Thermal Variation of the Pitch of Helical Spin Configurations

Abstract

When the method of Luttinger and Tisza for finding the classical ground state of a system of spins with Heisenberg interactions is applicable, it yields a configuration with the same periodicity as the ordered state existing just below the transition temperature. When the method of Luttinger and Tisza fails to yield the classical ground state then there can occur, with decreasing temperature, either additional transitions or a gradual change in the periodicity of the stable configuration. An example of the latter is the thermal change in pitch of a helical configuration. Such a situation can be described in the internal field approximation when the consistency equations admit as solutions helical states with a continuous range of pitches. The free energy of the stable state with a temperature-dependent pitch can then be obtained as the envelope of the free-energy curves belonging to the family of helical solutions. A one-dimensional diatomic chain whose ground state can be found by a generalization of the method of Luttinger and Tisza illustrates this possibility. It is also pointed out that anisotropic exchange interaction between nearest neighbors can give rise to helically ordered configurations.