We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

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Published in Magnetochemistry, v. 7, issue 3, 34.

© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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Research at the University of Kentucky was supported by the U.S. National Science Foundation Grant DMR-1506979.

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