Anisotropic magnetoresistance across Verwey transition in charge ordered Fe3O4 epitaxial films

The anisotropic magnetoresistance (AMR) near the Verwey temperature $({T}_{\mathrm{V}})$ is investigated in charge ordered ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ epitaxial films. When the temperature continuously decreases below ${T}_{\mathrm{V}}$, the symmetry of AMR in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$(100) film evolves from twofold to fourfold at a magnetic field of 50 kOe, where the magnetic field is parallel to the film surface, whereas AMR in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$(111) film maintains twofold symmetry. By analyzing AMR below ${T}_{\mathrm{V}}$, it is found that the Verwey transition contains two steps, including a fast charge ordering process and a continuous formation process of trimeron, which is comfirmed by the temperature-dependent Raman spectra. Just below ${T}_{\mathrm{V}}$, the twofold AMR in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$(100) film originates from uniaxial magnetic anisotropy. The fourfold AMR at a lower temperature can be ascribed to the in-plane trimerons. By comparing the AMR in the films with two orientations, it is found that the trimeron shows a smaller resistivity in a parallel magnetic field. The field-dependent AMR results show that the trimeron-sensitive field has a minimum threshold of about 2 kOe.