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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:mfrac> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:msqrt> <mml:mo>×</mml:mo> <mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:msqrt> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> , 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.