On the Symmetry Analysis of Surface Induced Effects

Abstract

The changes in the components of a wide variety of tensor physical properties, including piezomagnetic, piezomagnetic, magnetoelectric properties and toroidic properties, on traversing from the bulk to the surface of a crystalline material are explicitly tabulated.

Recent progress in the thermodynamics of ferrotoroidic materials

“…The free energy is then analysed to obtain a phase diagram in terms of the free energy coefficients indicating the various ferrotoroidic phase transitions. Note that Litvin has extended the symmetry analysis for ferroics to ferrotoroidic materials including the possible toroidic domains and domain walls [16,17,18]. This analysis is very helpful in obtaining the free energy for ferrotoroidic phase transitions for any crystal symmetry.…”

“…second harmonic generation. Litvin has provided a symmetry based classification of such domains [16] as well as ferrotoroidal crystals [17,18]. Another material, BCG (Ba 2 CoGe 2 O 7 ), also exhibits spontaneous toroidal moments [19].…”