Micromagnetic modelling of anisotropic damping in ferromagnet

We report a numerical implementation of the Landau-Lifshitz-Baryakhtar theory, which dictates that the micromagnetic relaxation term obeys the symmetry of the magnetic crystal, i. e. replacing the single intrinsic damping constant with a tensor of corresponding symmetry. The effect of anisotropic relaxation is studied in thin saturated ferromagnetic disk and ellipse with and without uniaxial magneto-crystalline anisotropy. We investigate the angular dependency of the linewidth of magnonic resonances with respect to the given structure of the relaxation tensor. The simulations suggest that the anisotropy of the magnonic linewidth is determined by only two factors: the projection of the relaxation tensor onto the plane of precession and the ellipticity of the later.Comment: 6 pages, 5 figures, submitted to PRB Rapid. Com

The design and verification of Mumax3

We report on the design, verification and performance of mumax3, an open-source GPU-accelerated micromagnetic simulation program. This software solves the time- and space dependent magnetization evolution in nano- to micro scale magnets using a finite-difference discretization. Its high performance and low memory requirements allow for large-scale simulations to be performed in limited time and on inexpensive hardware. We verified each part of the software by comparing results to analytical values where available and to micromagnetic standard problems. mumax3 also offers specific extensions like MFM image generation, moving simulation window, edge charge removal and material grains

Thermodynamically self-consistent non-stochastic micromagnetic model for the ferromagnetic state

In this work, a self-consistent thermodynamic approach to micromagnetism is presented. The magnetic degrees of freedom are modeled using the Landau-Lifshitz-Baryakhtar theory, that separates the different contributions to the magnetic damping, and thereby allows them to be coupled to the electron and phonon systems in a self-consistent way. We show that this model can quantitatively reproduce ultrafast magnetization dynamics in Nickel.Comment: 5 pages, 3 figure

Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics

A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by LL equation. Furthermore, we find that both the domain wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping.Comment: 10 pages, 6 figure

Time-Resolved X-ray Microscopy of Spin-Torque-Induced Magnetic Vortex Gyration

Time-resolved X-ray microscopy is used to image the influence of alternating high-density currents on the magnetization dynamics of ferromagnetic vortices. Spin-torque induced vortex gyration is observed in micrometer-sized permalloy squares. The phases of the gyration in structures with different chirality are compared to an analytical model and micromagnetic simulations, considering both alternating spinpolarized currents and the current's Oersted field. In our case the driving force due to spin-transfer torque is about 70% of the total excitation while the remainder originates from the current's Oersted field. This finding has implications to magnetic storage devices using spin-torque driven magnetization switching and domain-wall motion.Comment: 10 pages, 3 figure

Micromagnetic simulations on GPU, a case study : vortex core switching by high-frequency magnetic fields

Since magnetic vortex cores have two ground states, they are candidates for digital memory bits in future magnetic random access memory (MRAM) devices. Vortex core switching can be induced by exciting the gyrotropic eigenmode, e.g., by applying cyclic magnetic fields with typically a sub-gigahertz frequency. However, recent studies reveal that other modes exist that can be excited at higher frequencies, but still lead to switching with relatively small field amplitudes. Here, we perform a full scan of the frequency/amplitude parameter space to explore such excitation modes. The enormous amount of simulations can only be performed in an acceptable time span when the micromagnetic (CPU) simulations are drastically accelerated. To this aim, we developed MUMAX, a GPU-based software tool that speeds up micromagnetic simulations with about two orders of magnitude compared to standard CPU micromagnetic tools. By exploiting MUMAX's numerical power we were able to explore new switching opportunities at moderate field amplitudes in the frequency range between 5 and 12 GHz

Influence of disorder on vortex domain wall mobility in magnetic nanowires

A large amount of future spintronic devices is based on the control of the static and dynamic properties of magnetic domain walls in magnetic nanowires. For these applications, understanding the domain wall mobility under the action of spin polarized currents is of paramount importance. Numerous studies describe the spin-current driven domain wall motion in nanowires with ideal material properties, while only some authors take into account the influence of the nanowire edge roughness [1]. In this contribution we numerically investigate the influence of distributed disorder on the vortex domain wall mobility in Permalloy nanowires. To this aim, we use the GPU based micromagnetic software package MuMax[2] to simulate the propagation of vortex domain walls in nanowires with cross sectional dimensions of 400x10 nm². We apply spin polarized currents acting on the domain wall by means of the Spin Transfer Torque (STT) mechanism, considering a system with perfect adiabaticity (β=0) and with non-adiabatic STT contributions (β=α and β=2α, α is the Gilbert damping). As in [3], the disorder is simulated as a random distribution of 3.125x3.125nm² sized voids. For each current value, average domain wall velocities are computed considering 25 different realisations of the disorder. We find that even very small disorder concentrations have a huge impact on the domain wall mobility. In the non-adiabatic case (β=2α), the domain wall velocity is largely suppressed below the Walker breakdown since the disorder is able to pin the vortex structure hindering the formation of the transverse domain wall, characteristic to the movement in this current region. In the adiabatic case (β=0), the intrinsic depinning threshold is largely reduced. Even very small disorder densities disable the domain wall to internally balance the Landau-Lifshitz-Gilbert torques with the STT torques, resulting in a non-zero domain wall speed. At low currents, the disorder pins the domain wall structure

Direct excitation of propagating spin waves by focused ultrashort optical pulses

An all-optical experiment long utilized to image phonons excited by ultrashort optical pulses has been applied to a magnetic sample. In addition to circular ripples due to surface acoustic waves, we observe an X-shaped pattern formed by propagating spin waves. The emission of spin waves from the optical pulse epicenter in the form of collimated beams is qualitatively reproduced by micromagnetic simulations. We explain the observed pattern in terms of the group velocity distribution of Damon-Eshbach magnetostatic spin waves in the reciprocal space and the wave vector spectrum of the focused ultrafast laser pulse