Thermodynamic and thermoelectric properties of (Ga,Mn)As and related compounds

Various experimental results providing information on thermodynamic density of states in (Ga,Mn)As are analyzed theoretically assuming that holes occupy GaAs-like valence bands. Allowing for Gaussian fluctuations of magnetization, the employed model correctly describes a critical behavior of magnetic specific heat found experimentally in (Ga,Mn)As near the Curie temperature $T_{\text{C}}$ [S. Yuldashev et al., Appl. Phys. Express 3, 073005 (2010)]. The magnitudes of room-temperature thermoelectric power, as measured for GaAs:Be and (Ga,Mn)As [M. A. Mayer et al., Phys. Rev. B 81, 045205 (2010)], are consistent with the model for the expected energy dependencies of the hole mobility. The same approach also describes temperature variations of conductance specific to the Anderson-Mott localization, found for various dimensionality (Ga,Mn)As nanostructures at subkelvin temperatures [D. Neumaier et al., Phys. Rev. Lett. 103, 087203 (2009)]. We conclude that the examined phenomena do not provide evidence for an enhancement of density of states by the presence of an impurity band at the Fermi energy in ferromagnetic (Ga,Mn)As. Furthermore, for (Ga,Mn)As we provide expected values of both electronic specific heat at low temperatures $T\ll T_{\text{C}}$ and magnetization as a function of the magnetic field at $T_{\text{C}}$.

Figure 1

Theoretical temperature dependence of the magnetic specific heat calculated with no adjustable parameters for sample A (upper panel) and sample B (lower panel). The solid and dashed lines correspond to the Heisenberg ($n=3$) and Ising ($n=1$) models, respectively. Dots represent experimental data [after Yuldashev et al. (Ref. 17)].

Figure 2

Computed values of the proportionality coefficient between $M(H){}^3$ and $H$ for Mn magnetization $M$ in the magnetic field $H$ at $T_{\text{C}}$. The calculation has been performed within the $p$-$d$ Zener model for various effective Mn contents $x$ in (Ga,Mn)As.

Figure 3

Comparison of theoretical (solid line) and experimental (symbols) field dependence of magnetization at $T_{\text{C}}$ for sample A of Yuldashev et al.[17] The dashed line shows theoretical values reduced by a factor of 2.45 to match experimental data.

Figure 4

Room-temperature thermoelectric power in (Ga,Mn)As and GaAs:Be as a function of hole density changed by irradiation with high-energy Ne${}^{+}$ ions [after Mayer et al. (Ref. 18)]. Lines are calculated using the standard six-band model and GaAs parameters (Ref. 16) assuming that either ionized impurity or acoustic phonon scattering dominates. The actual value of thermopower $S$ should lie between lines obtained for heavy and light hole bands in each case.

Figure 5

Thermodynamic density of states as a function of the hole concentration in (Ga,Mn)As for various values of the parameter $B_{\text{G}}$ characterizing spin splitting of the hole subbands. The corresponding values of the Sommerfeld electronic specific-heat coefficient $\gamma$ are shown on the right axis.