Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K₂Co(SeO₃)₂

Supersolid phases are quantum-entangled states of matter exhibiting the dual characteristics of superfluidity and solidity. Theory predicts that hard-core bosons on a triangular lattice can form such phases at half filling and near complete filling. Leveraging an exact mapping between bosons and spin-12 degrees of freedom, here we show that these phases are realized in the triangular-lattice antiferromagnet K₂Co(SeO₃)₂. At zero field, neutron diffraction reveals the development of quasi-two-dimensional 3×3 magnetic order with Z₃ translational symmetry breaking (solidity), though with reduced amplitude indicating strong quantum fluctuations. These fluctuations manifest as equidistant bands of continuum neutron scattering, where the lowest-energy mode is gapless at K (1313), consistent with broken U(1) spin rotational symmetry (superfluidity). For c-axis-oriented magnetic fields near saturation, we find a second phase consistent with a high-field supersolid. These two supersolids are separated by a pronounced 1/3 magnetization plateau phase that supports coherent spin waves, from which we determine the underlying spin Hamiltonian.