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Edge Domain Walls in Ultrathin Exchange-Biased Films

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Abstract

We present an analysis of edge domain walls in exchange-biased ferromagnetic films appearing as a result of a competition between the stray field at the film edges and the exchange bias field in the bulk. We introduce an effective two-dimensional micromagnetic energy that governs the magnetization behavior in exchange-biased materials and investigate its energy minimizers in the strip geometry. In a periodic setting, we provide a complete characterization of global energy minimizers corresponding to edge domain walls. In particular, we show that energy minimizers are one-dimensional and do not exhibit winding. We then consider a particular thin-film regime for large samples and relatively strong exchange bias and derive a simple and comprehensive algebraic model describing the limiting magnetization behavior in the interior and at the boundary of the sample. Finally, we demonstrate that the asymptotic results obtained in the periodic setting remain true in the case of finite rectangular samples.

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Acknowledgements

R. G. Lund and C. B. Muratov were supported, in part, by NSF via Grants DMS-1313687 and DMS-1614948. V. Slastikov would like to acknowledge support from EPSRC Grant EP/K02390X/1 and Leverhulme Grant RPG-2014-226.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Ross G. Lund & Cyrill B. Muratov

  2. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Valeriy V. Slastikov

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  1. Ross G. Lund
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  2. Cyrill B. Muratov
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  3. Valeriy V. Slastikov
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Correspondence to Cyrill B. Muratov.

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Communicated by Dr. Anthony Bloch.

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Lund, R.G., Muratov, C.B. & Slastikov, V.V. Edge Domain Walls in Ultrathin Exchange-Biased Films. J Nonlinear Sci 30, 1165–1205 (2020). https://doi.org/10.1007/s00332-019-09604-w

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  • DOI: https://doi.org/10.1007/s00332-019-09604-w

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