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

The Strange World of Solids That Flow

Imagine a material that is both a rigid crystal and a frictionless fluid at the same time. This counterintuitive state, called a “supersolid,” has fascinated physicists for decades but has remained very hard to pin down in real materials. In this work, researchers show that a cobalt-based magnet, K2Co(SeO3)2, behaves in just this exotic way. By carefully mapping how its spins – tiny atomic magnets – arrange and fluctuate under extreme cold and strong magnetic fields, they reveal not one but two distinct supersolid phases, opening a new, experimentally accessible window into some of the strangest forms of quantum matter.

A Flat Magnetic Playground

The key to this discovery is geometry and frustration. In K2Co(SeO3)2, the magnetic cobalt ions sit on flat, triangular layers. On such a lattice, neighboring spins prefer to point in opposite directions, but three spins on a triangle cannot all satisfy that rule at once. This “frustration” leads to a huge number of nearly equivalent arrangements, like a jumbled deck of cards where many patterns cost almost the same energy. At zero magnetic field and low temperature, neutron scattering experiments show that the spins pick out a repeating pattern with a larger, three-site unit cell, breaking the regular spacing of the crystal. At the same time, the spins do not fully freeze: the size of the ordered moment is strongly reduced, indicating intense quantum motion that keeps the system hovering between order and disorder.

When Order and Flow Coexist

To uncover whether this restless state is a supersolid, the team looked at how the spins move, not just how they are arranged. Using very sensitive neutron spectroscopy, they found that the system supports broad bands of magnetic excitations rather than the sharp waves expected in a simple magnet. At a special wave vector set by the triangular pattern, they observed two key ingredients at once: a mode whose energy goes all the way to zero and another with a tiny but finite gap. In the language of symmetry, these features signal that the system both breaks a continuous spin-rotation symmetry (akin to a superfluid that can flow without resistance) and a discrete translation symmetry (akin to a crystal with a repeating density pattern). Together, these are the twin hallmarks of a supersolid in this magnetic setting.

A Quantum Phase Map in Magnetic Field

Applying a magnetic field along the easy axis of the spins allows the researchers to tune the balance between competing arrangements. Measurements of heat capacity and magnetization over a wide range of temperatures and fields reveal a detailed phase diagram. At moderate fields, the spins settle into an “up–up–down” pattern on each triangle, leading to a robust plateau where the magnetization locks to one-third of its maximum value. This phase transition behaves as predicted for a well-known two-dimensional Potts model, confirming that the underlying interactions are extremely close to an ideal theoretical case. At lower fields, the data show that the system crosses smoothly into the low-field supersolid regime, where long but not infinite correlation lengths effectively break the three-sublattice symmetry even in zero field.

A Second Supersolid Near Full Polarization

The surprises do not end at high fields. As the magnetization nears saturation, detailed magnetization and entropy measurements reveal an additional phase sandwiched between the one-third plateau and the fully aligned state. Theory for the same triangular-lattice model predicts that in this field window the system again hosts a supersolid: the spins are almost all aligned, but a small fraction can still move coherently, giving rise to a mixed state with both rigid pattern and quantum flow. The experiment matches these predictions, including the sharp, first-order-like jump expected when entering this high-field supersolid. By analyzing the spin-wave spectrum in the plateau phase, the team also pins down the interaction strengths and shows that only nearest neighbors matter significantly, making K2Co(SeO3)2 an unusually clean realization of the ideal model.

Why This Matters for Quantum Materials

For a non-specialist, the key message is that K2Co(SeO3)2 acts as a laboratory for matter that behaves in seemingly contradictory ways: solid and superfluid at once. In this magnet, the positions of spins form a repeating pattern like atoms in a crystal, while their quantum motion remains delocalized and coherent, as in a fluid. The combination produces supersolid phases that are not just theoretical curiosities but are now mapped out in detail and probed with powerful spectroscopic tools. Because the relevant energy scales are much higher than in earlier candidates, this material allows precise measurements and sharp tests of theory, making it a benchmark system for understanding how quantum fluctuations can sculpt entirely new states of matter.

Citation: Chen, T., Ghasemi, A., Zhang, J. et al. Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K₂Co(SeO₃)₂. Nat Commun 17, 2914 (2026). https://doi.org/10.1038/s41467-026-69661-0

Keywords: supersolid, frustrated magnetism, triangular lattice, quantum spin system, neutron scattering