Giuliano Bordignon

A new approach to (quasi) periodic boundary conditions in micromagnetics: The macrogeometry

We present a new method to simulate repetitive ferromagnetic structures. This macrogeometry 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 three-dimensional periodic boundary conditions in micromagnetism and (ii) is well suited for the efficient simulation of repetitive systems of any size.

Compression of boundary element matrix in micromagnetic simulations

A hybrid finite element method/boundary element method (FEM/BEM) is a standard approach for calculating the magnetostatic potential within micromagnetics [D. Fredkin and T. Koehler, IEEE Trans. Magn. 26, 415 (1990)]. This involves dealing with a dense N×N matrix Bij, with N being the number of mesh surface nodes. In order to apply the method to ferromagnetic structures with a large surface, one needs to apply matrix compression techniques on Bij. An efficient approach is to approximate Bij by hierarchical matrices (or H matrices). We have used HLIB [http://www.hlib.org], a library containing implementations of the hierarchical matrix methodology, together with the micromagnetic finite element solver NMAG in order to optimize the hybrid FEM/BEM. In this article we present a study of the efficiency of algorithms implemented in HLIB concerning the storage requirements and the matrix assembly time in micromagnetic simulations.

Micromagnetic simulation of the magnetic exchange spring system DyFe2∕YFe2

Magnetic measurements of [110] [50ADyFe2∕200AYFe2] reveal a rich switching behavior: the formation of exchange springs in this system of alternating hard and soft layers can be observed for low temperatures (LTs). For high temperatures (HTs), the appearance of the hysteresis loop changes significantly, implying a more complicated reversal process. In this article, we reproduce hysteresis loops for net and compound-specific magnetizations by means of micromagnetic simulations and assess the quality by a direct comparison to recent x-ray magnetic circular dichroism measurements. The HT switching characteristics, showing a magnetization reversal of the hard magnetic layer before the soft magnetic layer, are investigated and understood on the basis of detailed magnetic configuration plots. The crossover of LT to HT switching patterns is explained by energy considerations, and the dependence on different parameters is outlined.

Parallel execution and scriptability in micromagnetic simulations

We demonstrate the feasibility of an “encapsulated parallelism” approach toward micromagnetic simulations that combines offering a high degree of flexibility to the user with the efficient utilization of parallel computing resources. While parallelization is obviously desirable to address the high numerical effort required for realistic micromagnetic simulations through utilizing now widely available multiprocessor systems (including desktop multicore CPUs and computing clusters), conventional approaches toward parallelization impose strong restrictions on the structure of programs: numerical operations have to be executed across all processors in a synchronized fashion. This means that from the user’s perspective, either the structure of the entire simulation is rigidly defined from the beginning and cannot be adjusted easily, or making modifications to the computation sequence requires advanced knowledge in parallel programming. We explain how this dilemma is resolved in the NMAG simulation package in s...

Analysis of Magnetoresistance in Arrays of Connected Nano-Rings

We study the anisotropic magnetoresistance (AMR) of a 2-D periodic square array of connected permalloy rings with periodicity of 1 mum combining experimental and computational techniques. The computational model consists of two parts: 1) the computation of the magnetization and 2) the computation of the current density. For 1), we use standard micromagnetic methods. For 2), we start from a potential difference applied across the sample, compute the resulting electric potential, and subsequently the corresponding current density based on a uniform conductivity. We take into account the backreaction of the magnetoresistive effects onto the current density by self-consistently computing the current density and conductivity until they converge. We compare the experimentally measured AMR curve (as a function of the applied field) with the numerically computed results and find good agreement. The numerical data provides insight into the characteristics of the AMR data. Finally, we demonstrate the importance of taking into account the spatial variation of the current density when computing the AMR

In-plane anisotropy of coercive field in permalloy square ring arrays

Magnetic ring arrays are promising candidates for application in magnetic random access memory devices. The magnetic reversal processes and anisotropy of the coercivity in arrays of square-shaped nanorings with different spacings were investigated by vector magneto-optical Kerr effect magnetometry, magnetic force microscopy, and micromagnetic simulations. Two-step magnetization reversal demonstrates fourfold symmetry in the film plane resulting from the shape anisotropy in rings. Our numerical simulations show good agreement with the experiment.

Numerical studies of demagnetizing effects in triangular ring arrays

We study the effect of the magnetostatic field in a two-dimensional periodic square array of Permalloy triangular rings by means of micromagnetic simulations. The rings have a lateral size of 50nm, an edge width of 8nm, and the thickness is 10nm. Applying an external field to one of the elements and assuming the rest of the array to be in the remanent state, we show how the remanent magnetization and coercive field are affected by the magnetostatic field of the array, both as a function of the distance between the elements and as a function of the number of elements used to model the periodic array. We provide an estimate of the minimum distance for an independent behavior of the elements, and we show that a model with the first and second nearest neighbors of an element can accurately approximate the effect of a much larger array.

Micromagnetic Modelling of the Dynamics of Exchange Springs in Multi-Layer Systems

Exchange springs are formed in multilayers of alternating hard and soft ferromagnetic materials which are exchange coupled at their interfaces. These systems are rich of interesting physical properties, which can be tuned by selecting suitable geometries and compositions. In this paper, we present a computational study of the dynamics of a tri-layer DyFe2/YFe2/DyFe2 exchange spring system near the bending field (the field required to twist the magnetization of the soft YFe2 layer out of the aligned state). The dynamical reaction of the system to small variations of the applied field is studied and its oscillatory nature is analyzed numerically. The behaviors of the decay times, the frequencies, and amplitudes reveal enhanced responses of the system near the bending field

Spin-polarized currents in exchange spring systems

We present a computational study of the magnetization dynamics of a trilayer exchange spring system in the form of a cylindrical nanopillar in the presence of an electric current. A three-dimensional micromagnetic model is used, where the interaction between the current and the local magnetization is taken into account following a recent model by Zhang and Li [Phys. Rev. Lett. 93, 127204 (2004)] We obtain a stationary rotation of the magnetization of the system around its axis, accompanied by a compression of the artificial domain wall in the direction of the electron flow.