Analytical formula describing the non-saturating linear magnetoresistance in inhomogeneous conductors

The effective-medium theory (EMT) has proved successful in modeling the non-saturating linear magnetoresistance induced by inhomogeneity. However, calculating magnetoresistance using the EMT usually involves solving coupled integral equations which have no analytical solutions, and therefore, it is still difficult to directly compare the predictions of EMT with experimental data. Here we demonstrate that the linear magnetoresistance predicted by the EMT can be either exactly formulated or well approximated by a simple analytical equation $\Delta\rho/\rho_0=\sqrt{k^2B^2+a^2}-a$ in a number of known situations. The relations between the EMT parameters and the phenomenological parameters $k$ and $a$ are evaluated. Our results provide a convenient and effective method for extracting the EMT parameters from experimental data.