Spin and orbital Hall currents detected via current induced magneto-optical Kerr effect in V and Pt

We have studied the film thickness dependence of the current-induced magneto-optical Kerr effect in Pt and V thin films. The Kerr signal for Pt shows little dependence on the thickness in the range studied (20-80 nm). In contrast, the signal for V increases with increasing thickness and saturates at a thickness near 100 nm to a value significantly larger than that of Pt. These experimental results are accounted for assuming that spin and orbital Hall effects are responsible for the Kerr signal. We show that the Kerr signal is proportional to the product of the dc spin (orbital) Hall conductivity and the energy derivative of the ac spin (orbital) Hall conductivity. Contributions from the spin and orbital Hall effects mostly add up for V whereas they cancel out for Pt. Assuming that the orbital Hall conductivity matches that predicted from first-principles calculations, the thickness dependence of the Kerr signal suggests that the orbital diffusion length of V is considerably smaller compared to its spin diffusion length.