Origins of magnetic damping measurement variations using ferromagnetic resonance for nano-sized devices

Abstract

It is shown that ferromagnetic resonance measured in larger thin films yield varying results for damping in nanosized devices. Results are shown to critically depend on magnetic parameters, scalar and vector. Results here also explain why different experiments have concluded different size-dependent trends measuring damping with in-plane devices. The observed variation is due, in part, to a crossover in the dominant eigen-mode and unique eigen-mode evolution. However, antithesizing in-plane devices, we find that for out-of-plane magnetization, distinct symmetric eigen-modes demonstrates ideal stability, leading to no variation in apparent damping, suggesting a better measurement configuration using larger samples.

The effects of Dzyaloshinskii-Moriya interactions on the ferromagnetic resonance response in nanosized devices

“…2 shows two sets of spectral responses for two specific cases: (a) a system with no DMI D ¼ 0, under conditions that can lead to more than one eigenmode, which for in-plane anisotropy follows from sufficiently high saturation magnetization M s . 8,9 Fig. 2(a) also shows that in the case of a system without DMI, the two modes that form are quite different those that form in the presence of DMI, shown in Fig.…”

Damping of Confined Modes in a Ferromagnetic Thin Insulating Film: Angular Momentum Transfer across a Nanoscale Field-Defined Interface

“…This allows the effective field to be equal at every position inside the mode, and hence it can be described as an eigenmode with a single welldefined eigenfrequency. While mode splitting can con-tribute to the measured effective damping [15], the perpendicular geometry used in our study eliminates this possibility. Other well-established mechanisms for sizeor wavevector-dependent relaxation can also be eliminated due to their insufficient magnitude and differing phenomenology; 3-magnon confluence [30,31] manifests as a linewidth broadening that is linear in k but independent of frequency, while 4-magnon scattering [32] scales as k 2 .…”

“…The azimuthal symmetry of the out-ofplane geometry permits simple numerical analysis based on cylindrically symmetric Bessel function modes with a well-defined localization radius [11], similar to those seen in perpendicularly magnetized dots [14]. In addition, this geometry eliminates the effect of eigenmode splitting, which can cause additional broadening [15]. We demonstrate the control of confinement radius by the observation of discrete modes in an FMRFM experiment in the out-of-plane geometry in an unpatterned epitaxial yttrium iron garnet (YIG) film of thickness 25 nm grown by off-axis sputtering [16] on a (111)-oriented Gd 3 Ga 5 O 12 substrate.…”

Micromagnetic modeling of magnetization processes and magnetoelastic interactions

“…The same equation can be used to describe the dynamics of the magnetization vector, but the latter will precess around the local effective field originating from the various interaction involved in the system. However, due to the interaction with the physical environment, the magnetization dynamic is modified and instead of continuous precession the magnetization relaxes progressively and aligns with H eff due to energy dissipation [94,95]. Within continuum micromagnetic theory, this mechanism is phenomenologically described by the Landau-Lifshitz (LL) equation [96], which characterizes the spatially resolved magnetization dynamics in presence of an effective field H eff .…”