Non-Gilbert-damping Mechanism in a Ferromagnetic Heusler Compound Probed by Nonlinear Spin Dynamics P. Pirro, 1,* T. Sebastian, 1,† T. Brächer, 1,2 A. A. Serga, 1 T. Kubota, 3 H. Naganuma, 4 M. Oogane, 4 Y. Ando, 4 and B. Hillebrands 1 1 Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany 2 Graduate School Materials Science in Mainz, Gottlieb-Daimler-Straße 47, Germany 3 Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan 4 Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-05, Sendai 980-8579, Japan (Received 21 April 2014; published 26 November 2014) The nonlinear decay of propagating spin waves in the low-Gilbert-damping Heusler film Co 2 Mn 0.6 Fe 0.4 Si is reported. Here, two initial magnons with frequency f 0 scatter into two secondary magnons with frequencies f 1 and f 2 . The most remarkable observation is that f 1 stays fixed if f 0 is changed. This indicates, that the f 1 magnon mode has the lowest instability threshold, which, however, cannot be understood if only Gilbert damping is present. We show that the observed behavior is caused by interaction of the magnon modes f 1 and f 2 with the thermal magnon bath. This evidences a significant contribution of the intrinsic magnon-magnon scattering mechanisms to the magnetic damping in high- quality Heusler compounds. DOI: 10.1103/PhysRevLett.113.227601 PACS numbers: 76.50.+g, 75.30.Ds, 78.35.+c, 85.75.-d The field of spintronics has attracted huge interest in recent years due to a multitude of physical phenomena and applications related to the spin degree of freedom [1,2]. To develop this area further, intensive research efforts are devoted to design new materials with outstanding proper- ties, like, e.g., high spin-polarization. The class of ferro- magnetic Heusler materials [3] is of special interest since these materials potentially combine high spin polarization and Curie temperature with low magnetic Gilbert-damping [4–6]. Thus, these materials allow for a long-distance spin transport by magnons—the quanta of spin waves [7,8]. However, alongside with the decrease of the Gilbert-type relaxation, which results, in this case, from the reduced interaction of the magnetic excitations with the electron bath, other damping mechanisms, caused by, e.g., nonlinear magnon-magnon scattering, can play an important role [9–13]. Thus, the development of new ferromagnetic Heusler materials calls for a comprehensive study of the occurring nonlinear spin-wave phenomena since these will dominate the energy redistribution in magnetization dynamics. In this Letter, we investigate the spin-wave damping mechanisms in the Heusler compound Co 2 Mn 0.6 Fe 0.4 Si (CMFS) [4,5,7,8] by the experimental observation and theoretical analysis of the second order spin-wave insta- bility [12,14–18] in a microscaled magnonic waveguide. In this four-magnon scattering process, two initial magnons at frequency f 0 scatter into two magnons with frequencies f 1 and f 2 , named the unstable modes. We observe that the mode f 1 is a dominant unstable mode whose frequency is independent of the frequency f 0 of the initial spin waves. Such a dominant mode has not been reported previously for metallic ferromagnetic films. We show that it is a specific feature of the low-Gilbert- damping Heusler film caused by the influence of a non- Gilbert-damping mechanism, which significantly affects the total relaxation rate η of the individual spin-wave modes. It can be identified as an intrinsic relaxation caused by the interaction with the thermal magnon bath. The sample is sketched in Fig. 1(a):a 5-μm-wide CMFS waveguide [30 nm thick, 70 μm long, capped with Ta (5 nm)] grown on a MgO substrate with a 40 nm Cr buffer layer was patterned by electron-beam lithography and argon-ion milling. Then, a 1-μm-wide antenna (Ti-Cu) was produced on top of the CMFS waveguide by electron- beam evaporation. A microwave current with variable frequency f 0 is passed through the antenna to create dynamic Oersted fields which excite coherent propagating spin waves at the same frequency. k per k par H ext MW frequency (GHz) f 0 6 8 10 12 14 10 -3 10 -2 10 -1 10 0 I S L B ) s t i n u . b r a ( (b) (a) antenna h dyn BLS-laser FIG. 1 (color online). (a) Schematic view of the sample: spin waves are excited in a CMFS waveguide by means of a microstrip antenna. A bias field H ext is applied perpendicular to the waveguide’s long axis. (b) Brillouin light-scattering intensity I BLS in the linear regime as a function of the microwave excitation frequency f 0 . PRL 113, 227601 (2014) PHYSICAL REVIEW LETTERS week ending 28 NOVEMBER 2014 0031-9007=14=113(22)=227601(5) 227601-1 © 2014 American Physical Society