Recent Progress in the thermodynamics of ferrotoroidic materials
Antoni Planes, Teresa Castan, Avadh Saxena

TL;DR
This paper reviews recent advances in the thermodynamics of ferrotoroidic materials, covering theoretical models, experimental observations, phase transitions, and applications like the toroidocaloric effect.
Contribution
It provides a comprehensive overview of the latest theoretical and experimental developments in understanding ferrotoroidic materials and their thermodynamic properties.
Findings
Derivation of magnetic toroidal moment and toroidization expressions
Experimental observation of magnetic toroidal moments and domains
Application of Landau modeling to phase transitions and toroidocaloric effect
Abstract
Recent theoretical and experimental progress on the study of ferrotoroidic materials is reviewed. The basic field equations are first described and then the expressions for magnetic toroidal moment and toroidization are derived. Relevant materials and experimental observation of magnetic toroidal moment and toroidal domains are summarized next. The thermodynamics of such magnetic materials is discussed in detail with examples of ferrorotoidic phase transition studied using Landau modelling. Specifically, an example of application of Landau modelling to the study of toroidocaloric effect is also provided. Recent results of polar nanostructures with electrical toroidal moment are finally reviewed.
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