Equilibrium susceptibilities of superparamagnets: longitudinal and transverse, quantum and classical

The equilibrium susceptibility of uniaxial paramagnets is studied in a unified framework which permits us to connect traditional results of the theory of quantum paramagnets, S = 1/2,1,3/2,..., with molecular magnetic clusters, S∼5,10,20 all the way up (S = 30,50,100,...,) to the theory of classical superparamagnets. This is done using standard tools of quantum statistical mechanics and linear-response theory (the Kubo correlator formalism). Several features of the temperature dependence of the susceptibility curves (crossovers, peaks, deviations from Curie law) are studied and their scalings with S identified and characterized. Both the longitudinal and transverse susceptibilities are discussed, as well as the response of the ensemble with anisotropy axes oriented at random. For the latter case a simple approximate formula is derived too, and its range of validity assessed, which could be used in the modelization of experiments.