Anisotropic Thermopower and Planar Nernst Effect in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ Ferromagnetic Semiconductors

We present the first experimental study of the thermopower in Mn-doped GaAs ferromagnetic semiconductors. Large magnetothermopower effects in both longitudinal and transverse directions have been observed below the ferromagnetic transition temperature. Unlike magnetoresistance, neither the transverse thermopower (planar Nernst effect) nor the longitudinal thermopower explicitly depend on the strength of the in-plane magnetic field, but rather are intimately related to each other through the magnetization. These newly discovered effects can be satisfactorily explained by an extension of anisotropic magnetotransport model and place important constraints on potential microscopic descriptions of the scattering mechanisms in these materials.

Figure 1

(a) Angular dependence of longitudinal magnetothermopower $S_{xx}$ at 6 K; the sample is ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ($x=0.039$) and heat flow is applied in the $[\overline{1}10]$ direction. Top inset shows the angular dependence of magnetoresistance of the sample, and the bottom inset is a sketch of the relative orientation of heat flow $-\nabla T$ and external field $\mathit{H}$. (b) $S_{xx}$ vs $H$ when the applied heat flow is in the $[110]$ and $[\overline{1}10]$ directions at 15 K.

Figure 2

(a) Planar Nernst effect (PNE) and planar Hall effect at 6 K ${\Phi }_H=-30°$ for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ($x=0.039$). (b) Sketch of the relative orientation of $-\nabla T$, $\mathit{M}$ and $\mathit{H}$. Four directions marked as I, II, III, and IV are easy directions of $\mathit{M}$. (c) Angular dependence of PNE. (d) Comparison of $S_{xy}/S_{xx}$ and $R_H/R$, and sample magnetization $M$ measured by SQUID.

Figure 3

(a) Field dependence of $S_{xx}$ and $S_{xy}$ measured at $T=12\mathrm{K}$, ${\Phi }_H=90°$ for sample ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ($x=0.049$). Heat flow is applied along the $[110]$ direction. (b) Field dependence of the magnetization angle $\Phi$—the angle between $\mathit{M}$ and the heat flow $-\nabla T$, ${\Phi }_x$, and ${\Phi }_y$ are calculated from $S_{xx}$ and $S_{xy}$ data as described in the text.

Figure 4

(a) Temperature dependence of $S_{xx}$ for sample ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ($x=0.049$) with the heat flow applied in the $[110]$ direction. (b) Temperature dependence of the ratio of uniaxial to cubic anisotropy constants.