Infrared anomalous Hall effect in Ca_xSr_1-xRuO ₃ films

The midinfrared anomalous Hall effect (AHE) can provide critical new information for resolving the controversial origins of the dc AHE in Ca _xSr_1-xRuO₃. The complex Faraday and Kerr angles, as well as the complex Hall conductivity σ_xy, are measured in Ca_xSr_1-xRuO₃ films as a function of mid- and near-infrared energy E from 0.1 eV to 1.4 eV, magnetic field H, temperature T, and Ca concentration x. For the ferromagnetic state from x=0 to 0.4, the (d_xz,d_yz)-orbital tight-binding model is employed to investigate the quasiparticle role in the low energy response of the AHE σ_xy(E) since the Berry curvature term becomes weak at low energies. The infrared Hall sign reversals with T are observed only at x=0 and 0.13, which is narrower than the Ca concentration range in which the dc Hall sign reversal appears. The similarity of the infrared Hall angles between paramagnetic and ferromagnetic Ca_xSr_1-xRuO₃ compounds demonstrates the symmetric nature of the Hall response around the quantum phase transition at x=0.7.