On Calculation of the Stiffness Coefficients of Domain Boundaries in Magnetic and Electric Ordered Systems in Linear and Weakly Nonlinear Domains

Abstract

This paper presents the study of the features of domain boundaries dynamics based on the macroscopic approach. In addition, a methodology for the calculation of domain boundary stiffness coefficient due to its importance among the relaxation parameters of magnetic and electric ordered systems is included in the study.
 The proposed algorithm allows the calculation of stiffness coefficients of domain boundaries (DB) in ferromagnetic, ferroelectric, and ferroelectromagnetic materials in linear and weakly nonlinear DB displacement areas caused by an external force. The external force is identified as the difference in the densities of magnetoelastic (electroelastic) energies of crystals for domains separated by the DB. It is related to the difference of their energies because each domain has its own orientation of spontaneous magnetization IS and polarization PS vectors at the same equal values of external stress components σij. The desired stiffness coefficients of the DB are calculated as the second derivatives of magnetoelastic (electroelastic) subsystem energies with respect to DB displacements. The stiffness coefficients of the first k1 and the second k2 order of smallness are obtained in a similar way using cubic and biquadratic components of energies in terms of DB displacements, i.e. relative deformation of crystals.