Temperature dependent magnetic anisotropy in (Ga,Mn)As layers

It is demonstrated by SQUID measurements that (Ga,Mn)As films can exhibit perpendicular easy axis at low temperatures, even under compressive strain, provided that the hole concentration is sufficiently low. In such films, the easy axis assumes a standard in-plane orientation when the temperature is raised towards the Curie temperature or the hole concentration is increased by low temperature annealing. These findings are shown to corroborate quantitatively the predictions of the mean-field Zener model for ferromagnetic semiconductors. The in-plane anisotropy is also examined, and possible mechanisms accounting for its character and magnitude are discussed.

Figure 1

Scheme of valence band splitting in tetrahedrally coordinated semiconductors for compressive strain and for two orientations of magnetization $M$ with respect to the sample plane.

Figure 2

Field dependence of magnetization normalized by its saturation value at $5\mathrm{K}$ for two orientations of the film in respect to the magnetic field at two temperatures (a),(b) for as grown ${\mathrm{Ga}}_{0.947}{\mathrm{Mn}}_{0.053}\mathrm{As}$. Full and empty dots denote the data taken for the magnetic field along the [100] and [001] crystal direction, respectively. Note the flip of the easy axis direction from the perpendicular to the in-plane orientation on increasing temperature.

Figure 3

Temperature dependence of the remanent magnetization as measured in perpendicular [001] (a) and in plane [100] (b) configuration for the ${\mathrm{Ga}}_{0.947}{\mathrm{Mn}}_{0.053}\mathrm{As}$ sample prior to annealing (circles) and after annealing (diamonds and squares). Two experimental methods are presented. Temperature dependent $M_{\mathrm{REM}}$ (circles), the sample is cooled down through $T_C$ in the field $H_{\mathrm{FC}}=1\mathrm{kOe}$, which is at least by a factor of 10 higher than the coercive field $H_C$. Then, the field is removed at $5\mathrm{K}$, and the measurement of the magnetization component $M_{\mathrm{REM}}$ along the direction of $H_{\mathrm{FC}}$ commences on increasing temperature in the residual field $H_r⩽100\mathrm{mOe}$. Alternatively, (isothermal $M_{\mathrm{REM}}$, stars) the same $M_S$ component at selected temperatures $T<T_C$ is obtained by field cooling from above $T_C\text{to}T$ and then removing the external magnetic field. Both methods are seen to give essentially the same results. Note that upon annealing the development of the in-plane component of $M_{\mathrm{REM}}$ is accompanied by an equivalent quench of the perpendicular one. Bulk arrows mark the reorientation temperature $T_R$ when the crossover to in-plane magnetic anisotropy takes place. The thick dashed grey lines mark the results of FC measurements at $1\mathrm{kOe}$ for the as grown layer, and thus mimic the temperature dependence of the saturation magnetization.

Figure 4

Experimental (full points, taken from Fig. 3 for $x=5.3\%$ sample) and computed values (thick lines) for the ratio of reorientation and Curie temperatures in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ for perpendicular to in-plane magnetic anisotropy transition. For $x=3\%$ sample (the open circle) this transition is not detected above $5\mathrm{K}$, in an agreement with the presented calculations. Dashed lines mark expected temperatures for the in-plane reorientation of the easy axis between ⟨100⟩ and ⟨110⟩ directions.

Figure 5

Experimental evidence for the uniaxial anisotropy along [110] direction in ${\mathrm{Ga}}_{0.97}{\mathrm{Mn}}_{0.03}\mathrm{As}$ film. The magnetic remanence is measured for four major in-plane directions and its magnitude is normalized by the data of the [110] case. Note, that the sudden drop of $M_{\mathrm{REM}}$ along $\left[\overline{1}10\right]$ at $T⪡T_C$ may wrongly indicate too low value of $T_C$, if only this orientation is probed.