Thermodynamics of Multiferroic Materials
This chapter deals with the Thermodynamics of multiferroic materials. We first discuss the symmetry of the four primary ferroic order parameters related to ferromagnets, ferroelectrics, ferroelastics and ferrotoroidics and set up basic field equations. We
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Thermodynamics of Multiferroic Materials Teresa Castán, Antoni Planes and Avadh Saxena
Abstract This chapter deals with the Thermodynamics of multiferroic materials. We first discuss the symmetry of the four primary ferroic order parameters related to ferromagnets, ferroelectrics, ferroelastics and ferrotoroidics and set up basic field equations. We then develop a general thermodynamic description based on generalized displacements and the corresponding conjugated fields. We use these ideas to calculate multicaloric effects in these materials, in particular focussing on the toroidocaloric effect. Next we develop Landau free energy models for multiferroic materials and illustrate various ideas through three representative examples: (i) magnetoelectric transitions, (ii) magnetic shape memory transitions where elasticity plays a crucial role, and (iii) ferrotoroidic transitions. We also briefly discuss the role of disorder and its consequences for the existence of ferroic tweed as well as ferroic glass. Finally, we provide an outlook in terms of the open problems in this exciting field of research.
4.1 Introduction Ferroic properties such as ferroelasticity, ferroelectricity and ferromagnetism are related to the possibility of switching the strain, polarization and magnetization between two opposite or symmetry-related values by means of appropriate T. Castán (&) A. Planes Facultat de Física, Departament d’Estructura i Constituents de la Matèria, Diagonal 647, 08028 Barcelona, Catalonia, Spain e-mail: [email protected] A. Planes e-mail: [email protected] A. Saxena Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA e-mail: [email protected]
A. Saxena and A. Planes (eds.), Mesoscopic Phenomena in Multifunctional Materials, Springer Series in Materials Science 198, DOI: 10.1007/978-3-642-55375-2_4, Springer-Verlag Berlin Heidelberg 2014
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mechanical (stress), electric and magnetic fields, respectively. Each of these fields is thermodynamically conjugated to the corresponding ferroic property. The switching process is a highly non-linear process with associated hysteresis, with two opposite zero-field retained ferroic states (remanence) and two (usually symmetric) coercive fields (at which the ferroic property vanishes), that macroscopically characterizes the dependence of the ferroic property on its corresponding conjugated field. Materials are denoted multiferroic when switching occurs under cross-fields. The combination of more than one ferroic property in a given material is, from a practical viewpoint, important since it enables to achieve a rich multifunctional behaviour which opens new routes for novel technological applications [1]. In a given material, a ferroic property emerges spontaneously (absence of applied field) upon cooling from high temperature through a phase transition which involves a certain symmetry breaking. This fact, together with the effect of some compatibility constraints imposed by boundary conditions, results in a heterogeneous structu
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