Raman magnon spectroscopy of local interactions and ground state selection in $\mathrm{Sr_2IrO_4}$
Competing and coupled spin and charge interactions in quantum materials lead to a variety of ordered states where local configurations preferentially influence the long-range order. When these interactions are finely balanced in energy, disorder and fluctuations play an outsized role. Raman scattering is particularly well-suited to revealing the underlying physics in such situations because of its sensitivity to local environments and ability to reveal overall symmetries. We perform angle-resolved Raman polarization measurements on single crystals of the correlated, layered magnet, \ce{Sr2IrO4}, where the Mott insulating ground state arises from strong spin-orbit coupling. We characterize the symmetries of both the phonon and magnon modes through comprehensive measurements in both the $ab$-plane and out-of-plane geometries from 10 to 700 cm$^{-1}$, and trace the evolution of these modes in both configurations to 12 GPa in a diamond anvil cell with perforated diamonds. Pressure does not significantly alter the lattice as the phonon modes shift linearly under compression, but at the same time the magnon modes become position dependent and spread over a range of wavenumbers. We attribute this magnetic heterogeneity to pressure-enhanced variations in the weak interlayer interactions, which may locally favor competing magnetic stacking configurations, and compare our experimental results to the predictions of linear spin wave calculations. Our results demonstrate that Raman-active magnons amplify $\mu$eV-scale interactions responsible for ground-state selection into easily measurable spectral changes.