Estudo do problema padrão número 3 via simulação micromagnética utilizando interação dipolar

Abstract

Micromagnetism is a field theory of magnetic systems that use the semi-classically approximation to magnetic materials at the nanoscale. We can study the minimum energy states of cubic magnetic particles with a volume of L 3 , and a uniaxial anisotropy relative to the magnetostatic energy density of value equal to Q = 0.1, along one of the cubic axes. These systems are investigated as a function of the number of simulation cells N3 . In them, it is possible to find three configurations: the flower state, the twisted flower state, and the vortex state. This study is referred to as the µMAG Standard Problem #3, proposed by the NIST Micromagnetic Modeling Group, and is used as a reference for comparison between different methods in micromagnetic simulations. In this work, we compare our results obtained via micromagnetic simulation techniques, using dipolar interaction, with results found in the literature using demagnetization field. It is known that the critical edge length, defined by the ratio between the length L and the exchange length ltr, has an approximate value of 8.40 for the state changes (flower ⇒ vortex and twisted flower ⇒ vortex), as reported in the literature. In our studies, we vary the length L = N a, as a function of the number of simulation cells N and the distance a between the cells, to obtain the ratio L/ltr for each N. We verify that, starting from N ≥ 15, the ratio L/ltr converges to the approximate value of 8.43, not significantly varying for larger N sizes.