Magnetic vortex mobility for hollow Fe₃O₄ submicron particles studied by a hysteresis scaling technique

We report results of magnetic hysteresis scaling of minor loops for hollow Fe3O4 submicron particles with variable diameter of 400–720 nm. As in the case of bulk ferromagnetic materials, a power-law scaling with an exponent of ∼1.5 was found to universally hold true between hysteresis loss and remanence of minor loops, although the magnetization process is significantly different from a bulk ferromagnet where irreversible Bloch wall displacement plays a crucial role. The minor-loop coefficient decreases with inner/outer diameter ratio and is almost independent of temperature above T = 30 K. The behavior of the coefficient indicates that a mobility of a magnetic vortex under magnetic fields increases with increasing a inner/outer diameter ratio of a hollow sphere and is weakly temperature dependent. The results suggest that the coefficient can be a sensitive indicator of the particle geometry for vortex spherical particles.