Magnetic and Toroidal Symmetry of Lithium Transition Metal Orthophosphates

Abstract

LiCoPO4 is the foremost candidate material for a novel type of ferroic ordering calledferrotoroidicity. In this work, the synthesis of polycrystalline sample of LiCoPO4 is discussed, along with the structural analog LiMnPO4. Their magnetic susceptibility and magnetic structure were determined and analyzed and found to be consistent with previous reports on single crystal materials. This work also provides a thorough introduction to ferrotoroidicity, a history of its theoretical development, and a summary of the most studied candidate materials. The work then presents a detailed methodology for determining the toroidal structure which would result for the magnetic structure in candidate ferrotoroidal materials. The model provides a method for determining how many toroidal moments would be present, where they would be located within the unit cell, and along which crystallographic direction they would be oriented. Detailed examples for determining the magnetic structure are provided for LiCoPO4 and analogous structures with the olivine structure type, as well as several structures with the pyroxene structure type. The results demonstrate a method for understanding ferrotoroidal arrangements, anti-ferrotoroidal arrangements and non-toroidal structures.