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Spin supersolids and spin superfluids reveal complex canted spin structureswith independent order of longitudinal and transverse spin components. Thiswork addresses the question whether these exotic phases can exhibit spin-drivenferroelectricity. Here we report the results of dielectric and pyrocurrentmeasurements of MnCr2S4 as function of temperature and magnetic field up to 60T. This sulfide chromium spinel exhibits a Yafet-Kittel type canted spinstructure at low temperatures. As function of external magnetic field, themanganese spins undergo a sequence of ordering patterns of the transverse andlongitudinal spin components, which can be mapped onto phases as predicted bylattice-gas models including solid, liquid, super-fluid, and supersolid phases.By detailed dielectric and pyrocurrent measurements, we document a zoo ofmultiferroic phases with sizable ferroelectric polarization strongly varyingfrom phase to phase. Using lattice-gas terminology, the title compound revealsmultiferroic spin-superfluid and spin-supersolid phases, while theantiferromagnetic solid is paraelectric.

Multiferroic spin-superfluid and spin-supersolid phases in MnCr2S4