Magnetic and electronic phase transitions

Magnetism in materials originates with electron spins and their alignments. Groups of spins develop patterns and structures at low temperatures through interactions with each other. With temperature, pressure, and magnetic field, these spatial patterns of electron spins are altered, and several trends can be understood by thermodynamic considerations. This chapter describes how magnetic structures change with temperature. The emphasis is on magnetic moments localized to individual atoms, as may arise from unpaired 3 d electrons at an iron atom, for example. The strong intra atomic exchange interaction gives an atom a robust magnetic moment, but the magnetic moments at adjacent iron atoms interact through inter atomic exchange interactions. Interatomic exchange interactions are often weaker, having energies comparable to thermal energies. Interatomic exchange is analogous to chemical bonding between pairs of atoms in a binary alloy that develops chemical order. The critical temperature of chemical ordering T c corresponds to the Curie temperature for a magnetic transition T C , and short-range chemical order above the T c finds an analog in the Curie–Weiss law for paramagnetic susceptibility above T C . For chemical ordering the atom species are discrete types, whereas magnetic moments can vary in strength and direction as vector quantities. This extra freedom allows for diverse magnetic structures, including antiferromagnetism, ferrimagnetism, frustrated structures, and spin glasses.