Phase Diagram and Spectroscopic Signatures of Supersolids in Quantum Ising Magnet K$_2$Co(SeO$_3$)$_2$ (2402.15869v2)

Abstract: A supersolid is a quantum-entangled state of matter that exhibits the dual characteristics of superfluidity and solidity. \red{While theoretical studies have predicted that hard-core bosons with repulsive interactions on a triangular lattice can host a supersolid phase, experimental validation has remained elusive. Leveraging an exact mapping between bosons and spins, we investigate the supersolid phase in a spin-$\frac{1}{2}$ triangular-lattice antiferromagnet K$2$Co(SeO$_3$)$_2$.} Here, we present the magnetic phase diagram and neutron scattering results for K$_2$Co(SeO$_3$)$_2$, which features nearest-neighbor Ising-like interactions with $J_z = 2.96(2)$ meV and $J{\perp} = 0.21(3)$ meV. In zero field, neutron spectroscopy reveals the gradual development of a quasi-two-dimensional $\sqrt{3}\times\sqrt{3}$ magnetic order with Z$_3$ translational symmetry breaking (solidity) below 15 K. \red{At temperatures below 0.3 K, the fully developed supersolid phase is evidenced by the coexistence of a gapless Goldstone mode arising from broken U$(1)$ spin rotational symmetry (superfluidity), and a gapped pseudo-Goldstone mode associated with lifted accidental XY degeneracy (solidity).} In $\bf c$-axis-oriented magnetic fields 1.1 T $<$ $B$ $<$ 21 T, a prominent 1/3 magnetization plateau phase emerges, accompanied by a \red{plausible} high-field supersolid phase (17 T $<$ $B$ $<$ 21 T). Our results establish K$_2$Co(SeO$_3$)$_2$as an exceptional realization of a spin-$\frac{1}{2}$ triangular-lattice quantum Ising magnet, document its magnetic phase diagram featuring two supersolid phases, and uncover spectroscopic \red{signatures} of zero-field supersolidity in a triangular lattice antiferromagnet.