Nonlinear ac stationary response and dynamic magnetic hysteresis of quantum uniaxial superparamagnets

The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets-nanoscale solids or clusters with spin number S~100-104-in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components arising from the nonlinear response of the magnetization, dynamic magnetic hysteresis loops, etc., are then evaluated via matrix continued fractions indicating a pronounced dependence of the response on S arising from the quantum spin dynamics, which differ markedly from the magnetization dynamics of classical nanomagnets. In the linear response approximation, the results concur with existing solutions.