Magnetic relaxation in ferronematics in the mean-field description

We demonstrate that a ferronematic (a dilute suspension of ferromagnet nanoparticles in a nematogenic matrix) may display a direct analog of Néel superparamagnetism entailed by the orienting effect of the matrix on the embedded particles. The latter are assumed to be the objects with pronounced anisometricity; in magnetic aspect, they are single-domains with strong magnetic hardness (e.g. imposed by their rod-like shape) so that the magnetic moment is fixed inside the particle body. Above the isotropic-nematic transition point, the considered system is just a ferrofluid with random distribution of the particle axes. Below the transition, the particle-matrix coupling emerges that sets the axis of each particle (and, hence, its magnetic moment) under the same angle to the director. If this alignment is along the director, then each particle falls under the action of orientational potential with two equal wells (0° and 180°) separated by the energy barrier whose height is defined by the intensity of the surface particle-matrix interaction. Provided the thermal energy is of the order of the barrier height (the material estimates readily admit that), the Brownian motion makes the particle to randomly rotate between the orientational minima. This mechanism entails spontaneous inversions of the magnetic moment as well, thus ensuring relaxation of any initially established magnetization of the ferronematic; the reference time of this process depends exponentially on the hight of the energy barrier scaled with thermal energy. Treating the nematogenic matrix with the aid of mean field model and using the linear response theory to describe the magnetodynamics of the particles, we show that the “liquid-crystalline” superparamagnetism produces an easily identifiable signature in the dynamic magnetic susceptibility spectrum of a ferronematic.