Two-dimensional nonlinear spectroscopy as a probe for frustrated magnets with strong spin-orbit coupling*

Two-dimensional (2D) terahertz spectroscopy has emerged as a powerful technique for probing the nonlinear interactions present in condensed matter systems. Unlike neutron scattering methods, which often require large sample sizes for sufficient momentum space resolution, optical spectroscopy offers a distinct advantage by enabling investigations on smaller samples, especially when large single crystals are unavailable. Moreover, 2D spectroscopy can delineate between the nonlinear interactions that remain concealed within linear response techniques, allowing us to distinguish between nonlinear effects and fractionalization-induced phenomena. Here, we calculate the nonlinear responses of various frustrated magnets with strong spin orbit coupling, including the generalized Kitaev model. We present the unique signatures exhibited by these systems, shedding light on their responses in both magnetically ordered states, as well as classical and quantum spin liquid states.