Four-Wave Mixing at peV Energy Scales

Abstract

We measure the non-linear magnetic susceptibility $\ddot{I}{‡}^{(3)}$ of the disordered quantum Ising magnet, \lihofour, and demonstrate four-wave mixing due to coherent (anti-)Stokes Raman scattering at $\sim$ 100 Hz (p$e$V) energy scales. The temperature dependence of $\ddot{I}{‡}^{(3)}$ approximately follows a $\frac{1}{T}$ form, with a high-$T$ cutoff that can be linked to dissipation in the coherent spin clusters. $\ddot{I}{‡}^{(3)}$ also decreases monotonically with a transverse field, approaching a constant offset above a few kOe, suggesting the presence of both coherent, and spontaneous Raman scattering.