Temperature dependence of magnetization in GaMnAs film with critical strain

The temperature dependence of the magnetization properties of GaMnAs film, in which the strain was controlled to be in a critical condition by inserting a thin InGaAs layer, has been investigated by Hall measurements. The Hall resistance obtained with the magnetic fields perpendicular to the sample plane showed a slanted hysteresis, indicating the coexistence of in-plane and out-of-plane components of magnetization. The magnetic anisotropy fields of the sample were obtained from the angle dependence of the Hall resistance measurements. Using the magnetic anisotropy fields, the three-dimensional magnetic free energy diagrams were constructed for several temperatures. All energy diagrams show six energy minima along or near 〈100〉〈100〉 directions, implying the possibility of magnetization within the plane and/or along out-of-plane directions in the system. Though the energy minima presented in the film plane (i.e., within the (001) plane) are deeper than those appeared along the out-of-plane direction (i.e., along the [001] direction) at 10 K, the situation is reversed as the temperature increases. This change of free energy density results in the temperature dependence of the magnetization directions in GaMnAs film with critical strain condition.