Temperature dependence of the frustrated Heisenberg model in the fcc type-I configuration

The Heisenberg model for the fcc type-I configuration is studied with the use of the interacting spin-wave theory at the order 1/S, S being the spins coupled antiferromagnetically. The continuous degeneracy of the ground state of the nearest-neighbor Heisenberg Hamiltonian (H-nn) and the conditions for different types of interactions susceptible to stabilize a multi-k structure remain identical in the whole antiferromagnetic range in temperature. This set includes local anisotropy and four-spin and biquadratic exchange interactions as well as effects of the crystal electric field and quadrupolar interaction. The temperature dependence of the low-frequency magnetic excitations corresponding to H-nn is calculated analytically. For the double-k and triple-k configurations the quartic terms renormalize in great part the overall Heisenberg antiferro-coupling, giving schematically the behavior (root1-(n) over bar /S) roota+b(1-(n) over bar /S) where (n) over bar has the temperature dependence of the Bose-Einstein distribution. Concerning the terms to be added to H-nn to lift the degeneracy of the ground state, they can be separated into two classes following their leading temperature dependences which are 1-t (n) over bar /S, where t=1 or 3. Available experiments are discussed.