Non-linear dynamic response of superparamagnetic nanoparticles

Odd-order dynamic magnetic susceptibilities of an assembly of single-domain uniaxial particles in the low-temperature limit are considered. The solution of the micromagnetic Fokker-Planck equation is presented in the form of asymptotic series with respect to the parameter σ that is the ratio of the anisotropy energy barrier height to the thermal energy. The expressions for the set of susceptibilities up to the fifth order are presented for the case of an assembly of particles randomly oriented in a solid matrix. The validity of the derived asymptotic representation in a wide range of σ is proved by comparison with the numerical solution of the Fokker-Planck equation.