Dupré, Luc

Olyslager, Femke

Van de Wiele, Ben

Undetermined

Ghent University Academic Bibliography

HYSTERESIS MODELING AND MICROMAGNETICS 2007 - NAPLES JUNE 4-6 2007, ITALY 101Influence of space discretization size in3D micromagnetic modellingB. Van de Wiele, L. Dupre´, F. OlyslagerI. IntroductionTo improve the magnetic properties of ferromag-netic materials, one needs to qualify relations be-tween the microscopic material properties and themacroscopic magnetic behavior. Large computer re-sources nowadays allow to do this using micromag-netic ab initio simulations for larger, bulk like sam-ples. Here, the size of the sample is limited by com-puter resource restrictions on the number of spatialdiscretizations in the sample.II. Spatial discretizationIn the three dimensional numerical scheme, thesample is discretized in N cubic finite difference(FD) cells with edges of length ∆. The evolutionof the magnetization in every FD cell is computedthrough time stepping the Landau-Lifshitz equationusing time steps δt [1]. In each time step the ef-fective field incorporating the exchange, anisotropy,magnetostatic, magneto-elastic and applied field hasto be evaluated twice in every FD cell.In classical micromagnetic simulations, the ex-change length is seen as a maximum discretiza-tion size since on a larger scale, magnetization non-uniformities are possible. However, in order to sim-ulate larger bulk like samples, one could aim at alarger discretization size ∆ resulting in a local aver-aging of the variations in magnetization. To testthis, numerical experiments are performed on aniron sample with dimensions of 0.32µm×1.28µm×0.32µm. The discretization length ∆ is 2.5nm,which is slightly smaller then the exchange length inpure iron (2.8nm), 5.0nm and 10.0nm which leadsto respectively 8 388 608, 1 048 576 and 131 072 FDcells. The hysteresis loops are shown in Fig. 1. Theyare simulated when applying a magnetic field alongthe longest edge of the sample.The loops are almost identical: they have the sameslope and enclose a similar surface. Table I shows theused time step δt, the number of microscopic timesteps and the total CPU time. A smaller time step δtis needed when a smaller discretization ∆ is used[1],B. Van de Wiele and L. Dupre´ are with the Department ofElectrical Energy, Systems and Automation, F. Olyslager iswith the Department of Information Technology, both GhentUniversity, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Bel-gium. E-mail: ben.vandewiele@ugent.be−2 −1 0 1 2x 105−1−0.500.51Applied field [A/m]<M> [Ms]∆ = 2,5 nm∆ = 5 nm∆ = 10 nmFig. 1. Hysteresis loops for an identical iron sample usingdifferent discretization lengthsresulting in a massive increase in number of micro-scopic time steps needed to simulate the loops (cfr.column 3). Furthermore, the huge number of FDcells when a small ∆ is used, results in a slow evalu-ation of the effective field in each FD cell every timestep. Combined with the large number of time steps,it explains the massive differences in CPU time.TABLE ISimulation data for different discretization lengths∆ [nm] δt [ps] # δt CPU time2.5 0.5 27 036 103.25h5.0 1.0 14 627 8.55h10 5.0 1 463 7.46minIII. ConclusionsThe small differences in Fig. 1 justify the useof discretization lengths larger then the exchangelength in the model. However, the discretizationsize should be sufficiently small with respect to thethickness of domain walls (70nm in Fe) and the di-mensions of vortex states (about 35 nm in Fe). Con-sidering this together with the massive differences inCPU time and memory needs justifies the use of adiscretization length up to 10nm.References[1] B. Van de Wiele, F. Olyslager and L. Dupre´, ”Fast nu-merical 3D-scheme for the simulation of hysteresis in fer-romagnetic grains”, accepted for publication in Journalof Applied Physics.64

Influence of space discretization size in 3D micromagnetic modelling (abstract)

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Influence of space discretization size in 3D micromagnetic modelling (abstract)

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