Theory of the Hall coefficient of polycrystals: Application to a simple model for La2-xMxCuO4 (M=Sr, Ba).

Abstract

We calculate the low-field Hall coefficient ${R}_{H}$ of a polycrystalline sample of an anisotropic metal, using the effective-medium approximation. For a quasiplanar metal, with a single band of carriers, we find ${R}_{H}=\frac{4}{5}{R}_{H}^{0}$, where ${R}_{H}^{0}=\frac{1}{(\mathrm{nqc})}$ is the free-electron Hall coefficient for a density of $n$ carriers of charge $q$. With both electron and hole carriers, we obtain to first order in the ratios $\frac{{m}_{\mathrm{hx}}}{{m}_{\mathrm{hz}}}$ and $\frac{{m}_{\mathrm{ex}}}{{m}_{\mathrm{ez}}}$, ${R}_{H}=\frac{4}{5}\frac{1}{{n}_{h}\mathrm{ec}}\frac{[1\ensuremath{-}(\frac{{n}_{e}}{{n}_{h}}){Q}_{x}^{2}]}{{[1+(\frac{{n}_{e}}{{h}_{n}}){Q}_{x}]}^{2}} \left[1+4\frac{{m}_{\mathrm{hx}}}{{m}_{\mathrm{hz}}}\frac{[1\ensuremath{-}(\frac{{n}_{e}}{{n}_{h}}){Q}_{x}{Q}_{z}]}{[1\ensuremath{-}(\frac{{n}_{e}}{{n}_{h}}){Q}_{x}^{2}]}\right],$ where ${n}_{h}$ and ${n}_{e}$ are the number densities of holes and electrons, $\frac{{m}_{\mathrm{hx}}}{{m}_{\mathrm{hz}}}$ the ratio of in-plane to out-of-plane hole masses, and ${Q}_{i}$ is the ratio of electron-to-hole mobilities in the ith direction. The model agrees well with experimental results of Penney, Shafer, Olson, and Plaskett for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ as a function of $x$ at $T=50$ K.