Absence of high-field spin supersolid phase in Rb₂Co (SeO₃) ₂ with a triangular lattice

Magnetization, torque magnetometry, specific heat and nuclear magnetic resonance (NMR) are used to study the high field intermediate phase between the 1/3-magnetization plateau and polarized state in the quantum Ising antiferromagnet Rb₂Co (SeO₃) ₂ with a triangular lattice. The magnetic phase diagram with the magnetic field up to 30 T is mapped by the comprehensive experimental data. The "up-up-down" (UUD) spin configuration of the 1/3-magnetization plateau state is identified by NMR spectral analysis. At higher magnetic fields, this UUD structure persist to the intermediate phase, which is finally destroyed in the polarized state. This observation supplies unambiguous spectroscopic evidence for the absence of proposed high field spin supersolid phase. The high-field phase diagram of this quantum magnet proximate to the Ising-anisotropy limit contradicts with that proposed by theoretical studies.