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We study nonlinear magneto-optical responses of metals by a semiclassicalBoltzmann equation approach. We derive general formulas for linear and secondorder nonlinear optical effects in the presence of magnetic fields that includeboth Berry curvature and orbital magnetic moment. Applied to Weyl fermions, thesemiclassical approach (i) captures the directional anisotropy of linearconductivity under magnetic field as a consequence of an anisotropic $B^2$contribution, which may explain the low-field regime of recent experiments;(ii) predicts strong second harmonic generation proportional to $B$ that isenhanced as the Fermi energy approaches the Weyl point, leading to largenonlinear Kerr rotation. Moreover, we show that the semiclassical formula forthe circular photogalvanic effect arising from the Berry curvature dipole isreproduced by a full quantum calculation using a Floquet approach.

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals