Non-Langevin high-temperature magnetization of nanoparticles in a weak magnetic field

Experimental evidence and theoretical substantiation are presented for the asymptotic behavior of high-temperature magnetization of an ensemble of nanoparticles in a weak magnetic field, which was predicted earlier and which differs qualitatively from the "Langevin" limit for ideal superparamagnetic particles. It is shown that the physical reason for the new asymptotic behavior is the temperature-independent "positive" tilt of the uniform magnetization vector at local energy minima in the direction of the field; this asymptotic behavior is associated with the nonstandard thermodynamics of single-domain particles, which depends on the ratio of characteristic frequencies of regular precession and random diffusion of this vector. An alternative approach is proposed for describing the magnetic dynamics of an ensemble of nanoparticles in a magnetic field, and the precession orbits of the magnetization vector are considered as stochastic states of each particle, whereas each state is characterized by the trajectory-averaged value of magnetization.