serga, V.S. Tiberkevich, C.W. Sandweg,V.I. Vasyuchka, D.A. Bozhko, A.V. Chumak, T. Neu-mann, B. Obry, G.A. Melkov, A.N. Slavin, and B. Hille-brands,
Bose-Einstein condensation in an ultra-hot gasof pumped magnons , Nat. Commun. , 3452 (2014).[6] C. Safranski, I. Barsukov, H.K. Lee, T. Schneider,A.A. Jara, A. Smith, H. Chang, K. Lenz, J. Lindner,Y. Tserkovnyak, M. Wu, and I.N. Krivorotov, Spin ca-loritronic nano-oscillator , Nat. Commun. , 117 (2017).[7] P. Nowik-Boltyk, O. Dzyapko, V.E. Demidov,N.G. Berloff, and S.O. Demokritov, Spatially non-uniform ground state and quantized vortices in atwo-component Bose-Einstein condensate of magnons ,Sci. Rep. , 482 (2012).[8] D.A. Bozhko, A.A. Serga, P. Clausen, V.I. Vasyuchka,F. Heussner, G.A. Melkov, A. Pomyalov, V.S. L’vov,and B. Hillebrands, Supercurrent in a room-temperature Bose-Einstein magnon condensate ,Nat. Phys. , 1057 (2016).[9] K. Nakata, K.A. van Hoogdalem, P. Simon,and D. Loss, Josephson and persistent spin cur-rents in Bose-Einstein condensates of magnons ,Phys. Rev. B , 144419 (2014).[10] H. Skarsv˚ag, C. Holmqvist, and A. Brataas, Spin super-fluidity and long-range transport in thin-film ferromag-nets , Phys. Rev. Lett. , 237201 (2015).[11] B. Flebus, S.A. Bender, Y. Tserkovnyak, and R.A. Duine,
Two-fluid theory for spin superfluidity in magnetic insu-lators , Phys. Rev. Lett. , 117201 (2016).[12] G.E.W. Bauer, E. Saitoh, and B.J. van Wees,
Spincaloritronics , Nat. Mater. , 391 (2012).[13] V.G. Harris, Modern microwave ferrites , IEEE Trans.Magn. , 1075 (2012). [14] C. Felser, G.H. Fecher, and B. Balke, Spintronics: Achallenge for materials science and solid-state chemistry ,Angew. Chem. Int. Ed. , 668 (2007).[15] A. Hirohata, H. Sukegawa, H. Yanagihara, I. ˇZuti´c,T. Seki, S. Mizukami, and R. Swaminathan, Roadmapfor emerging materials for spintronic device applications ,IEEE Trans. Magn. , 0800511 (2015).[16] V. Cherepanov, I. Kolokolov, and V. L’vov, Thesaga of YIG: Spectra, thermodynamics, interactionand relaxation of magnons in a complex magnet ,Phys. Rep.—Rev. Sec. Phys. Lett. , 81 (1993).[17] C. Dubs, O. Surzhenko, R. Linke, A. Danilewsky,U. Br¨uckner, and J. Dellith,
Sub-micrometer yttriumiron garnet LPE films with low ferromagnetic resonancelosses , J. Phys. D: Appl. Phys. , 204005 (2017).[18] Y. Sun, Y.-Y. Song, H. Chang, M. Kabatek, M. Jantz,W. Schneider, M. Wu, H. Schultheiss, and A. Hoff-mann, Growth and ferromagnetic resonance proper-ties of nanometer-thick yttrium iron garnet films ,Appl. Phys. Lett. , 152405 (2012).[19] H. Chang, P. Li, W. Zhang, T. Liu, A. Hoff-mann, L. Deng, and M. Wu,
Nanometer-thick yt-trium iron garnet films with extremely low damping ,IEEE Mag. Lett. , 6700104 (2014).[20] A. Hamadeh, O. d’Allivy Kelly, C. Hahn, H. Meley,R. Bernard, A.H. Molpeceres, V.V. Naletov, M. Viret,A. Anane, V. Cros, S.O. Demokritov, J.L. Prieto,M. Muoz, G. de Loubens, and O. Klein, Full controlof the spin-wave damping in a magnetic insulator usingspin-orbit torque , Phys. Rev. Lett. , 197203 (2014).[21] H. Yu, O. dAllivy Kelly, V. Cros, R. Bernard, P. Bor-tolotti, A. Anane, F. Brandl, R. Huber, I. Stasinopou-los, and D. Grundler,
Magnetic thin-film insulator withultra-low spin wave damping for coherent nanomagnon-ics , Sci. Rep. , 6848 (2014).[22] L.J. Cornelissen, J. Liu, R.A. Duine, J. Ben Youssef, andB.J. van Wees, Long-distance transport of magnon spininformation in a magnetic insulator at room temperature ,Nat. Phys. , 1022 (2016).[23] M. Schreier, F. Kramer, H. Huebl, S. Gepr¨ags, R. Gross,S.T.B. Goennenwein, T. Noack, T. Langner, A.A. Serga,B. Hillebrands, and V.I. Vasyuchka, Spin Seebeck effect atmicrowave frequencies , Phys. Rev. B , 224430 (2016).[24] J. Barker and G.E.W. Bauer, Thermal spin dynam-ics of yttrium iron garnet , Phys. Rev. Lett. , 217201(2016).[25] J.D. Adam,
Analog signal processing with microwavemagnetics , Proc. IEEE , 159 (1988).[26] A.A. Serga, A.V. Chumak, and B. Hillebrands, YIGmagnonics , J. Phys. D: Appl. Phys., , 264002 (2010).[27] S.O. Demokritov and A.N. Slavin, Magnonics: From fun-damentals to applications (Springer, Berlin, 2013).[28] F. Hellman et al. , Interface-induced phenomena in mag-netism , Rev. Mod. Phys. , 025006 (2017).[29] P. Andrich, C.F. de las Casas, X. Liu, H.L. Bretscher,J.R. Berman, F.J. Heremans, P.F. Nealey, andD.D. Awschalom, Long-range spin wave medi-ated control of defect qubits in nanodiamonds ,npj Quantum Inf. , 28 (2017).[30] Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa,R. Yamazaki, K. Usami, Y. Nakamura et al. , Quan-tum magnonics: magnon meets superconducting qubit ,C. R. Physique , 729 (2016).[31] S. Klingler, H. Maier-Flaig, C. Dubs, O. Surzhenko, R. Gross, H. Huebl, S.T.B. Goennenwein, and M. Weiler,
Gilbert damping of magnetostatic modes in a yttrium irongarnet sphere , Appl. Phys. Lett. , 092409 (2017).[32] Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Ya-mazaki, K. Usami, and Y. Nakamura,
Coherent couplingbetween a ferromagnetic magnon and a superconductingqubit , Science , 405 (2015).[33] H. Huebl, C.W. Zollitsch, J. Lotze, F. Hocke, M. Greifen-stein, A. Marx, R. Gross, and T.B. Goennenwein,
High co-operativity in coupled microwave resonator ferrimagneticinsulator hybrids , Phys. Rev. Lett. , 127003 (2013).[34] Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki,K. Usami, and Y. Nakamura,
Hybridizing ferromagneticmagnons and microwave photons in the quantum limit ,Phys. Rev. Lett. , 083603 (2014).[35] S. Kosen, R.G.E. Morris, A.F. van Loo, and A.D. Karen-ovska,
Measurement of a magnonic crystal at millikelvintemperatures , (2017), arXiv:1711.00958.[36] R.G.E. Morris, A.F. van Loo, S. Kosen, and A.D. Karen-ovska,
Strong coupling of magnons in a YIG sphere tophotons in a planar superconducting resonator in thequantum limit , Sci. Rep. , 11511 (2017).[37] E.G. Spencer, R.C. LeCraw, and R.C. Linares, Jr., Low-temperature ferromagnetic relaxation in yttrium iron gar-net , Phys. Rev. , 1937 (1961).[38] C. Vittoria, P. Lubitz, P. Hansen, and W. Tolksdorf,
FMR linewidth measurements in bismuth–substitutedYIG , J. Appl. Phys. , 3699 (1985).[39] S.S. Kalarickal, P. Krivosik, M. Wu, and C.E. Pat-ton, Ferromagnetic resonance linewidth in metallicthin films: Comparison of measurement methods ,J. Appl. Phys. , 093909 (2006).[40] T. Kasuya and R.C. LeCraw, Relaxation mechanisms inferromagnetic resonance , Phys. Rev. Lett. , 223 (1961).[41] M.B. Jungfleisch, A.V. Chumak, V.I. Vasyuchka,A.A. Serga, B. Obry, H. Schultheiss, P.A. Beck,A.D. Karenowska, E. Saitoh, and B. Hillebrands, Temporal evolution of inverse spin Hall effect voltagein a magnetic insulator-nonmagnetic metal structure ,Appl. Phys. Lett. , 182512 (2011).[42] T. Sebastian, Y. Ohdaira, T. Kubota, P. Pirro,T. Br¨acher, K. Vogt, A.A. Serga, H. Naganuma,M. Oogane, Y. Ando, and B. Hillebrands, Low-damping spin-wave propagation in a micro-structured Co Mn . Fe . Si Heusler waveguide ,Phys. Lett. , 112402 (2012).[43] I. Razdolski, A. Alekhin, U. Martens, D. B¨urstel,D. Diesing, M. M¨unzenberg, U. Bovensiepen,and A. Melnikov,
Analysis of the time-resolvedmagneto-optical Kerr effect for ultrafast mag-netization dynamics in ferromagnetic thin films ,J. Phys.: Condens. Matter , 174002 (2017).[44] O. Klein, V. Charbois, V.V. Naletov, and C. Fer-mon, Measurement of the ferromagnetic relaxation in amicron-size sample , Phys. Rev. B , 220407(R) (2003).[45] D.E. Kaplan and C.F. Kooi, Magnetostatic echoes ,J. Appl. Phys. , 1005 (1966).[46] V.V. Danilov and A.V. Tychinski˘i, Magnetostatic echo inferrite films , JETP Lett. , 319 (1983).[47] G.A. Melkov, V.I. Vasyuchka, Yu.V. Kobljanskyj, andA.N. Slavin, Wave-front reversal in a medium withinhomogeneities and an anisotropic wave spectrum ,Phys. Rev. B , 224407 (2004). [48] A.G. Gurevich and A.N. Anisimov, Intrinsic spinwave relaxation processes in yttrium iron garnets ,Sov. Phys. JETP , 336 (1975).[49] T. Langner, A. Kirihara, A.A. Serga, B. Hillebrands,and V.I. Vasyuchka, Damping of parametrically excitedmagnons in the presence of the longitudinal spin Seebeckeffect , Phys. Rev. B , 134441 (2017).[50] H. Suhl, The theory of ferromagnetic resonance at highsignal powers , J. Phys. Chem. Solids, , 209 (1957).[51] E. Schl¨omann, J.J. Green and U. Milano, Recent devel-opments in ferromagnetic resonance at high power levels ,J. Appl. Phys. , S386 (1960).[52] T. Neumann, A.A. Serga, V.I. Vasyuchka, and B. Hille-brands, Field-induced transition from parallel to perpen-dicular parametric pumping for a microstrip transducer ,Appl. Phys. Lett. , 192502 (2009).[53] A.A. Serga, C.W. Sandweg, V.I. Vasyuchka,M.B. Jungfleisch, B. Hillebrands, A. Kreisel, P. Kopi-etz, and M.P. Kostylev, Brillouin light scatteringspectroscopy of parametrically excited dipole-exchangemagnons , Phys. Rev. B , 134403 (2012).[54] V.B. Bobkov, I.V. Zavislyak, and V.F. Romanyuk, Micro-wave spectroscopy of magnetostatic waves in epitaxial fer-rite films , J. Commun. Technol. Electron. , 196 (2003).[55] A.G. Gurevich and G.A. Melkov, Magnetization oscilla-tions and waves , (CRC Press, Boca Raton, 1996).[56] R.C. LeCraw and L.R. Walker,
Temperature depen-dence of the spin-wave spectrum of yttrium iron garnet ,J. Appl. Phys. , S167 (1961).[57] V.V. Danilov, D.L. Lyfar’, Yu.V. Lyubon’ko,A.Yu. Nechiporuk, and S.M. Ryabchenko Low-temperature ferromagnetic resonance in epi-taxial garnet films on paramagnetic substrates ,Soviet Physics Journal , 276 (1989).[58] E.E. Anderson, Molecular field model and the magnetiza-tion of YIG , Phys. Rev. , A1581 (1964).[59] P. Hansen, P. R¨oschmann, and W. Tolksdorf,
Saturationmagnetization of gallium-substituted yttrium iron garnet ,J. Appl. Phys. , 2728 (1974).[60] B. Obry, V.I. Vasyuchka, A.V. Chumak,A.A. Serga, and B. Hillebrands, Spin-wave prop-agation and transformation in a thermal gradient ,Appl. Phys. Lett. , 192406 (2012).[61] M. Kaack, S. Jun, S.A. Nikitov, and J. Pelzl,
Magnetostatic spin wave modes excitation inyttrium-iron-garnet film under various temperatures ,J. Magn. Magn. Mater. , 90 (1999).[62] M. Sparks,
Ferromagnetic relaxation theory , (McGraw-Hill, New York, 1964).[63] G.F. Dionne and G.L. Fitch,
Temperature dependenceof spin-lattice relaxation in rare-earth iron garnets ,J. Appl. Phys. , 4963 (2000).[64] P. Hansen, K. Witter, and W. Tolksdorf, Magnetic andmagneto-optic properties of lead- and bismuth-substitutedyttrium iron garnet films , Phys. Rev. B , 6608 (1983).[65] M.G. Balinskii, V.V. Danilov, A.Yu. Nechiporuk, andV.M. Talalaevskii, Damping of magnetostatic spinwaves in substrates , Radiophys. Quantum Electron. ,954 (1986).[66] V.V. Danilov, A.Yu. Nechiporuk, and L.V. Chevnyuk,, Temperature dependences of paramagnetic excitationthreshold and relaxation parameter of spin waves in gar-net structures , Low Temp. Phys.22