Kohler's rule

If one temperature-dependent relaxation scale controls a fixed carrier population and fixed orbital geometry, the magnetoresistance ratio can collapse onto a function of $B/\rho (0,T)$. This is Kohler's rule. For the equal-mobility compensated two-carrier magnetoresistance model, $[\rho (B)-\rho (0)]/\rho (0)=(\mu B{)}^2$ and $\mu =[2ne\rho (0){]}^{-1}$. Therefore plotting against $[B/\rho (0){]}^2$ gives a common straight line of slope $1/(4n^2{e}^2)$. A collapse tests the scaling relation; it does not by itself prove this particular microscopic carrier model. Multiple independently varying scattering times or carrier populations can spoil it.