Effect of spin group on the high harmonic generation of a two-dimensional hexagonal altermagnet

Motivated by extensive research works of altermagnets and a few recent theoretical studies of high harmonic generation (HHG) in square and metallic altermagnets, we performed theoretical and numerical studies of HHG of a two-dimensional hexagonal and insulating altermagnet. By carefully examining the symmetry, we found that the spin group of a hexagonal altermagnet gives rise to distinct selection rules compared to a hexagonal antiferromagnet. As the angle θ between the polarization direction of incident light and a fixed axis is zero, the parallel components of emitted harmonics for both antiferromagnets and altermagnets display only odd order harmonics, but the perpendicular components exhibit only even order harmonics for altermagnets and no harmonics for antiferromagnets. As θ = 90°, for the altermagnets, odd and even order harmonics of parallel components coexist while those of perpendicular components vanish together. These phenomena reflect the interference between spin-up and spin-down currents induced by the peculiar spin group symmetry of the altermagnet. Our theoretical methods and results may be useful for future theoretical calculations of HHG spectra and experimental explorations of spin group symmetry by ultra-strong and ultra-fast laser technologies.