Strong and nearly 100$\%$ spin-polarized second-harmonic generation from ferrimagnet Mn$_{2}$RuGa

Second-harmonic generation (SHG) has emerged as a promising tool for detecting electronic and magnetic structures in noncentrosymmetric materials, but 100$\%$ spin-polarized SHG has not been reported. In this work, we demonstrate nearly 100$\%$ spin-polarized SHG from half-metallic ferrimagnet Mn$_{2}$RuGa. A band gap in the spin-down channel suppresses SHG, so the spin-up channel contributes nearly all the signal, as large as 3614 pm/V about 10 times larger than that of GaAs. In the spin-up channel, $\chi_{xyz}^{(2)}$ is dominated by the large intraband current in three highly dispersed bands near the Fermi level. With the spin-orbit coupling (SOC), the reduced magnetic point group allows additional SHG components, where the interband contribution is enhanced. Our finding is important as it predicts a large and complete spin-polarized SHG in a all-optical spin switching ferrimagnet. This opens the door for future applications.