Direct Solution of the Landau-Lifshitz-Gilbert Equation for Micromagnetics

Abstract

A mathematical framework is presented for solving the Landau-Lifshitz-Gilbert equation expressed in Cartesian components of magnetization according to the backward difference method without conflicting with the constraint of constant magnetization. Test calculation shows that the method allows the use of a large time step almost independent of spatial mesh size and damping constant. The derived program is used to calculate the magnetization structure of a crosstie wall in a Permalloy film yielding calculated structures which closely resemble the electron-holography image of an actual cross-tie wall. It is also used to investigate magnetization reversal mechanisms in fine ferromagnetic particles by pursuing time dependent changes in magnetization structures. The paper gives detailed descriptions of the reversal mechanisms which differ depending on the size of the particle.

Energy-driven pattern formation

“…At the discontinuities (which are themselves walls) the angle changes by 90 degrees or less. Experimental images and numerical simulations very much like the figure can be found in [50] (see also [34]). The cross-tie wall forms because one-dimensional walls are very expensive when the wall angle is large.…”

“…As we shall explain in Section 3.2, the analysis of [1] finds the optimal wall structure explicitly. Prior to that work the structure was known only from numerical and physical experiments [50].…”

The temperature dependence of hysteretic processes in Co nanowires arrays

“…[1][2][3][4][5] The study of hysteretic processes in nanowire arrays is receiving a considerable experimental and theoretical attention due to the necessity of understanding the magnetization processes of these magnetic systems. 6 In this paper, we have analyzed the following important tasks:…”

Large-scale micromagnetics simulations with dipolar interaction using all-to-all communications

“…6 Using FFT methods, we not only calculate H d but can reduce the calculation complexity which is reduced to O(n log n), with n being the total number of cells. Our simulator employs a hybrid parallel computation in which we perform parallel computation using symmetric multiprocessing (SMP) and message passing interface (MPI).…”