Published online by Cambridge University Press: 24 April 2020
The quantum mechanical exchange interaction gives rise to magnetic moments and their interactions in materials, which give rise to patterns and structures in the orientations of magnetic moments at low temperatures. With increasing temperature, pressure, and magnetic field, magnetic structures are altered, and Chapter 21 describes several trends that can be understood by thermodynamics. The critical temperature of magnetic ordering, the Curie temperature TC, is calculated. Compared to chemical ordering, the strengths and alignments of magnetic moments have more degrees of freedom, allowing for diverse magnetic structures. These include ferrimagnetism, frustrated structures, and spin glasses. The vectorial character of spin interactions can give rise to localized spin structures such as skyrmions. An electromechanical phase transition can occur when the energy for a displacement of positive and negative ions in a unit cell is comparable to thermal energies. This ferroelectric transition has some similarities to the ferromagnetic transition, but is described by Landau theory. Domains in ferroelectric and ferromagnetic materials can reduce the energy in surrounding elastic and magnetic fields, and the width of a boundary between two magnetic domains is estimated.