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We propose a first-principles scheme for the description of themagneto-optical kerr effect within density functional theory (DFT). Though thecomputation of Kerr parameters is often done within DFT, starting from theconductivity or the dielectric tensor, there is no formal justification to thischoice.  As a first steps, using as reference materials iron, cobalt and nickel weshow that pseudo-potential based calculations give accurate predictions. Thenwe derive a formal expression for the full dielectric tensor in terms of thedensity-density correlation function. The derived equation is exact in systemswith an electronic gap, with the possible exception of Chern insulators, andwhenever the time reversal symmetry holds and can be used as a starting pointfor the inclusion of local fields and excitonic effects within time-dependentDFT for such systems.  In case of metals instead we show that, starting from the density-densitycorrelation function, the term which describes the anomalous Hall effect isneglected giving a wrong conductivity.

physical review. b, condensed matter and materials physics

Pseudo-potentials based first-principles approach to the magneto-optical  Kerr effect: from metals to the inclusion of local fields and excitonic  effects