AbstractThe spin-polarized second harmonic generation (SHG) of the recently synthesized CaCoSO single crystal is performed based on the calculated electronic band structure. The calculation reveals that the spin-up (↑) channel of CaCoSO possesses a direct energy gap (Γ^v-Γ^c) of about 2.187 eV, 1.187 eV (K^v-K^c) for the spin-down (↓) channel and an indirect gap (Γ^v-K^c) of about 0.4 eV for the spin-polarized CaCoSO single crystal. The linear optical properties obtained reveal that the recently synthesized crystal exhibits considerable anisotropy with negative uniaxial anisotropy and birefringence favor to enhance the SHG. We have calculated the three non-zero tensor components of the SHG and found the "Equation missing" is the dominat component, one with a large SHG of about (d₃₃ = 6.936 pm/V at λ = 1064 nm), the half value of KTiOPO₄ (KTP). As the values of (↑)"Equation missing" < (↓)"Equation missing" < spin-polarized "Equation missing" are related to the values of the energy gap of (↑) 2.187 eV> (↓) 1.187 eV> spin-polarized gap 0.4 eV; therefore, a smaller energy gap gives better SHG performance. Furthermore, the microscopic first hyperpolarizability, β_ijk, is calculated.