Modulated, or long-periodic, magnetic structures of crystals

The experimental results on modulated magnetic structures and the basic regularities of phase transitions between them are reviewed and are analyzed on the basis of the phenomenological theory of phase transitions with the use of the Ginzburg-Landau functionals for inhomogeneous distributions of the order parameter. Lists of presently known crystals, in which modulated magnetic structures have been observed, are presented and for many of them the form of these functionals, taking into account the crystalline anisotropy and the interaction with a magnetic field, is established. For systems admitting a Lifshitz invariant which is linear with respect to the gradient, a soliton picture of the structure of the incommensurate phase is established and the phase transition into the commensurate phase under the action of temperature or a magnetic field is analyzed. It is shown that this transition is accompanied by a "locking" of the wave vector to the commensurate value. For systems without Lifshitz invariants, which include most crystals with modulated structures, nonlinear equations for the distribution of the order parameter are investigated by asymptotic methods, and these solutions permit describing the entire complex of observed phenomena: the temperature and field dependence of the wave vector, the appearance of higher-order satellites in the neutron duffraction pattern, and the sequence of magnetic phases. Thus a systematic and complete exposition of the present experimental and theoretical status of long-periodic magnetic structures of crystals, such as the spiral structure, the longitudinal and transverse spin-wave structures, the fan structure, and others, is given in this review. The review is written so as to be accessible and of interest to a wide range of readers who are interested in both the theoretical and experimental aspects of the study of magnetic phase transitions in crystals.