Davies, Z.; (2009) Application of representation theory to magnetic and structural phase transitions. Doctoral thesis , UCL (University College London).

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Abstract

The tools of representation theory offer us a powerful insight in those terms in a system’s Hamiltonian which cause it to become ordered. Such is its power that, in many fields, the vocabulary of representations has become conventional; crystallography remains a notable exception. This thesis develops the existing methods for applying representation theory to symmetry lowering phase transitions in crystalline systems, and presents examples of its use. The opening section reviews the foundations and previous applications of representation theory to magnetic and structural phase transitions. Complimentary to the mathematical framework is a discussion of the physical interpretation of irreducible representations and basis vectors, the building blocks of any system model constructed in this way. Symmetry arguments are used to qualitatively discuss the symmetry breaking in ferroelectric materials and the role of phase factors in the loss of centro-symmetry. The body of this work is concerned with developing fast, reliable and repeatable methods for applying representation theory to displacive transitions. Calculation of a system’s basis vectors requires both a reliable method, and suitable starting resources. In this section, the first verifiable validation of the tables of Kovalev is presented, along with a strategy for determining the appropriate set of trial functions for use with the method of projection operators. Further, a new module in SARAh-Refine has been written which performs basis vector refinement of powder diffraction data to facilitate quantitative analysis using these techniques. Finally, the techniques of representation theory are applied to two experimental investigations: iron oxyborate and potassium selenate. The use of a single symmetry framework to discuss the structural, magnetic and charge-ordering transitions in these systems demonstrate the power of this technique. Representation theory provides a bridge between structure and properties; this work aims to strengthen the foundations of that bridge.

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