Magnetic order in the frustrated Heisenberg model for the fcc type-I configuration

The Heisenberg model for the fcc type-I configuration with various types of interactions is studied with use of the noninteracting spin-wave theory. It is shown that local anisotropy, four-spin exchange interactions, and biquadratic interactions can lift the continuous degeneracy of the ground state through the stabilization of a noncollinear magnetic state. Moreover, in the particular case of a pyrite structure, a Dzyaloshinsky-Moriya term or a symmetric anisotropic exchange stabilizes the double-k configuration. The single-k state is also discussed. We prove, in particular, that quantum fluctuations favor such a case. Consequences for the magnetic moment reduction and for the spin-wave spectra of the presence of such stabilizing terms are calculated and compared with data. Experiments seem to indicate that the minimal model built from the nearest-neighbor Heisenberg interaction and a stabilizing term is not satisfactory.