LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization

Exl, Lukas; Bance, Simon; Reichel, Franz; Schrefl, T.; Stimming, Hans Peter; Mauser, Norbert J.

doi:10.1063/1.4862839

Cited by 107 publications

(84 citation statements)

References 19 publications

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“…In our calculations, we used a 1 nm grid and 1 Oe field steps to produce the hysteresis loops. At each field step, we computed equilibrium magnetic states by directly minimizing energy using the steepest descent method [35,36] as implemented in MuMax3. To simulate the (Fe-Co)-rich magnetic phase, we have assumed a saturation magnetization of µ 0 M s = 2.1 T and exchange stiffness of A = 11 pJ/m.…”

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confidence: 99%

Simulation of alnico coercivity

Skomski

Hoffmann

et al. 2017

Applied Physics Letters

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Micromagnetic simulations of alnico show substantial deviations from Stoner-Wohlfarth behavior due to the unique size and spatial distribution of the rod-like Fe-Co phase formed during spinodal decomposition in an external magnetic field. The maximum coercivity is limited by single-rod effects, especially deviations from ellipsoidal shape, and by interactions between the rods. Both the exchange interaction between connected rods and magnetostatic interaction between rods are considered, and the results of our calculations show good agreement with recent experiments. Unlike systems dominated by magnetocrystalline anisotropy, coercivity in alnico is highly dependent on size, shape, and geometric distribution of the Fe-Co phase, all factors that can be tuned with appropriate chemistry and thermal-magnetic annealing.

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confidence: 99%

Simulation of alnico coercivity

Skomski

Hoffmann

et al. 2017

Applied Physics Letters

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“…Exl et al reported that this new method is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two 45) . The steepest descent energy minimization method was also implemented on a graphic processor unit (GPU) resulted in 4.8 times faster calculation time compared to that of single-core central processing unit (CPU) 45) . Using the same approach, Furuya et al also reported a successful simulation of a permanent magnet including 20.7 million elements 46) .…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…Hence, development of a new algorithm that can speed up the calculation time is necessary enabling us to simulate large scaled models. Recently, Exl et al has introduced a steepest decent energy minimization method for micromagnetics to simulate quasistatic hysteresis loops 45) . Exl et al reported that this new method is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two 45) .…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…Recently, Exl et al has introduced a steepest decent energy minimization method for micromagnetics to simulate quasistatic hysteresis loops 45) . Exl et al reported that this new method is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two 45) . The steepest descent energy minimization method was also implemented on a graphic processor unit (GPU) resulted in 4.8 times faster calculation time compared to that of single-core central processing unit (CPU) 45) .…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

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Micromagnetic Simulations of Magnetization Reversals in Nd-Fe-B Based Permanent Magnets

2016

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Finite element micromagnetic simulation was employed to explain how the microstructure of Nd-Fe-B permanent magnets such as grain size, grain shape, and grain boundary composition in uence the magnetization reversals and coercivity. Micromagnetic simulations showed that local demagnetization factor decreases as grain size decreases, which is attributed to a higher coercivity in ne-grained anisotropic permanent magnets. Lower demagnetization factor is also responsible for a lower temperature dependence of coercivity in the magnets with a smaller grain size. It was also found that the reduction of the magnetization of the grain boundary phase in hot-deformed Nd-Fe-B magnets leads to the coercivity enhancement due to a stronger pinning force against magnetic domain wall motion. The coercivity of Nd-Fe-B magnets cannot be enhanced by the reduction of the grain size alone unless the grain boundary phase become non-ferromagnetic, indicating that the role of the grain boundary phase is more pronounced in the Nd-Fe-B magnets with a smaller grain size.

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“…8,9 Recently, an energy minimization method was applied to Nd-Fe-B magnets, which accelerates the calculation speed by searching for the local minimum state of magnetic free energy quite efficiently. 10,11 In this study, the energy minimization method enables the simulation of a large model with 20 million elements within several hours of calculation time, as the calculation speed is accelerated by a factor of 20 compared to the conventional micromagnetic treatment. It is also reported that the energy minimization method is suitable for massive parallel computers such as the K computer because it exhibits high parallel calculation efficiency.…”

Section: Introductionmentioning

confidence: 99%

Large-scale micromagnetic simulation of Nd-Fe-B sintered magnets with Dy-rich shell structures

et al. 2016

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Large-scale micromagnetic simulations have been performed using the energy minimization method on a model with structural features similar to those of Dy grain boundary diffusion (GBD)-processed sintered magnets. Coercivity increases as a linear function of the anisotropy field of the Dy-rich shell, which is independent of Dy composition in the core as long as the shell thickness is greater than about 15 nm. This result shows that the Dy contained in the initial sintered magnets prior to the GBD process is not essential for enhancing coercivity. Magnetization reversal patterns indicate that coercivity is strongly influenced by domain wall pinning at the grain boundary. This observation is found to be consistent with the one-dimensional pinning theory.

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LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization

Cited by 107 publications

References 19 publications

Simulation of alnico coercivity

Simulation of alnico coercivity

Micromagnetic Simulations of Magnetization Reversals in Nd-Fe-B Based Permanent Magnets

Large-scale micromagnetic simulation of Nd-Fe-B sintered magnets with Dy-rich shell structures

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