Experimental evidence of crystal-field, Zeeman-splitting, and spin-phonon excitations in the quantum supersolid Na2BaCo(PO4)2

Abstract

Drawing inspiration from the recent breakthroughs in the Na2BaCo(PO4)2 quantum magnet, renowned for its spin supersolidity phase and its potential for solid-state cooling applications, our study delves into the interplay among lattice, spin, and orbital degrees of freedom within this compound. Using temperature-, field-, and pressure-dependent Raman scattering techniques, we present experimental evidence revealing crystal-electric-field (CEF) excitations, alongside the interplay of CEF-phonon interactions. We performed density functional theory calculations for the phonon frequencies and compared them with the experimentally observed modes. In addition, our experiments elucidated electronic transitions from j1/2 to j3/2 and from j1/2 to j5/2, with energy levels closely aligned with theoretical predictions based on point-charge models. Moreover, the application of a magnetic field and pressure revealed Zeeman splittings characterized by Landé-g factors as well as the CEF-phonon resonances. The anomalous shift in the coupled peak at low temperatures originated from the hybridization of CEF and phonon excitations due to their close energy proximity and shared symmetry. These findings constitute a significant step towards unraveling the fundamental properties of this exotic quantum material for future research in fundamental physics or engineering application.