Curie Point Singularity in the Temperature Derivative of Resistivity in (Ga,Mn)As

We observe a singularity in the temperature derivative $d\rho /dT$ of resistivity at the Curie point of high-quality (Ga,Mn)As ferromagnetic semiconductors with $T_c$’s ranging from approximately 80 to 185 K. The character of the anomaly is sharply distinct from the critical contribution to transport in conventional dense-moment magnetic semiconductors and is reminiscent of the $d\rho /dT$ singularity in transition metal ferromagnets. Within the critical region accessible in our experiments, the temperature dependence on the ferromagnetic side can be explained by dominant scattering from uncorrelated spin fluctuations. The singular behavior of $d\rho /dT$ on the paramagnetic side points to the important role of short-range correlated spin fluctuations.

Figure 1

(a) Temperature-dependent SQUID magnetization of an optimized 12.5% Mn-doped (Ga,Mn)As measured at 5 and 1000 Oe. (b) Measured resistivity $\rho (T)$ at zero field (1), the fit of $\rho (T)$ by ${\rho }_{\mathrm{fit}}(T)=c_0+c_{nm}T+c_{m2}{M}^2(T)+c_{m4}{M}^4(T)$ (2), and the difference $\rho (T)-{\rho }_{\mathrm{fit}}(T)$ for the 0 and 1000 Oe-field measurements (right-hand scale). For details on the fitting, see the main text. (c) Temperature derivative of the measured resistivity at 0 and 1000 Oe. The peak in zero-field $d\rho /dt$ coincides, within the experimental error, with the SQUID $T_c=185\mathrm{K}$.

Figure 2

(a) Resistivities $\rho (T)$ and (b) temperature derivatives $d\rho /dT$ for optimized (Ga,Mn)As films (of thicknesses between 13 and 33 nm) prepared in Prague and Nottingham MBE systems. Data normalized to maximum $\rho (T)$ and $d\rho /dT$ are plotted in (c) and (d), respectively. Curves in (a), (c), and (d) are ordered from top to bottom according to increasing Mn doping and $T_c$: 4.5% Mn-doped sample with $T_c=81$ K, 6% with 124 K, 10% with 161 K, 12% with 179 K (Prague and Nottingham samples), and 12.5% doped sample with 185 K Curie temperature. In (c) and (d), curves are offset for clarity.

Figure 3

Upper panel: Magnetization curves of one 12.5% Mn-doped (Ga,Mn)As specimen annealed in several successive steps. From left to right: as grown, 10, 40, and 120 minutes, and 14 hours annealed at $160°\mathrm{C}$ in air. Bottom panel: Normalized $d\rho /dT$ curves measured in the same annealing steps. Resistivity curves are shown in the inset with the highest $\rho (T)$ corresponding to the as-grown state of the sample.

Figure 4

Left panel: $\log (M)-\log (t)$ plot of a $T_c=185\mathrm{K}$ sample measured at zero magnetic field. The fitted straight line shows a power law with an exponent 0.36. The top inset shows the linear $M(T)$ plot. Right panel: $\log (d\rho /dT)-\log (t)$ plots for the 6%–12.5% doped samples of Fig. 2 (horizontally shifted to overlap). A straight line corresponding to exponent $-0.12$ ($c_v$ in Fe) is included for comparison. Lower inset: Schematics of the uncorrelated part and Fourier components of the spin-spin correlation function for different ratios between the wave vector and inverse of the spin separation.