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Micromagnetic simulation of μMAG standard problem No. 3: Evaluating the standard dipole-dipole interaction |
| A. K. F. Silva†, D. C. Carvalho, H. S. Assis, and P. Z. Coura |
| Departamento de Física, Laboratório de Simulação Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, 36036-330 Minas Gerais, Brazil |
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Abstract Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy ($Q = 0.1$) aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states. In this system, three fundamental magnetization configurations are identified: (i) the flower state, (ii) the twisted flower state, and (iii) the vortex state. This problem corresponds to standard problem No. 3 proposed by the NIST Micromagnetics Modeling Group, widely adopted as a benchmark for validating computational micromagnetics methods. In this work, we approach the problem using a computational method based on direct dipolar interactions, in contrast to conventional techniques that typically compute the demagnetizing field via finite difference-based fast Fourier transform (FFT) methods, tensor grid approaches, or finite element formulations. Our results are compared with established literature data, focusing on the dimensionless parameter $\lambda=L/l_{\rm ex}$, where $L$ is the cube edge length and $l_{\rm ex}$ is the exchange length of the material. To analyze equilibrium state transitions, we systematically varied the size $L$ as a function of the simulation cell number $N$ and intercellular spacing $a$, determining the critical $\lambda$ value associated with configuration changes. Our simulations reveal that the transition between the twisted flower and vortex states occurs at $\lambda \approx 8.45$, consistent with values reported in the literature, validating our code (Grupo de Física da Matéria Condensada - UFJF), and shows that this standard problem can be resolved using only interaction dipolar of a direct way without the need for sophisticated additional calculations.
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Received: 05 August 2025
Revised: 16 October 2025
Accepted manuscript online: 24 October 2025
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PACS:
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75.78.-n
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(Magnetization dynamics)
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75.78.Cd
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(Micromagnetic simulations ?)
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75.40.Mg
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(Numerical simulation studies)
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75.10.Hk
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(Classical spin models)
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Corresponding Authors:
A. K. F. Silva
E-mail: antonio.kaeliton@estudante.ufjf.br
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Cite this article:
A. K. F. Silva, D. C. Carvalho, H. S. Assis, and P. Z. Coura Micromagnetic simulation of μMAG standard problem No. 3: Evaluating the standard dipole-dipole interaction 2026 Chin. Phys. B 35 017501
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