Field-induced magnetic quantum phase transitions in a bilayer triangular lattice antiferromagnet K$_2$Co$_2$(HPO$_3$)$_2$(C$_2$O$_4$)(H$_2$O)$_2$

Abstract We present a $^{31}$P nuclear magnetic resonance (NMR) study on the spin-$1/2$ bilayer triangular-lattice antiferromagnet K$_2$Co$_2$(HPO$_3$)$_2$(C$_2$O$_4$)(H$_2$O)$_2$. Measurements were performed at temperatures down to 0.06 K and magnetic fields up to 26 T. In the field range of 0.5 T to 4 T, the low-temperature spin-lattice relaxation rate $1/T_1$ exhibits a peak, signaling the onset of a magnetically ordered state. Within this ordered phase, $1/T_1$ shows gapless behavior, suggesting a spin supersolid phase. This ordering is suppressed around 4 T. Between 6 T and 18 T, clear splittings of the NMR spectra are observed, indicating the emergence of a second ordered magnetic phase. The field derivative of the low-temperature Knight shift $K_{\rm n}$ reveals changes in slope at approximately 10 T, 15.5 T, and 18 T. The first two features correspond to bulk magnetizations of $1/3$ and $2/3$ of the fully saturated moment, respectively, while the last one marks a quantum phase transition from the second ordered phase to the fully polarized state. These results establish the studied compound as a platform for investigating field-induced quantum phase transitions and emergent phases in frustrated bilayer triangular-lattice antiferromagnets.