One of the most fascinating topics in current quantum physics are hybridised systems, in which different quantum resonators are strongly coupled. Prominent examples are circular resonators with high quality factors that allow the coupling of optical whispering gallery modes 1-5 to microwave cavities 6 or magnon resonances in optomagnonics 7-9 . Whispering gallery modes play a special role in this endeavour because of their high quality factor and strong localisation, which ultimately increases the overlap of the wavefunctions of quantum particles in hybridised systems. The hybridisation with magnons, the collective quantum excitations of the electron spins in a magnetically ordered material, is of particular interest because magnons can take over two functionalities: due to their collective nature they are robust and can serve as a quantum memory 10 and, moreover, they can act as a wavelength converter between microwave and THz photons 9 . However, the observation of whispering gallery magnons has not yet been achieved due to the lack of efficient excitation schemes for magnons with large wave vectors in a circular geometry. To tackle this problem, we studied nonlinear 3-magnon scattering 11-14 as a means to generate whispering gallery magnons. This Letter discusses the basics of this non-linear mechanism in a confined, circular geometry from experimental and theoretical point of view.Whispering gallery magnons can only live in systems with rotational symmetry. This not only applies to the geometry of the magnetic element but also to the magnetisation texture therein. For that reason, we study a Ni 81 Fe 19 disc that inherently exhibits a magnetic vortex structure [15][16][17][18][19] . The arrows in Fig. 1a depict the generic features of such a vortex state: the magnetic moments curl in plane along circular lines around the vortex core, a nanoscopic region in the center of the disc where the magnetisation tilts out of plane. According to this rotational symmetry, the magnon eigenmodes in a vortex are characterised by mode numbers (n, m), with n = 0, 1, 2, ... counting the number of nodes across the disc radius and m = 0, ±1, ±2, ... counting the number of nodes in azimuthal direction over half the disc 20,21 .Other than commonly known waves, like sound, water or electromagnetic waves, magnons exhibit a strongly anisotropic dispersion relation in in-plane magnetised thin films 20 . In a vortex, this results in increasing (decreasing) mode energies for increasing n (m) as shown by the analytic calculations in Fig. 1b. The four exemplary intensity profiles for the eigenmodes (0, 0), (0, 10), (0, 20), and (0, 30), that are shown in Fig. 1c, reveal the character of whispering gallery magnons: the larger m, the more the magnon intensity is pushed toward the perimeter of the disc which can be understood intuitively by the reduction of exchange energy: Leaving an extended area around the vortex core with zero amplitude avoids a strong tilt of neighbouring spins close to the vortex core and, therefore, reduces the total ...

We report ultra-low intrinsic magnetic damping in Co 25 Fe 75 heterostructures, reaching the low 10 −4 regime at room temperature. By using a broadband ferromagnetic resonance technique in out-of-plane geometry, we extracted the dynamic magnetic properties of several Co 25 Fe 75 -based heterostructures with varying ferromagnetic layer thickness. By measuring radiative damping and spin pumping effects, we found the intrinsic damping of a 26 nm thick sample to be α 0 3.18 × 10 −4 . Furthermore, using Brillouin light scattering microscopy we measured spin-wave propagation lengths of up to (21 ± 1) µm in a 26 nm thick Co 25 Fe 75 heterostructure at room temperature, which is in excellent agreement with the measured damping.Itinerant ferromagnets (FM) are advantageous for spintronic and magnonic devices. They benefit from, e.g., large magnetoresistive effects and current-induced spinorbit torques 1 . In many magneto-resistive technologies (e.g., anisotropic magnetoresistance, giant magnetoresistance, tunnel magnetoresistance) electronic conductivity is indispensable. Moreover, due to high saturation magnetization in metallic FMs, spin-wave (SW) group velocities are in general significantly higher than in insulating ferrimagnets 2-5 . High saturation magnetizations in general ease detection. Nevertheless, itinerant FMs typically have considerable magnetic damping 6,7 . This is unfavorable for many applications. For example, low damping is crucial for oscillators based on spin transfer torques and spin orbit torques as well as for achieving large spin-wave propagation lengths (SWPL) 8-10 . The need for thin film materials with low magnetic damping has triggered the interest in the insulating ferrimagnet yttrium-iron garnet (Y 3 Fe 5 O 12 , YIG) 11-13 . Although for YIG, very small total (Gilbert) damping parameters in the order of α G ≈ 10 −5 , and large SWPLs of a few tens of micrometers (up to ∼ 25 µm) in thin films (∼ 20 nm) have been reported 5,13,14 , its insulating properties and requirement for crystalline growth are challenges for large scale magnonic applications.Schoen et al. recently observed ultra-low intrinsic magnetic damping in Co 25 Fe 75 (CoFe) metallic thin films (α 0 = (5 ± 1.8) × 10 −4 ) 15 , and Krner et al. reported PLs of 5 µm − 8 µm in CoFe using time resolved scanning magneto-optical Kerr microscopy 4 . This motivated our study on sputter-deposited CoFe-based thin film heterostructures. We use broadband ferromagnetic resonance (BB-FMR) spectroscopy 16 in outa) Electronic of-plane (OOP) geometry and Brillouin light scattering (BLS) microscopy 17 and find intrinsic damping parameters in the lower 10 −4 regime as well as SWPLs of more than 20 µm. The damping is therefore comparable to YIG/heavy metal (HM) heterostructures 18 and the SWPL is comparable to that of state-of-the-art YIG thin films 5,13 . Thin film CoFe is a promising candidate for all-metal magnonic devices, as it combines low magnetic damping with good electrical conductivity and large saturation magnetization, while enabling easy fab...

We report on the impact of nonlinear four-magnon scattering on magnon transport in microstructured Co 25 Fe 75 waveguides with low magnetic damping. We determine the magnon propagation length with microfocused Brillouin light scattering over a broad range of excitation powers and detect a decrease of the attenuation length at high powers. This is consistent with the onset of nonlinear four-magnon scattering. Hence, it is critical to stay in the linear regime, when deriving damping parameters from the magnon propagation length. Otherwise, the intrinsic nonlinearity of magnetization dynamics may lead to a misinterpretation of magnon propagation lengths and, thus, to incorrect values of the magnetic damping of the system.In the growing field of magnonics, 1-4 one aims at the use of magnons, the excitation quanta in magnetically ordered systems, to transport and process information. In order to allow for coherent long-distance transport of signals in complex magnonic networks, the search for materials with low magnetic damping was reinitiated. In 2016, ferromagnetic resonance (FMR) measurements of continuous films revealed intrinsic damping values as low as (5±1.8)×10 −4 for the conductor Co 25 Fe 75 , 5 approaching values found for the ferrimagnetic insulator yttrium iron garnet 6 , with the added benefit of seminconductor compatibility. As a consequence, studies of the propagation characteristics in Co 25 Fe 75 microstructures followed, comparing damping values obtained from FMR to those derived from magnon propagation lengths. [7][8][9] In Ref. 7, a 2.5 times higher damping is reported for magnon transport measurements than for FMR analysis of extended films, which is attributed to significant extrinsic contributions to the magnetic damping in the microstructured sample, such as local inhomogeneities and two-magnon scattering.