Spin Reorientation Transition in Single-Domain $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$

We demonstrate that the interplay of in-plane biaxial and uniaxial anisotropy fields in $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ results in a spin reorientation transition and an anisotropic ac susceptibility which is fully consistent with a simple single-domain model. The uniaxial and biaxial anisotropy constants vary, respectively, as the square and fourth power of the spontaneous magnetization across the whole temperature range up to $T_{\mathrm{C}}$. The weakening of the anisotropy at the transition may be of technological importance for applications involving thermally assisted magnetization switching.

Figure 1

Remnant magnetization along $[1\overline{1}0]$, $[110]$, and $[100]$ axes vs increasing temperature; (line) remnant magnetization along $[100]$ extracted from the $[1\overline{1}0]$ and $[110]$ curves assuming single-domain behavior; (corresponding half-filled symbols) remnant magnetization calculated from Eq. (1) using the anisotropy constants obtained from the analysis of $M(H)$ loops measured at selected temperatures.

Figure 2

Symbols as in Fig. 1. $M(H)$ loops along the $[1\overline{1}0]$, $[110]$, and $[100]$ axes at 5 K, with the arrows indicating the intersection points which are used to obtain $K_{\mathrm{U}}$ and $K_{\mathrm{C}}$ at low temperature. (inset) $M(H)$ loops along the $[1\overline{1}0]$ and $[110]$ axes at 50 K, plus the fit (thick gray line) to the hard axis curve used to obtain $K_{\mathrm{U}}$ and $K_{\mathrm{C}}$. The arrow indicates the intersection point for uniaxial hard axis measurement.

Figure 3

$K_{\mathrm{U}}$ and $K_{\mathrm{C}}$, extracted from $M(H)$ loops, vs temperature; (inset) $K_{\mathrm{U}}$ and $K_{\mathrm{C}}$ vs saturation magnetization.

Figure 4

(a), (b) Real and imaginary parts of the linear ac susceptibility under a 5 Oe, 11 Hz driving field, for measurements along $[110]$, $[1\overline{1}0]$, and $[100]$ axes. (c), (d) Calculated linear ac susceptibility under 5 Oe, using Eq. (1) and the measured dependence of $K_{\mathrm{C}}$ and $K_{\mathrm{U}}$ on $M_{\mathrm{S}}$ (taken from inset to Fig. 3).