Strongly nonlinear ferromagnetic resonance of Bi-doped YIG nanodisks

Abstract

One current goal of spintronics is the development of a sustainable information technology based on the transport of pure spin currents. One promising way to do this is to use spin waves (SWs), the elementary excitations of magnetically ordered materials: by collective precession of magnetic moments, they can transport angular momentum. SW information processing also offers interesting alternatives to conventional microelectronics [1]. For this, yttrium iron garnet (YIG), an insulating ferrimagnet, is the ideal material because it has the lowest magnetic damping. Furthermore, thanks to the spin orbit torque (SOT), it is possible to control the relaxation time of SWs in YIG by an electric current injected into an adjacent platinum layer [2]. However, such metal/insulator hybrid devices presently have certain limitations, as a sudden drop in the amplitude of the main mode beyond a certain excitation threshold, which originates from nonlinear coupling with other SW modes [2].Different strategies can be considered to overcome these issues. In nanopatterned samples the available SW modes become quantized, which severely limits the available nonlinear processes. As a result, nonlinear saturation thresholds are postponed, which allows to reach much higher amplitudes of single mode dynamics [3]. The perpendicular magnetic anisotropy (PMA) can also be used to control the sign of the nonlinear frequency shift. Recently, the growth of ultra-thin films of Bismuth doped YIG (BiYIG) with tunable PMA has been achieved while preserving a high dynamic quality [4]. It was shown that the emission characteristics of SWs emitted by SOT in thin BiYIG films where PMA compensates the in-plane shape anisotropy are greatly improved [5].Here, we study the magnetization dynamics in individual nanodisks patterned from such a 30 nm thick BiYIG film, with diameters ranging from 1 µm down to 200 nm. The static magnetic field is applied perpendicularly to the sample plane. To excite the ferromagnetic resonance (FMR) of the BiYIG nanodisks, we use the spatially uniform in-plane microwave field produced by an antenna integrated on top. To detect it, we employ a magnetic resonance force microscope [6] in which a cobalt nanosphere grown at the tip of a soft cantilever [7] is dipolarly coupled to the longitudinal component of the magnetization of the nanodisk positioned underneath (Fig. 1).By studying the SW spectra of these BiYIG nanodisks in the linear regime, we find that their effective anisotropy field is weakly dependent of the diameter and negative, about -10 mT, which means that the PMA slightly overcompensates the shape anisotropy. The damping parameter is found to increase as the diameter is decreased and lies in the high 10-4 – low 10-3 range for all disks.We then perform measurement of the main resonance line, corresponding to the quasi-uniform mode, as a function of the microwave power injected into the antenna, which is varied by up to four orders of magnitude (excitation field ranging from 0.03 mT to 3 mT at 5 GHz). For all the disks, we observe a distortion of the resonance line at intermediate excitation power, corresponding to the onset of foldover. As expected, due to the negative effective anisotropy field, the resonance line shifts towards higher magnetic field as the precession angle increases, which is opposite to the behavior reported on undoped YIG nanodisks [3]. For the largest BiYIG disks, the dynamics witnessed at higher power is quite more complex and interesting, as shown in Fig. 2 for the 700 nm diameter nanodisk. We observe a rapid saturation of the peak amplitude, corresponding to average precession angles of the order of 10° to 20°, accompanied with a broadening of the line towards both lower and higher magnetic field. To understand this behavior, we perform extensive micromagnetic simulations. Using the magnetic parameters extracted in the linear regime and the nominal geometry of the nanodisks, these simulations reproduce the main characteristics of the measured FMR lines in the strongly nonlinear regime. They reveal that a dynamic instability is responsible of the observed behavior: as the amplitude of the quasi-uniform mode increases with the driving field, its precession profile gets more and more localized at the center of the disk, which eventually leads to the formation of a dynamic soliton similar to a wave bullet [8]. Moreover, this soliton is not stable over time, resulting in a rich temporal dynamics, which, depending on the exact driving conditions, can be quasi-periodic or intermittent. To experimentally access this complex temporal dynamics, we use the method introduced in [3], which consists in applying a second, much weaker excitation field of varying frequency, in addition to the main driving field at high power. The obtained frequency modulation spectra indeed reflect the existence of rich low-frequency temporal variations in the dynamics of the magnetization, as suggested by the simulations. **