Supersolids and Anomalous Hysteresis in Frustrated Spin-Dimer Systems

We study the ground-state properties of weakly coupled spin dimers on a triangular lattice. The competition of the two (direct and crossed) interdimer interactions and the geometry of the triangular lattice lead to a strong frustration. By using a large-size cluster mean-field method and the cluster-size scaling, we determine the quantitative magnetic phase diagram of the system under the presence of a magnetic field. The strong intradimer interaction provides a gapped spin-singlet ground state. If the magnetic field exceeds a certain critical value, the system undergoes a phase transition to a magnetically ordered state, which is known as a Bose-Einstein condensation (BEC) of spin-triplet excitations called ``triplons.'' We find that for strong magnetic fields, the magnetization curve shows plateaus at 1/3 and 2/3 of the total magnetization, in which the local singlet and triplet states form a superlattice pattern. This state can be regarded as a solid of triplons. We also find that if increasing (decreasing) the magnetic field from the 1/3 (2/3) plateau, the BEC of triplons occurs on the superlattice background, leading to the transition into ``magnon supersolid'' phase. The region of supersolid phase in the phase diagram is reasonably large compared to the square-lattice case.