Phase Diagram and Spectroscopic Evidence of Supersolids in Quantum Ising Magnet K₂Co (SeO₃) ₂

A supersolid is a quantum entangled state of matter that combines features of both superfluids and solids. Despite predictions of its analog in quantum magnets, the experimental realization was lacking until recent claims in triangular-lattice compounds. Here, we report the magnetic phase diagram and neutron scattering for a spin-1/2 triangular-lattice antiferromagnet, K₂Co (SeO₃) ₂. In zero field, neutron spectroscopy reveals the gradual development of a 3 sqrt3 magnetic order associated with Z₃ symmetry breaking for temperatures 5 K < T < 15 K. Below 5 K, the emergence of a Goldstone mode from low-energy continuum scattering suggests that the system enters a supersolid phase characterized by the breaking of both Z₃ and spin rotational U (1) symmetry. In c-axis-oriented magnetic fields 1. 1 T < B < 21 T, a prominent 1/3 magnetization plateau phase emerges, accompanied by a distinct high-field supersolid phase (18 T < B < 21 T). From the coherent spin wave excitations in the 1/3 magnetized plateau phase, we infer the spin Hamiltonian, which features nearest neighbor interactions with Jᵦ = 2. 98 (2) meV and J ₏₄ₑ₏ = 0. 21 (3) meV. Our work demonstrates that K₂Co (SeO₃) ₂ is a spectacular example of a spin-1/2 triangular-lattice quantum Ising antiferromagnet, documents its magnetic phase diagram highlighting two supersolid phases, and provides spectroscopic evidence of zero-field supersolidity.