Simple mechanism that breaks the Hall-effect linearity at low temperatures

Hall resistance ${R}_xy$ is commonly suggested to be linear-in-magnetic-field $B$, provided the field is small. We argue here that at low temperatures this linearity is broken due to weak localization/antilocalization phenomena in inhomogeneous systems, while in a uniform medium the linear-in-field dependence of ${R}_xy(B)$ is preserved. We calculate the Hall resistance for different two-component media using a mean-field approach and show that this nonlinearity is experimentally observable.