Broken Symmetry, Ferroic Phase Transitions and Multifunctional Materials

Abstract

A phase transition is associated with a change of certain symmetry. This symmetry change is captured by an order parameter which is zero above the transition temperature (or pressure) and non-zero below it. An important class of functional materials is that of ferroics which are characterized by two or more orientation states with the ability to switch between them via an applied field. In terms of broken spatial inversion and time reversal symmetry, there are four types of primary ferroics: ferroelectrics described by polarization (a polar vector with broken spatial inversion symmetry), ferromagnets described by magnetization (an axial vector with broken time reversal symmetry), ferrotoroidics described by torodization (an axio-polar vector with both spatial inversion and time reversal symmetries broken) and ferroelastics described by strain ε (a symmetric second rank polar tensor with neither spatial inversion nor time reversal symmetry broken but with broken rotational symmetry). Materials possessing two or more ferroic properties are called multiferroics. In particular, crystals exhibiting simultaneous ferroelectricity and magnetism are called magnetoelectrics. We consider the effect of disorder in these crystals which above the transition temperature may result in a tweed structure whereas it may lead to a glassy state below the transition. We also explore the properties of ferroics at nanoscale which are dominated by the surface/interface energy contribution. Finally, we describe in detail the magnetic symmetry of low-dimensional multiferroic materials and study a representative phase transition.

Keywords:

• Order parameter
• Magnetic symmetry
• Multiferroics
• Magnetoelectrics
• Ferrotoroidics
• Disorder
• Tweed
• Free energy