Stochastic Landau-Lifshitz-Gilbert Simulations for Spherical Particles with Uniaxial Magnetic Anisotropy

We developed a simulation method that enables the simultaneous analysis of the behavior of magnetic moments and the viscous motion of spherical particles, from a viewpoint of application of magnetic hyperthermia therapy. The behavior of the magnetic moments was analyzed by solving the stochastic Landau-Lifshitz-Gilbert equation, while the viscous motion of the particles was evaluated using the Brownian dynamics method. We addressed a single-particle system to investigate the orientational properties of both the particle and the magnetic moment. If the magnetic anisotropy energy is significantly smaller than the thermal energy, the magnetic particle shows superparamagnetic behavior. The magnetic moment rotates within the particle and tends to incline in the magnetic field direction as the magnetic field strength increases. With respect to the magnetization curve, the present simulation method gives rise to the theoretical solution (the Langevin function). Furthermore, we conclude that the orientational characteristics of the particle and the magnetic moment are strongly influenced by the magnitude relationship between the magnetic field and the magnetic anisotropy.