Torque undergone by assemblies of single-domain magnetic nanoparticles submitted to a rotating magnetic field

International audienceIn the last 10 years, it has been shown in various types of experiments that it is possible to induce biological effects in cells using the torque generated by magnetic nanoparticles submitted to an alternating or a rotating magnetic field. In biological systems, particles are generally found under the form of assemblies because they accumulate at the cell membrane, are internalized inside lysosomes, or are synthesized under the form of beads containing several particles. The torque undergone by assemblies of single-domain magnetic nanoparticles has not been addressed theoretically so far and is the subject of the present article. The results shown in the present article have been obtained using kinetic Monte Carlo simulations, in which thermal activation is taken into account, so the torque undergone by ferromagnetic and superparamagnetic nanoparticles could both be simulated. The first system under study is a single ferromagnetic particle with its easy axis in the plane of the rotating magnetic field. Then, elements adding complexity to the problem are introduced progressively and the properties of the resulting system presented and analyzed: random anisotropy axes, thermal activation, assemblies, and finally magnetic interactions. The most complex studied systems are particularly relevant for applications and are assemblies of interacting superparamagnetic nanoparticles with randomly oriented anisotropy axes. Whenever it is possible, analytical equations describing the torque properties are provided, as well as their domain of validity. Although the properties of an assembly naturally derive from those of single particles, it is shown here that several of them were unexpected and are particularly interesting with regard to the maximization of torque amplitude in biological applications. In particular, it is shown that, in a given range of parameters, the torque of an assembly increases dramatically in the direction perpendicular to the plane of the rotating magnetic field. This effect results from a breaking of time reversal symmetry when the field is rotated and is comprehensively explained. This strong enhancement occurs only if the magnetic field rotates, not if it oscillates. When this enhancement does not occur, the total torque of an assembly scales with the square root of the number of particles in the assembly. In the enhancement regime, the total torque scales with a power exponent larger than 1/2. It is also found that, in superparamagnetic nanoparticles, this enhancement is induced by the presence of magnetic interactions so that, in a rather large range of parameters, interacting superparamagnetic particles display a much larger torque than otherwise identical ferromagnetic particles. In all cases studied, the conditions required to obtain this enhancement are provided. The concepts presented in this article should help chemists and biologists in synthesizing nano-objects with optimized torque properties. For physicists, it would be interesting to test experimentally the results described in this article. For this purpose, torque measurements on well-characterized assemblies of nanoparticles should be performed and compared with numerical simulations