  In the probe limit, we investigate holographic paramagnetism-ferromagnetism
phase transition in the four-dimensional (4D) and five-dimensional(5D) Lifshitz
black holes by means of numerical and semi-analytical methods, which is
realized by introducing a massive 2-form field coupled to the Maxwell field. We
find that the Lifshitz dynamical exponent $z$ contributes evidently to magnetic
moment and hysteresis loop of single magnetic domain quantitatively not
qualitatively. Concretely, in the case without external magnetic field, the
spontaneous magnetization and ferromagnetic phase transition happen when the
temperature gets low enough, and the critical exponent for the magnetic moment
is always $1/2$, which is in agreement with the result from mean field theory.
And the increasing $z$ enhances the phase transition and increases the DC
resistivity which behaves as the colossal magnetic resistance effect in some
materials. Furthermore, in the presence of the external magnetic field, the
magnetic susceptibility satisfies the Cure-Weiss law with a general $z$. But
the increase of $z$ will result in shortening the period of the external
magnetic field.
