Electromagnetic fields induced by a point source in a uniaxial multiferroic full-space, half-space, and bimaterial space
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Multiferroic magnetoelectrics are materials that are both ferroelectric and ferromagnetic in the same phase. In addition, electric and magnetic polarizations are strongly coupled in some magnetoelectric multiferroic materials. In this work, by virtue of the image method, exact closed-form Green’s functions are derived for a uniaxial multiferroic full-space, half-space, and bimaterial space. While for the bimaterial space case the interface is assumed to be perfect, for the half-space case four different sets of surface conditions are considered. The point source can be either an electric or a magnetic charge. Numerical results are presented to demonstrate the differences among the infinite-space, half-space, and bimaterial space Green’s functions.
I. INTRODUCTION
Magnetoelectric multiferroic materials are novel compounds that exhibit both ferromagnetism and ferroelectricity simultaneously. In addition, magnetic and electric polarizations are strongly coupled in some magnetoelectric multiferroic materials. These materials may exhibit a spontaneous magnetic polarization that can be switched with an electric field and/or a spontaneous electric polarization that can be switched with a magnetic field. Possible applications of magnetoelectric multiferroics include multiple-state memory elements, giant magnetic resistance devices, electric-field-controlled ferromagnetic-resonance devices, and variable transducers with either magnetically modulated piezoelectricity or electrically modulated piezomagnetism. Recently, various aspects of the fundamental physics of multiferroic materials, including first principles1–4 and micromechanics,5–7 were investigated. In terms of fundamental/analytical solutions, while the bimaterial Green’s functions in anisotropic and fully coupled magneto-electro-elastic materials were derived by virtue of the Stroh formalism,8 a three-dimensional (3D) solution of plates made of multiferroic composites,9 was also available. In a more recent study, Li and Li10 derived the explicit Green’s functions for a uniaxial multiferroic material full-space induced by a point-electric or magnetic charge, and then used the Green’s functions to determine the electromagnetic fields in an ellipsoidal inclusion with
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2007.0269 2144 J. Mater. Res., Vol. 22, No. 8, Aug 2007 http://journals.cambridge.org Downloaded: 13 Mar 2015
spontaneous polarization and magnetization embedded in a multiferroic material. As the fundamental solutions to various governing systems of equations, Green’s functions represent the very basic relation between the response at the field point and the excitation at the source point. Therefore, they can be directly applied to the analysis of material behaviors in certain simple cases or used as kernel functions in a boundary integral equation for analyzing more complicated problems. Green’s functions are also fundamental for the prediction of the effective material properties in composites such as the multif
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