Magnetism-induced second-order nonlinear optical responses in multiferroic BiFeO3

Nonlinear optical (NLO) responses of noncentrosymmetric nonmagnets have drawn a lot of attention in the past decades because of their significance in materials characterization, green energy, and device applications. On the other hand, magnetism not only can break the inversion symmetry in centrosymmetric crystals but also introduce additional NLO phenomena in noncentrosymmetric materials, thus enabling the magnetic field control of light-matter interactions. However, the magnetism-induced NLO responses have rarely been studied so far. In this paper, we study the magnetism-induced NLO responses of multiferroic bismuth ferrite (${\mathrm{BiFeO}}_{3}$) based on density-functional-theory calculations. First, we find that the calculated magnetism-induced second-harmonic generation (SHG) susceptibilities are large and the SHG intensity is tunable with the reversal of magnetization. In particular, the interference between crystallographic SHG and magnetically induced SHG components results in a strong magnetic contrast of the SHG signal of $\ensuremath{\sim}440$% at SHG photon energy of 4.82 eV, thus enabling a magnetic control of the SHG in multiferroic ${\mathrm{BiFeO}}_{3}$. Also, because of the sensitivity of the SHG signal to the direction of the N\'eel vector, the SHG can be utilized to detect the reversal of the N\'eel vector in the AFM materials, which is an important issue for AFM spintronics. Second, the calculated bulk photovoltaic effects (BPVE) in ${\mathrm{BiFeO}}_{3}$ are also strong, being larger than some well-known NLO compounds such as ${\mathrm{BaTiO}}_{3}$, GaAs, CdS, and CdSe. Finally, we analyze the origins of the prominent features in the NLO response spectra in terms of the calculated quantum geometric quantities. Our interesting findings suggest that the magnetism-driven NLO responses in ${\mathrm{BiFeO}}_{3}$ are significant, anisotropic, and tunable and that understanding the magnetism-driven components of both SHG and BPVE is essential for their applications in, e.g., multiferroic-based photovoltaic devices and second-harmonic generation.