Magnetic Hysteresis Loop in a Superparamagnetic State

Magnetization curves of superparamagnetic nanoparticles in ac magnetic field are numerically studied by Brownian dynamics simulation with considering a more precisely estimated magnetic torque. Consequently, we confirmed that rotatable nanoparticles with magnetic easy axes show magnetic hysteresis loops without remanence, even when the thermal fluctuations of the magnetizations are much faster than the oscillation of the magnetic fields. The origin is that magnetic alignments of the easy axes by the magnetic torque in the peak period of the oscillations of field alternate with their randomizations by Brownian relaxation in the period when the field becomes almost zero. Because the equilibrium magnetization curve of the aligned nanoparticles is steeper than that of randomly oriented ones, a new kind of hysteresis appears when both the Brownian relaxation time and the characteristic time of the field-driven rotation are comparable to the alternation period of magnetic field. This finding sheds a new light on the widely accepted association between superparamagnetism and the anhysteretic magnetization curves. Furthermore, this knowledge will help reconsideration of the design of biomedical application using magnetic nanoparticles, since it has been optimized assuming magnetic response described by Langevin function.