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 ¹. In this work, we systematically study the electrical transport properties of ECA, where itinerant electrons serve as a sensitive probe for the spin supersolid states. We observe anomalies both in the temperature-dependent resistivity and field-dependent magnetoresistance and Hall signals, which are attributed to response of electrons to the Eu²⁺ spins and their fluctuations. Moreover, Shubnikov-de Haas quantum oscillations at high magnetic field 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.