Magnetically Ordered Systems

Abstract

A particularly interesting class of crystalline solids is constituted by those materials that exhibit regularity not only in the spatial arrangement of atoms but also in the alignment of their magnetic moments. It was shown in Chapter 3 that in a stand-alone atom or ion the orbital angular momentum L and the spin S of electrons on incomplete shells give rise to a magnetic moment −g J µ B J , where J is the dimensionless total angular momentum. Since the d-and f-electrons of ionic cores are usually localized in solids, too, these atomic moments are observed in the crystalline phase as well-although the crystalline field due to neighboring atoms may split the multiply degenerate ground state of the free ion, and therefore the moment may be modified. When the interaction between magnetic moments-namely, the quantum mechanical exchange interaction-is sufficiently strong on the scale of thermal energies, the magnetic moments of neighboring atoms may mutually align each other in some direction. It may occur that, in contrast to paramagnets, the orientation of each spin is rigidly fixed, however no correlation is observed in the orientation of magnetic moments, and the correlation function of spins drops off rapidly with distance. Since this static disorder is similar to the situation encountered in glasses, where atomic positions show a similar disorder, such systems are referred to as spin glasses. We shall analyze the properties of such materials in Chapter 36 of Volume 3. In the present chapter we shall be concerned with materials in which magnetic moments are aligned in some-usually crystallographically determined, high-symmetry-direction in such a way that their orientation shows long-range correlations. Such structures are said to be magnetically ordered. First we shall get acquainted with the magnetic structure of ferromagnets, antiferromagnets, and ferrimagnets, which are the most common families of magnetically ordered materials. Then we shall examine the interactions that are responsible for magnetic ordering. At sufficiently high temperatures thermal fluctuations disrupt this order; the mechanism is similar to the melting of crystal lattices. First the simplest description provided by the mean-field theory will be presented, and then the behavior around the critical point will be