Second harmonic generation ellipticity to probe critical fluctuations

Second harmonic generation (SHG) has been explored extensively in revealing broken point symmetries and has been applied in a broad class of materials including magnets. With the focus on point symmetries, most existing SHG experiment focuses on the tensor form of SHG susceptibility tensors and often overlooks the phase information of their tensor elements. Yet, critical fluctuations and their induced-damping effects are encoded in the imaginary part of these elements. Here, we develop a full ellipticity rotational-anisotropy second-harmonic generation technique to access the phases of the complex tensor elements and therefore use it to explore the critical fluctuations in condensed matter system. We will test this idea in a model van der Waal magnet CrSBr where strong spin fluctuations exist.