Thermodynamic perturbation theory for dipolar superparamagnets

Abstract

Thermodynamic perturbation theory is employed to derive analytical expressions for the equilibrium linear susceptibility and specific heat of lattices of anisotropic classical spins weakly coupled by the dipole-dipole interaction. The calculation is carried out to the second order in the coupling constant over the temperature, while the single-spin anisotropy is treated exactly. The temperature range of applicability of the results is, for weak anisotropy ${(A/k}_{\mathrm{B}}T\ensuremath{\ll}1),$ similar to that of ordinary high-temperature expansions, but for moderately and strongly anisotropic spins ${(A/k}_{\mathrm{B}}T\ensuremath{\gtrsim}1)$ it can extend down to the temperatures where the superparamagnetic blocking takes place ${(A/k}_{\mathrm{B}}T\ensuremath{\sim}25),$ provided only that the interaction strength is weak enough. Besides, taking exactly the anisotropy into account, the results describe as particular cases the effects of the interactions on isotropic $(A=0)$ as well as strongly anisotropic $(|A\stackrel{\ensuremath{\rightarrow}}{|}\ensuremath{\infty})$ systems (discrete orientation model and plane rotators).