A Systematic Approach to Multiphysics Extensions of Finite-Element-Based Micromagnetic Simulations: Nmag

Abstract

Abstract-Extensions of the basic micromagnetic model that include effects such as spin-current interaction, diffusion of thermal energy or anisotropic magnetoresistance are often studied by performing simulations that use case-specific ad-hoc extensions of widely used software packages such as OOMMF or Magpar.We present the novel software framework 'Nmag' that handles specifications of micromagnetic systems at a sufficiently abstract level to enable users with little programming experience to automatically translate a description of a large class of dynamical multifield equations plus a description of the system's geometry into a working simulation.Conceptually, this is a step towards a higher-level abstract notation for classical multifield multiphysics simulations, similar to the change from assembly language to a higher level humanand-machine-readable formula notation for mathematical terms (FORTRAN) half a century ago.We demonstrate the capability of this approach through two examples, showing (i) a reduced dimensionality model and use of arbitrary order shape functions, and (ii) the computation of a spatial current density distribution for anisotropic magnetoresistance (AMR).For cross-wise validation purposes, we also show how Nmag compares to the OOMMF and Magpar packages on a selected micromagnetic toy system. We furthermore briefly discuss the limitations of our framework and related conceptual questions.

Fabrication and simulation of nanostructures for domain wall magnetoresistance studies on nickel

“…Simulated DW lengths for the nanostructures featured in Figure 1, are displayed as an inset in Figure 2. For the calculation of the anisotropic magnetoresistance (AMR) plotted in Figure 3b we used nmag (a multiphysics package based on the finite element method developed at Southampton University [13]) and followed the methodology employed by Bordignon et al in Reference [14]. The advantage of using this method is, that it takes into account the back reaction of the AMR effect onto the current distribution hence it provides a more accurate AMR estimation.…”

Multiscale approach to spin transport in magnetic multilayers

“…On the other hand it is becoming increasingly clear that the magnetization dynamics of real devices cannot be properly captured by simple (analytically tractable) models and that numerical simulations that treat the magnetic and transport degrees of freedom on an equal footing need to be developed. Several steps have already been taken in that direction [34][35][36][37][38] and should eventually lead to simulations of good predictive capabilities. Let us mention, as example, the recent experiments on spin torque induced ferromagnetic resonance in the nonlinear regime 39 which has been successfully compared to coupled simulations at the macrospin level for the magnetic part and onedimensional semi-classical level for spin transport.…”

Micromagnetic simulations of cylindrical magnetic nanowires

“…Nowadays there are several micromagtetic packages available, both open source (Scholz, 2003;Donahue, 2006;Fischbacher, 2007) and commercial (Scheinfein, 2003;Berkov, 2007), allowing for reseachers to run their own simulations.…”