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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS

Inhomogeneous Configurations of Magnetization of Ferromagnetic Films with Biaxial Anisotropy Yu. I. Dzhezheryaa, M. V. Sorockinb, and E. A. Bubukc a

Institute of Magnetism, National Academy of Sciences and the Ministry of Education and Science of Ukraine, Kiev, 03142 Ukraine b Institute for Problem of Mathematical Machines and Systems, National Academy of Sciences of Ukraine, Kiev, 03187 Ukraine c National Technical University (KPI), Kiev, 03056 Ukraine e-mail: [email protected] Received April 18, 2006; in final form, May 8, 2007

Abstract—The system of the Landau–Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out. PACS numbers: 75.60.Ch DOI: 10.1134/S1063776107100081

1. INTRODUCTION The distribution of magnetization of a nonconducting ferromagnetic system is determined by the joint solution of the Landau–Lifshitz and magnetostatic equations. Since these equations are nonlinear in the general case and contain integral terms, the problem of determining the magnetization field cannot be solved analytically in the general case. Simplified models of magnetic configurations, including an isolated strip domain, a cylindrical magnetic domain (CMD), as well as a strip domain structure and a CMD lattice in a film with transverse uniaxial anisotropy can be analyzed more or less comprehensively. Such systems are analyzed using various methods simplifying the problem. For example, the period of a strip domain structure and the equilibrium CMD diameter can be effectively calculated using an approach in which domain walls are treated as infinitely thin (model of geometrical domain walls). The effective surface energy is the only parameter characterizing a domain wall. In the framework of the given approximation, the dependence of the properties of domain structure on the parameters of the material and on the ferromagnetic film thickness was established [1–4]. This approximation has been used recently to analyze the effect of the ferromagnetic plate width on the parameters of a strip domain structure [5] (for a film with longitudinal anisotropy). Modifications of this methods for ultrathin films with a thickness on the order of ten atomic monolayers, which take into account the nature of anisotropy on the film surface, were also proposed [6, 7].

The model of geometric domain walls is effective in the case when the domain wall thickness is much smaller than the period of the domain structure (e.g., for CMD materials with a high Q-factor (Q = Ha/4πM0
1), where Ha is the effective magnetic anisotropy field and M0 is the saturation magneti