Thermal renormalization of the order wave vector in Heisenberg helimagnets

Abstract

In spite of a great deal of experimental and theoretical work on the helimagnetism, the actual possibility of evaluating the temperature dependence of the helical-order wave vector arising from the magnon-magnon interaction is quite unsatisfactory, in particular for Heisenberg helimagnets. For Heisenberg ferromagnets with planar anisotropy and for XY helimagnets, the self-consistent harmonic approximation (SCHA) of Villain provides an efficient tool which reduces to the well-known self-consistent renormalized (SCR) spin-wave approach in the ferromagnetic case when no anisotropy is present. If we try to extend the SCHA to Heisenberg helimagnets, we face a serious shortcoming: for zero anisotropy the Goldstone theorem is violated at the helix wave vector and zero-point motion contributions are certainly overestimated. This failure arises because the SCHA takes into account the four-operator potential but neglects at all the three-operator potential that has been recently proved to give contributions of the same weight in 1/S. So we have modified the SCHA in order to bypass the above shortcoming and we fit this approach on NiBr2: elastic and inelastic neutron scattering data meet our theory in a satisfactory semiquantitative way but some qualitative features, as, for instance, the observed first-order helix-antiferromagnet phase transition, claim further theoretical effort.