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Journal of Intelligent Material Systems and Structures
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A Finite Dimensional Model Problem in Ferromagnetism

Michael K. Keane

Department of Mathematics and ICAM Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0123

Robert C. Rogers

Department of Mathematics and ICAM Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0123

In this article we calculate magnetic equilibria of a finite dimensional model of a polycrystalline ferromagnetic body. Our model incorporates recent advances on frustration and microstructure in ferromagnetism. In particular, we will use minimizing sequences or Young- measures to model equilibrium states, and we make use of nonlocal exchange energies. We show that our model problem has a rich class of relative equilibria. Furthermore, this set of solutions can be interpreted as representing a quasistatic hysteresis diagram that exhibits hysteresis subloops and the Barkhausen effect.

Journal of Intelligent Material Systems and Structures, Vol. 4, No. 4, 463-468 (1993)
DOI: 10.1177/1045389X9300400404
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