The magnetic properties of erbium gallium garnet under the high magnetic field

A theoretical investigation on the magnetic properties of erbium gallium garnet (Er3Ga5O12) is reported. According to quantum theory by exactly solving the secular equation, the magnetization (M) in Er3Ga5O12 single crystal is firstly calculated at 4.2K when the applied magnetic field (H) is parallel to the [100] and [111] directions. An anisotropy of the magnetization is found under high magnetic field, and when the magnetic field is small, no anisotropy exists, which conforms to the experimental conclusion. The temperature (T) dependence of magnetization is analyzed for H parallel to the [100] and [111] crystallographic directions at the temperature between 5 and 295K. It is shown that the saturation of the M(T) along the [111] axis is attained at about 15K and H∼240kOe. Finally, it is demonstrated that the mixing of the different multiplets (4I15/2 and 4I13/2) has little influence on the magnetic properties.