Identifying and tracking magnetically induced polarization in Fe₂Mo₃O₈ by static and time-resolved second harmonic generation

Multiferroic materials offer a promising platform for ultrafast optical control of coupled magnetic and polar orders. However, a prerequisite for such control is to precisely identify how the magnetically induced polarization manifests itself on the ultrafast timescale, and then to probe its dynamics upon external perturbations. Here, we address this issue in the polar magnet Fe₂Mo₃O₈ by combining static and time-resolved second harmonic generation (SHG). Temperature-dependent static SHG reveals that, among the symmetry-allowed tensor elements, only χ_ccc⁽²⁾ exhibits a pronounced anomaly at the antiferromagnetic transition (T_N ≈ 60 K), identifying χ_ccc⁽²⁾ as the nonlinear susceptibility tensor element coupled to the magnetically induced polarization. Guided by this result, time-resolved SHG selectively tracks the dynamics of this tensor element following ultrafast photoexcitation. We observe a rapid enhancement of the χ_ccc⁽²⁾-related SHG signal, followed by biexponential recovery. The response is independent of the pump polarization and reaches saturation at a remarkably low fluence, indicating a highly efficient coupling between optical excitation and the magnetically induced polarization. These results establish SHG as tensor-selective probe of ultrafast magnetoelectric dynamics and demonstrate the high sensitivity of the magnetically induced polarization in Fe₂Mo₃O₈ to optical excitation.