Spin waves in the AF state of the t-t' Hubbard model on the fcc lattice: competing interactions, frustration, and instabilities

Spin waves in the type-III ordered antiferromagnetic state of the frustrated $t$-$t'$ Hubbard model on the fcc lattice are calculated to investigate finite-$U$-induced competing interaction and frustration effects on magnetic excitations and instabilities. Particularly strong competing interactions generated due to interplay of fcc lattice geometry and magnetic order result in significant spin wave softening. The calculated spin wave dispersion is found to be in qualitative agreement with the measured spin wave dispersion in the pyrite mineral $\rm Mn S_2$ obtained from inelastic neutron scattering experiments. Instabilities to other magnetic orders (type I, type II, spiral, non-collinear), as signalled by spin wave energies turning negative, are also discussed.