Fig. 3: NLO spin current of MBT.

a Atomic structure of bilayer MnBi₂Te₄. The atomic structure has both inversion symmetry \({\mathcal{P}}\) and mirror symmetry \({{\mathcal{M}}}^{x}\). The inversion center is in between the two layers (black square). The magnetic momentum on Mn is indicated by the red arrows. Considering magnetism, both \({\mathcal{P}}\) and \({{\mathcal{M}}}^{x}\) break. b Band structure of MBT with (black) and without (red) SOC. c, d The NLO spin and charge photoconductivity of bilayer MnBi₂Te₄ with SOC. Both spin and charge currents have nonzero components and exhibit complementary behavior. e, f The NLO charge conductivity without SOC. The spin-up and spin-down states are treated separately. The photoconductivity from spin-up and spin-down states are exactly opposite to each other. Therefore, the total charge conductivity is zero. But the spin-\(z\) conductivity is nonzero.