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 〉 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.