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.

We study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat is simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a function of time is computed.For effectively three-dimensional substrates (where the substrate thickness greatly exceeds the nanowire length), we identify three different regimes of heat propagation through the substrate: regime (i), where the nanowire temperature increases approximately logarithmically as a function of time. In this regime, the nanowire temperature is well-described analytically by You et al.[ APL89, 222513 (2006)]. We provide an analytical expression for the time tc that marks the upper applicability limit of the You model. After tc, the heat flow enters regime (ii), where the nanowire temperature stays constant while a hemispherical heat front carries the heat away from the wire and into the substrate. As the heat front reaches the boundary of the substrate, regime (iii) is entered where the nanowire and substrate temperature start to increase rapidly.For effectively two-dimensional substrates (where the nanowire length greatly exceeds the substrate thickness), there is only one regime in which the temperature increases logarithmically with time for large times, before the heat front reaches the substrate boundary. We provide an analytical expression, valid for all pulse durations, that allows one to accurately compute this temperature increase in the nanowire on thin substrates.

Abstract-We propose a standard micromagnetic problem, of a nanostripe of permalloy. We study the magnetization dynamics and describe methods of extracting features from simulations. Spin wave dispersion curves, relating frequency and wave vector, are obtained for wave propagation in different directions relative to the axis of the waveguide and the external applied field. Simulation results using both finite element (Nmag) and finite difference (OOMMF) methods are compared against analytic results, for different ranges of the wave vector.

We study the spin-wave spectra in magnonic antidot waveguides (MAWs) for two limiting cases (strong and negligible) of the surface anisotropy at the ferromagnet/air interface. The MAWs under investigation have the form of a thin stripe of permalloy with a single row of periodically arranged antidots in the middle. The introduction of a magnetization pinning at the edges of the permalloy stripe and the edges of antidots is found to modify the spin-wave spectrum. This effect is shown to be necessary for magnonic gaps to open in the considered systems. Our study demonstrates that the surface anisotropy can be crucial in the practical applications of MAWs and related structures and in the interpretation of experimental results in one-and two-dimensional magnonic crystals. We used three different numerical methods i.e. plane waves method (PWM), finite difference method and finite element method to validate the results. We showed that PWM in the present formulation assumes pinned magnetization while in micromagnetic simulations special care must be taken to introduce pinning.

We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of 3d periodic boundary conditions in micromagnetism and (ii) is well suited for the efficient simulation of repetitive systems of any size.Introduction One often wants to quantitatively understand the behaviour of highly regular extended periodic magnetic structures created, for example, by selfassembly methods. As these structures often are too large for full micromagnetic simulation, some physically justifiable assumptions have to be made to reduce the computational complexity.One attractive simplification is to define a 'primary' simulation cell C 0 in the bulk of the sample (which may contain one or multiple elementary lattice cells) and demand that the magnetization in every other 'image' cell C j is constrained to behaving as a translated copy of the magnetization in cell C 0 . While this approximation loses long range multicell structures (such as the domain wall structure of extended materials) and field deviations near surfaces, it is useful in other situations such as magnetic films in strong external fields. This idea is usually described by the term 'periodic boundary conditions' (PBC). We note that there is a conceptual difference between using PBC to remove surface artefacts in multi-particle statistical mechanics simulations (e.g. of a gas of hard spheres) and using PBC to describe real periodic structures with long-range interactions (such as magnetic repulsion).While no problem arises for structures that are periodic in one or two directions only, micromagnetism requires a modification of the PBC approach for 3d periodic systems, as taking the infinite size limit leaves essential information about the shape of the (now 2d) surface unspecified which here matters for long-range interactions (see also discussion in section 3 in [1]).To show why the shape matters, we consider two different structures s A and s B made of one billion individual cells each: s A being a cube of 1000×1000×1000 cells, and s B being a film of 10000 × 10000 × 10 cells. If both structures are homogeneously magnetized, a cell in the center of each experiences a demagnetizing field H = −T M . The demagnetizing tensor T must satisfy (a consequence of the Maxwell equation div B = 0): tr T = 1. For s A , we have T (A) = diag(1/3, 1/3, 1/3), while for s B , we get T (B) = diag(0, 0, 1). The form of T depends on the shape