Double Magnon-Roton Excitations in the Triangular-Lattice Spin Supersolid

Abstract

Supersolid is an exotic quantum state of matter that spontaneously hosts the features of both solid and superfluid, which breaks the translation and U(1) gauge symmetries. Here we study the spin dynamics in the triangular-lattice compound Na${}_2$BaCo(PO${}_4$)${}_2$, which is revealed in [Xiang et al., Nature 625, 270-275 (2024)] as a quantum magnetic analog of supersolid. We simulate the easy-axis Heisenberg model with tensor network approach and uncover unique dynamic traits. These features are manifested in two branches of excitations that can be associated with the spin solidity and superfluidity, respectively. One branch contains the U(1) Goldstone and roton modes, while the other comprises pseudo-Goldstone and roton modes. The gapless Goldstone modes of the in-plane superfluid order are confirmed by our inelastic neutron scattering measurements. Together with the evident out-of-plane solid order indicated by the magnetic Bragg peaks, our findings provide spectroscopic evidence for spin supersolidity in this easy-axis antiferromagnet. Akin to the role of phonon-roton modes -- Landau elementary excitations -- in shaping the helium superfluid thermodynamics, the intriguing double magnon-roton dispersion here determines the low-temperature thermodynamics of spin supersolid down to sub-Kelvin regime, explaining the recently observed giant magnetocaloric effect in Na${}_2$BaCo(PO${}_4$)${}_2$.

8+9 pages, 4+9 figures

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Cited by in corpus (18)

• Phase Diagram of the Easy-Axis Triangular-Lattice $J_1-J_2$ Model
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Wannier states and spin supersolid physics in the triangular antiferromagnet K${}_2$Co(SeO${}_3$)${}_2$
• Zeeman split Kramers doublets in spin-supersolid candidate Na${}_2$BaCo(PO${}_4$)${}_2$
• Easy-axis Heisenberg model on the triangular lattice: from supersolid to gapped solid
• From continuum excitations to sharp magnons via transverse magnetic field in the spin-1/2 Ising-like triangular lattice antiferromagnet Na2BaCo(PO4)2
• Possible Observation of Quadrupole Waves in Spin Nematics
• Spin Seebeck Effect of Triangular-lattice Spin Supersolid
• Pseudo-Majorana functional renormalization for frustrated XXZ spin-1/2 models with field or magnetization along the spin-Z direction at finite temperature
• Field tunable BKT and quantum phase transitions in spin-1/2 triangular lattice antiferromagnet
• Emergent Spin Supersolids in Frustrated Quantum Materials
• Interplay of short-range bond order and A-type antiferromagnetic order in metallic triangular lattice GdZn${}_3$P${}_3$
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model
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