Finite-temperature spin dynamics and phase transitions in spin-orbital models

We study finite temperature properties of a generic spin-orbital model relevant to transition metal compounds, having coupled quantum Heisenberg-spin and Ising-orbital degrees of freedom. The model system undergoes a phase transition, consistent with that of a two-dimensional Ising model, to an orbitally ordered state at a temperature set by short-range magnetic order. At low temperatures the orbital degrees of freedom freeze out and the model maps onto a quantum Heisenberg model. The onset of orbital excitations causes a rapid scrambling of the spin spectral weight away from coherent spin waves, which leads to a sharp increase in uniform magnetic susceptibility just below the phase transition, reminiscent of the observed behavior in the Fe-pnictide materials.