Application of a generalized matrix averaging method for the calculation of the effective properties of thin multiferroi
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DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Application of a Generalized Matrix Averaging Method for the Calculation of the Effective Properties of Thin Multiferroic Layers A. S. Starkova and I. A. Starkovb* a
Institute of Refrigeration and Biotechnology, St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, 191002 Russia b SIX Research Centre, Brno University of Technology, Brno, 61600 Czech Republic *email: [email protected] Received March 28, 2014
Abstract—It is proposed to use a generalized matrix averaging (GMA) method for calculating the parameters of an effective medium with physical properties equivalent to those of a set of thin multiferroic layers. This approach obviates the need to solve a complex system of magnetoelectroelasticity equations. The required effective characteristics of a system of multiferroic layers are obtained using only operations with matrices, which significantly simplifies calculations and allows multilayer systems to be described. The proposed approach is applicable to thinlayer systems, in which the total thickness is much less than the system length, radius of curvature, and wavelengths of waves that can propagate in the system (longwave approximation). Using the GMA method, it is also possible to obtain the effective characteristics of a periodic structure with each period comprising a number of thin multiferroic layers. DOI: 10.1134/S1063776114110120
1. INTRODUCTION In the past decade, researchers have devoted con siderable interest to thin multiferroic films due to their broad spectrum of possible applications [1–6]. The use of multiferroics is based on the magnetoelectric (ME) effect, which consists in the appearance of a magnetic field under the action of an external electric field and vice versa. In the natural multiferroic Cr2O3, the maximum ME coefficient is attained at a temper ature of 260 K and amounts to 3.7 pS m–1 [7]. Unfor tunately, this is insufficient for practical applications. Values greater by about two orders of magnitude were reported for TbPO4 [8] and Ho2BaNiO5 [9], but a sig nificant ME effect was only observed at low tempera tures. As a result, the attention of researchers has been focused on artificial multiferroics, in which the mutual coupling of electric and magnetic fields are mediated by an elastic stress field. In multiferroic composites, i.e., structures consisting of alternating piezoelectric and magnetostrictive layers, the maximum ME effect reaches about 20 pS m–1 in a constant magnetic field and up to 10–100 pS m in an alternating magnetic field at the electromechanical resonance frequency, which depends on the sample size and parameters of the composite [10–13]. Calculation of the properties of composite materi als is quite a laborious task because of the complexity of equations describing the interrelation of electric, magnetic, and elastic fields [13, 14]. In order to sim
plify these calculations, we propose to use a general ized matrix averaging (GMA) method
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