Nature News · Feb 11, 2026 · Collected from RSS
Data availabilityThe datasets generated and analysed during the current study are available from the corresponding authors on reasonable request. Source data are provided with this paper.Code availabilityThe Monte Carlo simulations were conducted with the SpinToolkit (github.com/spintoolkit-dev/SpinToolkit_py) simulation package. Additional code that supports the findings of this study is available from the corresponding authors upon reasonable request.ReferencesXiang, J. et al. Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2. Nature 625, 270–275 (2024).Article ADS CAS PubMed Google Scholar Andreev, A. F. & Lifshitz, I. M. Quantum theory of defects in crystals. Sov. Phys. JETP 29, 1107–1113 (1969).ADS Google Scholar Leggett, A. J. Can a solid be “superfluid”? Phys. Rev. Lett. 25, 1543–1546 (1970).Article ADS CAS Google Scholar Chester, G. V. Speculations on Bose-Einstein condensation and quantum crystals. Phys. Rev. A 2, 256–258 (1970).Article ADS Google Scholar Penrose, O. & Onsager, L. Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576–584 (1956).Article ADS CAS Google Scholar Kim, E. & Chan, M. H. W. Probable observation of a supersolid helium phase. Nature 427, 225–227 (2004).Article ADS CAS PubMed Google Scholar Kim, D. Y. & Chan, M. H. W. Absence of supersolidity in solid helium in porous Vycor glass. Phys. Rev. Lett. 109, 155301 (2012).Article ADS PubMed Google Scholar Boninsegni, M. & Prokof’ev, N. Supersolid phase of hard-core bosons on a triangular lattice. Phys. Rev. Lett. 95, 237204 (2005).Article ADS PubMed Google Scholar Wessel, S. & Troyer, M. Supersolid hard-core bosons on the triangular lattice. Phys. Rev. Lett. 95, 127205 (2005).Article ADS PubMed Google Scholar Heidarian, D. & Damle, K. Persistent supersolid phase of hard-core bosons on the triangular lattice. Phys. Rev. Lett. 95, 127206 (2005).Article ADS PubMed Google Scholar Melko, R. G. et al. Supersolid order from disorder: hard-core bosons on the triangular lattice. Phys. Rev. Lett. 95, 127207 (2005).Article ADS CAS PubMed Google Scholar Li, J.-R. et al. A stripe phase with supersolid properties in spin-orbit-coupled Bose-Einstein condensates. Nature 543, 91–94 (2017).Article ADS CAS PubMed Google Scholar Léonard, J., Morales, A., Zupancic, P., Esslinger, T. & Donner, T. Supersolid formation in a quantum gas breaking a continuous translational symmetry. Nature 543, 87–90 (2017).Article ADS PubMed Google Scholar Tanzi, L. et al. Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Nature 574, 382–385 (2019).Article ADS CAS PubMed Google Scholar Norcia, M. A. et al. Two-dimensional supersolidity in a dipolar quantum gas. Nature 596, 357–361 (2021).Article ADS CAS PubMed Google Scholar Sengupta, P. & Batista, C. D. Field-induced supersolid phase in spin-one Heisenberg models. Phys. Rev. Lett. 98, 227201 (2007).Article ADS CAS PubMed Google Scholar Sengupta, P. & Batista, C. D. Spin supersolid in an anisotropic spin-one Heisenberg chain. Phys. Rev. Lett. 99, 217205 (2007).Article ADS CAS PubMed Google Scholar Gao, Y. et al. Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2. npj Quantum Mater. 7, 89 (2022).Article ADS Google Scholar Wang, J. et al. Plaquette singlet transition, magnetic barocaloric effect, and spin supersolidity in the Shastry-Sutherland model. Phys. Rev. Lett. 131, 116702 (2023).Article ADS CAS PubMed Google Scholar Chen, T. et al. Phase diagram and spectroscopic signatures of supersolids in quantum Ising magnet K2Co(SeO3)2. Preprint at arxiv.org/abs/2402.15869 (2024).Zhu, M. et al. Continuum excitations in a spin supersolid on a triangular lattice. Phys. Rev. Lett. 133, 186704 (2024).Article ADS CAS PubMed Google Scholar Gao, Y. et al. Double magnon-roton excitations in the triangular-lattice spin supersolid. Phys. Rev. B 110, 214408 (2024).Article ADS CAS Google Scholar Sheng, J. et al. Continuum of spin excitations in an ordered magnet. Innovation 6, 100769 (2025).CAS PubMed PubMed Central Google Scholar Popescu, T. I. et al. Zeeman split Kramers doublets in spin-supersolid candidate Na2BaCo(PO4)2. Phys. Rev. Lett. 134, 136703 (2025).Article ADS CAS PubMed Google Scholar Chi, R., Hu, J., Liao, H.-J. & Xiang, T. Dynamical spectra of spin supersolid states in triangular antiferromagnets. Phys. Rev. B 110, L180404 (2024).Article ADS CAS Google Scholar Gao, Y., Huang, Y., Maekawa, S. & Li, W. Spin Seebeck effect of triangular lattice spin supersolid. Phys. Rev. Lett. 135, 236504 (2025).Article ADS MathSciNet CAS PubMed Google Scholar Tokiwa, Y. et al. Frustrated magnet for adiabatic demagnetization cooling to milli-Kelvin temperatures. Commun. Mater. 2, 42 (2021).Article CAS Google Scholar Liu, X.-Y. et al. Quantum spin liquid candidate as superior refrigerant in cascade demagnetization cooling. Commun. Phys. 5, 233 (2022).Article CAS Google Scholar Wikus, P., Canavan, E., Heine, S. T., Matsumoto, K. & Numazawa, T. Magnetocaloric materials and the optimization of cooling power density. Cryogenics 62, 150–162 (2014).Article ADS CAS Google Scholar Shirron, P. J. Applications of the magnetocaloric effect in single-stage, multi-stage and continuous adiabatic demagnetization refrigerators. Cryogenics 62, 130–139 (2014).Article ADS CAS Google Scholar Wang, Z., Barros, K., Chern, G.-W., Maslov, D. L. & Batista, C. D. Resistivity minimum in highly frustrated itinerant magnets. Phys. Rev. Lett. 117, 206601 (2016).Article ADS PubMed Google Scholar Zhu, L., Garst, M., Rosch, A. & Si, Q. Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points. Phys. Rev. Lett. 91, 066404 (2003).Article ADS PubMed Google Scholar Garst, M. & Rosch, A. Sign change of the Grüneisen parameter and magnetocaloric effect near quantum critical points. Phys. Rev. B 72, 205129 (2005).Article ADS Google Scholar Van Sciver, S. W. in Helium Cryogenics 2nd edn, Ch. 2, 19–47 (Springer, 2012).Pobell, F. Matter and Methods at Low Temperatures 3rd edn (Springer, 2007).Li, N. et al. Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet Na2BaCo(PO4)2. Nat. Commun. 11, 4216 (2020).Article ADS CAS PubMed PubMed Central Google Scholar Tokiwa, Y. et al. Super-heavy electron material as metallic refrigerant for adiabatic demagnetization cooling. Sci. Adv. 2, e1600835 (2016).Article ADS PubMed PubMed Central Google Scholar Gruner, T. et al. Metallic local-moment magnetocalorics as a route to cryogenic refrigeration. Commun. Mater. 5, 63 (2024).Article CAS Google Scholar Jang, D. et al. Large magnetocaloric effect and adiabatic demagnetization refrigeration with YbPt2Sn. Nat. Commun. 6, 8680 (2015).Article ADS CAS PubMed PubMed Central Google Scholar Shimura, Y. et al. Magnetic refrigeration down to 0.2 K by heavy fermion metal YbCu4Ni. J. Appl. Phys. 131, 013903 (2022).Article ADS CAS Google Scholar Zhang, X. et al. YbNi4Mg: superheavy fermion with enhanced Wilson ratio and magnetocaloric effect. Phys. Rev. Mater. 9, 014402 (2025).Article CAS Google Scholar Zhang, X. et al. Sub-kelvin magnetocaloric effect in frustrated intermetallic NdNi4Mg. J. Appl. Phys. 138, 063903 (2025).Article ADS CAS Google Scholar Watanabe, K., Shimura, Y., Umeo, K., Onimaru, T. & Takabatake, T. Minimization of temperature reached by adiabatic demagnetization refrigeration in Ce-based intermetallic Ce2(Cu1−xNix)2In. Appl. Phys. Lett. 126, 092401 (2025).Article ADS CAS Google Scholar Wu, L. S. et al. Orbital-exchange and fractional quantum number excitations in an f-electron metal, Yb2Pt2Pb. Science 352, 1206–1210 (2016).Article ADS CAS PubMed Google Scholar Li, X. Y. et al. Frustrated spin-1/2 chains in a correlated metal. Nat. Mater. 24, 716–721 (2025).Article ADS CAS PubMed Google Scholar Lee, J., Rabus, A., Lee-Hone, N. R., Broun, D. M. & Mun, E. The two-dimensional metallic triangular lattice antiferromagnet CeCd3P3. Phys. Rev. B 99, 245159 (2019).Article ADS CAS Google Scholar Cho, A. Helium-3 shortage could put freeze on low-temperature research. Science 326, 778–779 (2009).Article ADS CAS PubMed Google Scholar Kramer, D. Helium users are at the mercy of suppliers. Phys. Today 72, 26–29 (2019).ADS Google Scholar Osato, K. et al. Quantum criticality in YbCu4Ni. Phys. Rev. B 109, 024435 (2024).Article ADS CAS Google Scholar Kaczorowski, D., Rogl, P. & Hiebl, K. Magnetic behavior in a series of cerium ternary intermetallics: Ce2T2In (T = Ni, Cu, Rh, Pd, Pt, and Au). Phys. Rev. B 54, 9891–9902 (1996).Article ADS CAS Google Scholar Turban, K. & Schäfer, H. Zur kenntnis des BaFe2Al9-strukturtyps: Ternäre aluminide at2Al9 MIT A = Ba, Sr und T = Fe, Co, Ni. J. Less Common Met. 40, 91–96 (1975).Article CAS Google Scholar Vajenine, G. V. & Hoffmann, R. Magic electron counts for networks of condensed clusters: vertex-sharing aluminum octahedra. J. Am. Chem. Soc. 120, 4200–4208 (1998).Article ADS CAS Google Scholar Thiede, V. M. T. & Jeitschko, W. Crystal structure of europium cobalt aluminide (1/2/9), EuCo2Al9. Z. Kristallogr. New Cryst. Struct. 214, 149–150 (1999).Article CAS Google Scholar Meier, W. R. et al. A catastrophic charge density wave in BaFe2Al9. Chem. Mater. 33, 2855–2863 (2021).Article CAS Google Scholar Xu, L., Shi, X., Jiao, Y., Yang, J. & Wang, Z. SpinToolkit v.1.4.2. GitHub https://github.com/spintoolkit-dev/SpinToolkit_py (2026).Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).Article CAS Google Scholar Pippard, A. B. Magnetoresistance in Metals (Cambridge Univ. Press, 1989).Wang, Z. & Batista, C. D. Resistivity minimum in diluted metallic magnets. Phys. Rev. B 101, 184432 (2020).Article ADS CAS Google Scholar Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4. Nat. Commun. 1