Hydrodynamic time-correlation functions of a Heisenberg ferrofluid

Using our previous results [Physica A 220 (1995) 325 and A 234 (1996) 129], where the generalized transport equations for a Heisenberg-like model of a ferrofluid were obtained and the hydrodynamic collective mode spectrum has been studied, we derive the analytical expressions for hydrodynamic time-correlation functions of a Heisenberg model ferrofluid in a homogeneous magnetic field and in the limit of small wave numbers k and frequencies ω. These results, being exact in the hydrodynamic limit, are presented in the form, where contributions from each of the hydrodynamic modes are separated. It is shown that the sound excitations contribute to the time-correlation function of ‘spin density–spin density’, and the weight of this contribution depends on the value of an external magnetic field. On the other side, the spin diffusive mode contributes to the central line of the dynamic structure factor. Both of these functions may be extracted from scattering experiments. The Landau–Placzek ratios for the dynamic structure factor S(k,ω) and the magnetic dynamic structure factor Sm(k,ω) are calculated.