Electrical Transport and Quantum Oscillations in the Metallic Spin Supersolid EuCo₂Al₉

The discovery of spin supersolid and its giant magnetocaloric effect has opened a new arena in frustrated quantum magnets and cutting-edge cryogenics. The intermetallic EuCo₂Al₉(ECA), for the first time, extends this intriguing phase from Mott insulators to a highly conductive metal. In this work, we systematically study the electrical transport properties of ECA, where itinerant electrons serve as a sensitive probe of the spin supersolid state. We observe anomalies both in the temperature-dependent resistivity and in the field-dependent magnetoresistance and Hall signals, which are attributed to the response of electrons to the Eu^2+ spins and their fluctuations. Moreover, Shubnikov-de Haas quantum oscillations at high magnetic fields reveal pronounced band splitting in the spin-polarized state. Our results reveal an intimate correspondence between electrical transport and magnetic transitions in ECA, deepening the understanding of this metallic spin supersolid.