Theory of the Hall coefficient of polycrystals: Application to a simple model for La/sub 2-//sub x/M/sub x/CuO4 (M = Sr, Ba)

We calculate the low-field Hall coefficient R/sub 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/sub H/ = (4/5R/sub H/0; where R/sub H/0 = 1/(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 m/sub h//sub x//m/sub hz/ and m/sub e//sub x//m/sub ez/, R/sub H/ = (4/51/n/sub h/ec[1-(n/sub e//n/sub h/) Q/sub x/2]/[1+(n/sub e//h/sub n/)Q/sub x/]2 (1+4m/sub hx//m/sub hz/[1 -(n/sub e//n/sub h/)Q/sub x/Q/sub z/] ]/[1-(n/sub e//n/sub h/)Q/sub x/2]), where n/sub h/ and n/sub e/ are the number densities of holes and electrons, m/sub h//sub x//m/sub hz/ the ratio of in-plane to out-of-plane hole masses, and Q/sub 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 La/sub 2-//sub x/Sr/sub x/CuO4 as a function of x at t = 50 K