Probing the antiferromagnetic structure of bilayer CrI3 by second harmonic generation: A first-principles study

Abstract

Two-dimensional antiferromagnetic materials with robust second harmonic generation (SHG) have been attracting significant research interest. In recent experiments, enhanced SHG from layered antiferromagnet (AFM) bilayer chromium trioxide $({\mathrm{CrI}}_{3})$ with $A$-type antiferromagnetic order has been observed. However, bilayer ${\mathrm{CrI}}_{3}$ with $A$-type, $C$-type, and $G$-type antiferromagnetic order may simultaneously occur in experimental synthesis, as the total free-energy difference between the three AFMs is small. Here, based on symmetry analysis and first-principles calculations, we study the three kinds of bilayer AFMs with and without the spin-orbit coupling (SOC) effect. We find that for all three types, the $i$-type SHG response vanishes due to the centrosymmetric lattice structure. However, significant $c$-type SHG response can arise in $A$-type and $C$-type AFMs but still vanishes for $G$-type AFM. Under normal incidence, both $A$-type and $C$-type AFMs exhibit three independent nonvanishing SHG components. Remarkably, the nonvanishing SHG components of $A$-type and $C$-type AFMs are mutually exclusive, namely, the SHG components that are finite for $A$-type vanish for $C$-type and vice versa. In particular, the SHG of both $A$-type and $C$-type AFMs is sensitive to the SOC effect and it becomes enhanced when the SOC effect is fully considered. Hence, the SHG response would be an efficient method for probing bilayer ${\mathrm{CrI}}_{3}$ with different antiferromagnetic orders.