Free Energy

Whenever a system has a topological defect or soliton, the orientational order depends on position. These spatial variations increase the elastic free energy of the system. This chapter explains how to minimize the elastic free energy around a defect or soliton, calculate the optimum configuration of orientational order, and hence determine the free energy associated with the defect or soliton. It further shows how to minimize the elastic free energy around a pair of defects or solitons, and hence find the interaction between them. For defects, it is a long-range interaction, similar to Coulomb’s law. For solitons, it is a short-range, exponentially decaying interaction. The theory also demonstrates that solitons can become stable features of the ground state in a chiral material, such as a magnetic system with Dzyaloshinskii-Moriya interaction.