Linear and nonlinear spin-wave dynamics in ultralow-damping microstructured Co2FeAl Heusler waveguide Sheng Wang, Junjia Ding, Xiawei Guan, Matthias B. Jungfleisch, Zhizhi Zhang, Xiaojie Wang, Wei Gu, Yunlai Zhu, John E. Pearson, Xiaomin Cheng, Axel Hoffmann, and Xiangshui Miao
Citation: Appl. Phys. Lett. 113, 232404 (2018); doi: 10.1063/1.5038836 View online: https://doi.org/10.1063/1.5038836 View Table of Contents: http://aip.scitation.org/toc/apl/113/23 Published by the American Institute of Physics
Reuse of AIP Publishing content is subject to the terms at:
https://publishing.aip.org/authors/rightsand-permissions. Downloaded to: 198.181.43.57 on 07 December 2018, At: 20:47
APPLIED PHYSICS LETTERS 113, 232404 (2018)
Linear and nonlinear spin-wave dynamics in ultralow-damping microstructured Co2FeAl Heusler waveguide Sheng Wang,1,2 Junjia Ding,2 Xiawei Guan,1 Matthias B. Jungfleisch,3 Zhizhi Zhang,1,2 Xiaojie Wang,1 Wei Gu,1 Yunlai Zhu,1 John E. Pearson,2 Xiaomin Cheng,1,a) Axel Hoffmann,2 and Xiangshui Miao1
1 Wuhan National Research Center for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China 2 Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA 3 Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
(Received 6 May 2018; accepted 10 November 2018; published online 5 December 2018) We report on the investigation of linear and nonlinear spin-wave dynamics of a microstructured Co2FeAl Heusler waveguide using the microfocus Brillouin light scattering technique. A significantly increased decay length of 19.55 lm owing to decreased Gilbert damping has been observed for waves propagating in the linear regime. Furthermore, the localized edge mode caused by the demagnetizing field leads to the nonlinear generation of high-order harmonics at double and triple excitation frequencies at high powers. The obtained results provide valuable insights into the linear and nonlinear spin wave dynamics of the Heusler waveguide and could potentially be applied in the implementation of spin wave frequency multipliers for magnonic applications. Published by AIP Publishing. https://doi.org/10.1063/1.5038836 Magnonics is a newly emerging field aiming at highly efficient information transport and processing with the collective procession of the electrons’ spin rather than the dissipative translation of charge.1–5 The wide variety of linear and nonlinear spin-wave phenomena6–8 has aroused people’s extensive interest and attention for their great potential for technical applications. Up to now, the most commonly used materials in related investigations are polycrystalline Permalloy (Py) and single-crystal yttrium–iron–garnet (YIG). YIG has the lowest magnetic damping9 among all practicable materials, but also has several disadvantages severely retarding its technical application. Typically, high-quality YIG films possessing extremely low damping are bulk materials with a thickness of a few micrometers. In addition, common methods used for high-quality YIG fabrication are liquidphase epitaxy10 (LPE) and pulsed-laser deposition11 (PLD), which prevent it from mass production on the industrial level. Recent progress in the growth of YIG films allows for the fabrication of low-damping nanometer-thick YIG films with sputtering.12,13 However, YIG has much worse experimental reproducibility compared with ferromagnetic metals due to its complicated crystalline and magnetic structure.14 The issues of growth and microstructuring can be easily overcome by the utilization of metallic Permalloy. However, it suffers from much worse damping property that only allows for reliable spin-wave detection in the range of a few micrometers.15 Thus, both YIG and Permalloy can partially fulfill the purpose of practical magnonic applications. In order to promote the practical application of magnonics, intensive theoretical and experimental efforts have been devoted to the development of novel materials.16,17 Among the possible candidates, cobalt-based full Heusler compound materials are the most promising alternatives. a)
Author to whom correspondence should be addressed: xmcheng@hust. edu.cn
0003-6951/2018/113(23)/232404/5/$30.00
There exists tremendous research interest in Heusler compounds stimulated by the fantastic property combination of high spin polarization, high saturation magnetization, high Curie temperature, and low magnetic Gilbert damping.18 The Gilbert damping of Co2FeAl (CFA) is found to be of the order of 0.001,19 which is almost the lowest among cobaltbased full Heusler compounds. The utilization of ultralow damping metallic CFA as a waveguide ensures the feasibility of the realization of magnonic crystals with a submicrometer or even nanometer spatial scale,20 which is critically important to keep up with the ongoing miniaturization trend of semiconductors. Because of the weak decay of spin waves in CFA compared with that in permalloy, it seems possible to implement structures such as a T-shaped power divider and so on for signal processing and generation.21 The decreased Gilbert damping not only gives rise to increased propagation distances,22 but also brings about a pronounced occurrence of novel nonlinear effects due to lower thresholds as already observed in Co2Mn0.6Fe0.4Si.23 Thus, a systematic study concerning the linear and nonlinear spin-wave dynamics of the ultralow-damping Co2FeAl Heusler waveguide is essential for future magnonic applications. In this work, we present a detailed experimental study on linear and nonlinear spin-wave dynamics of a microstructured CFA waveguide utilizing microfocus Brillouin light scattering (lBLS) spectroscopy. The exponential decay behavior of spin wave intensity is observed along the propagation direction, and the decay length is determined to be much longer than other ferromagnetic metals at low excitation power. A localized edge mode is formed by the inhomogeneous effective field configuration, which leads to further nonlinear frequency multiplication in the nonlinear regime. The CFA thin film with a thickness of 20 nm was deposited by magnetron sputtering on a single crystal MgO(001) substrate at RT with a base pressure better than 7 108 Torr. After the growth of CFA, an ex-situ post annealing was
113, 232404-1
Published by AIP Publishing.
232404-2
Wang et al.
Appl. Phys. Lett. 113, 232404 (2018)
performed immediately at 600 C for 2 h in 4 108 Torr. The dynamic magnetization response of the unpatterned film was extracted from a flip chip measurement made using a vector network analyzer ferromagnetic resonance (VNA-FMR) spectrometer. The resonance frequency f as a function of resonance field H is shown in Fig. 1(a). Angular-dependent magnetic remanence of the CFA thin film measured with a Vibrating Sample Magnetometer (VSM) reveals an in-plane fourfold anisotropy with two easy axes of the CFA [110] and [1 10] directions. A fit obtained using the following formula24 f ¼
jcj pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l ðH 2K4 =l0 Ms ÞðH þ MS þ K4 =l0 Ms Þ 2p 0
(1)
yields the parameters gyromagnetic ratio jcj/2p ¼ 29.47 6 0.10 GHz/T, in-plane fourfold anisotropy constant K4 ¼ 1.57 kJ/m3 and saturation magnetization MS ¼ 850.87 6 7.80 kA/m, corresponding to 4.31 lB/f.u., which are in accord with the reported values.25 It is well established that the FMR full linewidth at half maximum (FWHM) DH in CFA is anisotropic, with minima along the h110i axis and maxima along the h100i.19 Here, we present the frequency f dependent DH for the film with an applied field along the [110] direction as shown in Fig. 1(b). With a linear fit obtained using the following equation,26 we can determine the Gilbert damping a and the inhomogeneous linewidth broadening DH0 as DH ¼ DH0 þ
4paf : jcj
(2)
The fitting gives DH0 ¼ 52.17 6 0.13 Oe and a pretty low damping constant a ¼ (1.56 6 0.08) 103 (for comparison, a(Ni81Fe19) ¼ 8 103).27 As we can see, the magnetic losses are mostly defined by DH0, which is comparable to that in MgO buffered CFA samples28 (DH0 ¼ 45 Oe).
However, the inhomogeneous bordering is rather large compared with that in PLD YIG.29 This discrepancy is mainly due to the difference in the inhomogeneity of magnetic films resulting from different crystallographic textures of singlephase PLD YIG and polycrystalline CFA alloy.30 The slight deviation from rigorous linear relation in frequency dependent linewidth is deemed to result from the two magnon scattering by the dislocation defects.19 As we can see from the static magnetization measurement performed at 300 K in Fig. 1(c), the coercive field Hc is 5 Oe and the film is saturated above 200 Oe. The saturation magnetization Ms is 970 kA/m, which is slightly higher than the effective magnetization obtained from FMR measurements. In a subsequent microfabrication process, the CFA waveguide of 5 lm width was patterned by a laser writer and ion milling. In order to excite spin dynamics in the spin wave waveguide, a ground-signal-ground (GSG), coplanar waveguide (CPW) shorted at one end made of Ti (5 nm)/Au (150 nm) was patterned on top of the CFA waveguide. The antenna oriented perpendicularly to the CFA microstripe was electrically isolated from the waveguides by a layer of SiO2 with a thickness of 150 nm. A uniform magnetic bias field was applied transversely to the long axis of the waveguide in the y direction as shown by the sketch in Fig. 1(d), corresponding to the propagation geometry of Damon-Eshbach waves.31 The microstructured sample was first characterized by transmitting through the antenna a microwave current at varying frequency under different bias fields and measuring the intensity of the excited spin waves utilizing lBLS at a distance of 3 lm from the antenna in the center of the waveguide. The microwave power was chosen as P ¼ 2 dBm, which is sufficiently low to avoid possible nonlinear effects. As seen from Fig. 2(a), spin waves can be efficiently excited in a wide frequency band. A typical excitation characteristic
FIG. 1. (a) Ferromagnetic resonance frequency over the resonance field. (b) FMR linewidth DH as a function of frequency f with the magnetic field applied in the plane of film along the [110] direction. The red solid lines in (a) and (b) represent fits to the experimental data. (c) In-plane hysteresis loop of the unpatterned film measured at 300 K. (d) Schematic illustration of the device structure. The device includes a 20 nm thick 5 lm wide CFA waveguide separated from the CPW by 150 nm of SiO2. The GSG coplanar waveguide was made of Ti (5 nm)/Au (150 nm) with a signal line width (Ws) of 4 lm, a ground line width (Wg) of 3 lm and the edge-to-edge separation between the signal and the ground line (g) of 3 lm. The bias magnetic field is applied in the y-direction and normal to the spin wave propagation direction.
232404-3
Wang et al.
obtained for H ¼ 525 Oe is shown in Fig. 2(b). It exhibits an intensity peak at f ¼ 6.95 GHz corresponding to the uniform ferromagnetic resonance. The efficient spin wave excitation frequency band is located between 6.95 and 7.8 GHz and the signal goes below the noise level at a frequency above 9 GHz. In the next step, we excited the spin wave at a fixed excitation frequency fe ¼ 3.5 GHz which is far below the FMR frequency at H ¼ 525 Oe and detected the spin wave intensities over a frequency region of interest simultaneously with different excitation microwave powers. A color-coded spin wave intensity map taken at a distance of 1 lm from the antenna in the center of the waveguide is shown in Fig. 2(c). Starting from a certain power, in addition to the directly excited spin wave at fd ¼ fe ¼ 3.5 GHz, higher-order harmonics at double- and triple-excitation frequencies were also observed. Figure 2(d) shows the nonlinear increase in intensity for a directed excited spin wave, where a rapid increase from 15 dBm can be clearly observed. Although the
FIG. 2. (a) Color-coded measured spin-wave intensity as a function of the microwave frequency and the applied magnetic field. (b) Dependence of the spin-wave intensity on the excitation frequency for H ¼ 525 Oe. (c) Colorcoded spin-wave intensity dependent on the excitation microwave power and the detection frequency. The measurement was performed at a distance of 1 lm from the antenna at the center of the waveguide for H ¼ 525 Oe and fe ¼ 3.5 GHz. (d) Dependence of the spin-wave intensity on the excitation power for fd ¼ fe ¼ 3.5 GHz. (e) An exemplary BLS spectrum taken for a microwave power of P ¼ 29.5 dBm.
Appl. Phys. Lett. 113, 232404 (2018)
nonlinear generation is a thresholdless process,32 a reliable detection should account for the background noise. Figure 2(e) illustrates a spectrum taken at a microwave power of 29.5 dBm, in which peaks at 2fe and 3fe appear in addition to the directly excited one. The intensity at fd ¼ fe can be ascribed to nonresonant forced excitation by the dynamic microwave field generated by CPW and the higher harmonics are expected to be excited resonantly by nonlinear magnon-magnon interactions23 at the point of observation. The spatial maps of the BLS intensity with a spatial resolution of 250 nm can be obtained by rastering the probing laser spot in the two lateral directions. The color map of the two-dimensional BLS intensity distribution was recorded for spin waves excited at a magnetic field H ¼ 525 Oe, excitation microwave frequency f ¼ 7.0 GHz and microwave power P ¼ 2 dBm [Fig. 3(a)]. Intensity variation, especially nodal line observed across the width of the waveguide can be explained by the multi-mode propagation and the resulting interference mainly caused by the transverse modes n ¼ 1 and n ¼ 3. To further reveal the decay feature of spin wave intensity in the CFA waveguide, BLS intensity as a function of the distance from the antenna for some exemplary excitation frequencies at H ¼ 525 Oe is shown in Fig. 3(b). The measurements were taken at a distance in the range from 3 to 10 lm to avoid the possible deviation from a simple exponential decay caused by a shadow effect from the ground line of the CPW.33 The BLS intensity was then integrated over the width of the waveguide to diminish the influence caused by multi-mode propagation. Solid lines indicate exponential fits to the data as follows: 2x þ c; (3) IðxÞ ¼ I0 exp d where x is the distance from the antenna, I0 denotes the spin wave intensity at x ¼ 0, d is the exponential decay length of the spin wave amplitude, and c accounts for the offset given by the experiment noise level. The fitting procedure yields a decay length rather large compared with the commonly used permalloy waveguide (4 lm for a 5.1 lm wide and 20 nm thick Py stripe34). This dramatic increase in the decay length can be attributed to the highly reduced magnetic damping of CFA. As is seen from Fig. 3(b), the spin-wave decay length d increases with increasing excitation frequencies as the decay becomes slighter. The FMR lifetime s is given by 1=s ¼ acl0 ðHext þ Ms =2Þ. As indicated in Fig. 1(b), the Gilbert damping remains constant for different spin-wave modes; thus, the decay length exclusively depends on the group velocity for d ¼ G s. Figure 3(c) shows the calculated dispersion curve and the corresponding group velocity using the parameters estimated from FMR.35 As is seen from Fig. 3(c), the analytical calculation agrees quite well with the experimental findings in a qualitative sense and can serve as an explanation for the observation of varying decay lengths. The spin-wave lifetime s is estimated to be 5.90 ns. So, if we compare the value of the measured propagation length with the one estimated from the FMR lifetime, a quantitative agreement of calculation and experiment could not be found. The major reason for this is in connection with the accurate calculation of the group velocity if we take into account the
232404-4
Wang et al.
Appl. Phys. Lett. 113, 232404 (2018)
FIG. 3. (a) Color-coded spatial map of the spin-wave intensity for an excitation frequency of fe ¼ 7.0 GHz, a microwave power of 2 dBm, and an external field H ¼ 525 Oe. (b) Integrated spin-wave intensity as a function of the position along the spin wave waveguide for different excitation frequencies. Solid lines are exponential fits. (c) Analytical calculated dispersion curve (blue line) and group velocity (red line) for n ¼ 1 mode.
fact that the calculated group velocity has a strong dependence on the material and the geometrical parameters and the model it is based on. Towards the higher excitation frequency, a further increase and an eventual drop in the decay length can be expected to follow the same trend as revealed for the group velocity.22 These significantly increased decay lengths guarantee a reliable spin-wave signal transmission and processing over large distances. In the latter part, we turn to the nonlinear spin wave dynamics emerging at large excitation microwave powers. The generation of harmonics at multiples of the exciting frequency can be generally interpreted by the intrinsic nonlinearity of the Landau-Lifshitz-Gilbert equation which governs spin dynamics.36 The magnetic system was excited at fe ¼ 3.5 GHz, which is far below the resonance (6.95 GHz) with a bias field of 525 Oe applied. A microwave power of P ¼ 30 dBm was chosen for the experiment in the nonlinear regime. Two-dimensional intensity distribution maps for fd ¼ fe, fd ¼ 2fe, and fd ¼ 3fe are shown in Fig. 4. It is obvious that the directly excited mode is strongly localized at the edges of the spin wave waveguide as shown in Fig. 4(a). As mentioned above, the resonance frequency in the center of the waveguide is well above the excitation frequency; thus, the directly excited mode cannot be excited resonantly and propagates in the center. Close to the edge, the effective field is strongly decreased by the demagnetizing effects resulting in inhomogeneous magnetization. Therefore, the localized spin wave mode at fd ¼ fe can be judged as a resonantly excited edge mode.37 As can be seen from Figs. 4(b) and 4(c), the nonlinearly generated high-order harmonics of the excitation frequency
can be clearly observed. It is worthwhile mentioning that the high-order harmonics whose frequencies are above the lower cutoff frequency radiated from the edge underneath the antenna and propagated towards the center of the waveguide. The second harmonic generation can be comprehended qualitatively given the strong demagnetizing field. The precession of the magnetization vector M in the edge modes excited at the frequency fe is elliptical because of the anisotropy of the demagnetization fields.38,39 As a consequence of the dynamic demagnetization field effect, the projection of M on the y axis has a time dependent dynamic component 32 1 2 2 4M ðmx mz Þ cos ½2pð2fe Þt, which oscillates at a frequency 2fe. The dynamic component then gives rise to a dynamic dipolar field at the double frequency, which can be treated as a linear excitation source for the second harmonic. A further expansion of the series for the projection of M on the y axis simultaneously taking into account the fe and 2fe components will lead to a term with fe þ 2fe ¼ 3fe. As a result, the observed frequency tripling can be ascribed to the frequency mixing in the nonlinear system,40 where the 1st and the 2nd harmonics are present. In conclusion, we have investigated experimentally the linear and nonlinear spin-wave dynamics in a microstructured Co2FeAl Heusler waveguide using lBLS technique. Spin wave propagation can be detected over a large distance and a significantly increased decay length of 19.55 lm has been observed for waves propagating in the linear regime. The profound increase in the decay length owing to the decreased Gilbert damping as low as 1.56 103 is of great importance for a reliable spin-wave signal transmission and processing over large distances. In addition, the nonlinear
FIG. 4. Spatial distributions of lBLS intensity measured at P ¼ 30 dBm for (a) fd ¼ fe ¼ 3.5 GHz, (b) fd ¼ 2fe, and (c) fd ¼ 3fe. All have been normalized to their respective maximum for a given detection frequency.
232404-5
Wang et al.
generation of higher-order harmonics has been observed at high powers. A so-called edge mode is localized at the edges by the demagnetizing field and leads to the emission of highorder harmonics. Our findings may provide an insight into the linear and nonlinear spin wave dynamics of the Heusler waveguide and throw light on the implementation of spin wave frequency multipliers for magnonic applications. The work in Huazhong University of Science and Technology was supported by the National Natural Science Foundation of China under Grant No. 61474052. The work in Argonne National Laboratory, including sample fabrication and lBLS measurements, was supported by the U. S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. # DE-AC0206CH11357. Wang gratefully acknowledges inspiring discussions with Dr. Peng Li (Stanford University, USA), Pavel N. Lapa (University of California San Diego, USA), Changjiang Liu, and Deshun Hong (Argonne National Laboratory, USA). 1
A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nat. Phys. 11(6), 453–461 (2015). 2 A. Hoffmann and S. D. Bader, Phys. Rev. Appl. 4(4), 047001 (2015). 3 D. Grundler, Nat. Phys. 11(6), 438–441 (2015). 4 A. Haldar, D. Kumar, and A. O. Adeyeye, Nat. Nanotechnol. 11(5), 437–443 (2016). 5 X. S. Wang, H. W. Zhang, and X. R. Wang, Phys. Rev. Appl. 9(2), 024029 (2018). 6 S. O. Demokritov, Spin Wave Confinement: Propagating Waves, 2nd ed. (Pan Stanford Publishing, 2017). 7 S. O. Demokritov and A. N. Slavin, Magnonics: From Fundamentals to Applications (Springer Science & Business Media, 2012). 8 D. D. Stancil and A. Prabhakar, Spin Waves (Springer, 2009). 9 A. Serga, A. Chumak, and B. Hillebrands, J. Phys. D: Appl. Phys. 43(26), 264002 (2010). 10 R. Henry, P. Besser, D. Heinz, and J. Mee, IEEE Trans. Magn. 9(3), 535–537 (1973). 11 P. Dorsey, S. Bushnell, R. Seed, and C. Vittoria, J. Appl. Phys. 74(2), 1242–1246 (1993). 12 T. Liu, H. Chang, V. Vlaminck, Y. Sun, M. Kabatek, A. Hoffmann, L. Deng, and M. Wu, J. Appl. Phys. 115(17), 17A501 (2014). 13 C. Houchen, L. Peng, Z. Wei, L. Tao, A. Hoffmann, D. Longjiang, and W. Mingzhong, IEEE Magn. Lett. 5, 1–4 (2014). 14 V. E. Demidov, S. Urazhdin, A. B. Rinkevich, G. Reiss, and S. O. Demokritov, Appl. Phys. Lett. 104(15), 152402 (2014). 15 M. Madami, S. Bonetti, G. Consolo, S. Tacchi, G. Carlotti, G. Gubbiotti, ˚ kerman, Nat. Nanotechnol. 6(10), 635 F. Mancoff, M. A. Yar, and J. A (2011). 16 S. Trudel, O. Gaier, J. Hamrle, and B. Hillebrands, J. Phys. D: Appl. Phys. 43(19), 193001 (2010).
Appl. Phys. Lett. 113, 232404 (2018) 17
H. Ulrichs, B. Lenk, and M. M€ unzenberg, Appl. Phys. Lett. 97(9), 092506 (2010). 18 ˚ kerman, A. V. Chumak, Y. Otani, G. E. R. L. Stamps, S. Breitkreutz, J. A Bauer, J.-U. Thiele, M. Bowen, S. A. Majetich, and M. Kl€aui, J. Phys. D: Appl. Phys. 47(33), 333001 (2014). 19 S. Mizukami, D. Watanabe, M. Oogane, Y. Ando, Y. Miura, M. Shirai, and T. Miyazaki, J. Appl. Phys. 105(7), 07D306 (2009). 20 S. A. Nikitov, D. V. Kalyabin, I. V. Lisenkov, A. Slavin, Y. N. Barabanenkov, S. A. Osokin, A. V. Sadovnikov, E. N. Beginin, M. A. Morozova, Y. A. Filimonov, Y. V. Khivintsev, S. L. Vysotsky, V. K. Sakharov, and E. S. Pavlov, Phys.-Usp. 58(10), 1002–1028 (2015). 21 T. Br€acher, P. Pirro, A. A. Serga, and B. Hillebrands, Appl. Phys. Lett. 103(14), 142415 (2013). 22 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, Appl. Phys. Lett. 100(11), 112402 (2012). 23 T. Sebastian, T. Bracher, P. Pirro, A. A. Serga, B. Hillebrands, T. Kubota, H. Naganuma, M. Oogane, and Y. Ando, Phys. Rev. Lett. 110(6), 067201 (2013). 24 Z. Chen, W. Kong, K. Mi, G. Chen, P. Zhang, X. Fan, C. Gao, and D. Xue, Appl. Phys. Lett. 112(12), 122406 (2018). 25 M. Belmeguenai, F. Zighem, Y. Roussigne, S. M. Cherif, P. Moch, K. Westerholt, G. Woltersdorf, and G. Bayreuther, Phys. Rev. B 79(2), 024419 (2009). 26 S. S. Kalarickal, P. Krivosik, M. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, and J. P. Nibarger, J. Appl. Phys. 99(9), 093909 (2006). 27 Z. Liu, F. Giesen, X. Zhu, R. D. Sydora, and M. R. Freeman, Phys. Rev. Lett. 98(8), 087201 (2007). 28 G. Ortiz, M. S. Gabor, J. T. Petrisor, F. Boust, F. Issac, C. Tiusan, M. Hehn, and J. F. Bobo, J. Appl. Phys. 109(7), 07D324 (2011). 29 M. C. Onbasli, A. Kehlberger, D. H. Kim, G. Jakob, M. Kl€aui, A. V. Chumak, B. Hillebrands, and C. A. Ross, APL Mater. 2(10), 106102 (2014). 30 D. Zhang, J. J. Yue, Z. X. Kou, L. Lin, Y. Zhai, and H. R. Zhai, AIP Adv. 6(5), 056125 (2016). 31 R. W. Damon and J. Eshbach, J. Phys. Chem. Solids 19(3), 308–320 (1961). 32 V. E. Demidov, M. P. Kostylev, K. Rott, P. Krzysteczko, G. Reiss, and S. O. Demokritov, Phys. Rev. B 83(5), 054408 (2011). 33 T. Bracher, M. Fabre, T. Meyer, T. Fischer, S. Auffret, O. Boulle, U. Ebels, P. Pirro, and G. Gaudin, Nano Lett. 17(12), 7234–7241 (2017). 34 V. E. Demidov, S. O. Demokritov, K. Rott, P. Krzysteczko, and G. Reiss, Phys. Rev. B 77(6), 064406 (2008). 35 K. An, D. R. Birt, C.-F. Pai, K. Olsson, D. C. Ralph, R. A. Buhrman, and X. Li, Phys. Rev. B 89(14), 140405(R) (2014). 36 V. E. Demidov, H. Ulrichs, S. Urazhdin, S. O. Demokritov, V. Bessonov, R. Gieniusz, and A. Maziewski, Appl. Phys. Lett. 99(1), 012505 (2011). 37 C. Bayer, J. P. Park, H. Wang, M. Yan, C. E. Campbell, and P. A. Crowell, Phys. Rev. B 69(13), 134401 (2004). 38 I. Lisenkov, V. Tyberkevych, S. Nikitov, and A. Slavin, Phys. Rev. B 93(21), 214441 (2016). 39 J. Jorzick, S. O. Demokritov, B. Hillebrands, M. Bailleul, C. Fermon, K. Y. Guslienko, A. N. Slavin, D. V. Berkov, and N. L. Gorn, Phys. Rev. Lett. 88(4), 047204 (2002). 40 G. Boyd, T. Bridges, C. Patel, and E. Buehler, Appl. Phys. Lett. 21(11), 553–555 (1972).
