Spin supersolids and spin superfluids reveal complex canted spin structures with independent order of longitudinal and transverse spin components. This work addresses the question whether these exotic phases can exhibit spin-driven ferroelectricity. Here we report the results of dielectric and pyrocurrent measurements of MnCr2S4 as function of temperature and magnetic field up to 60 T. This sulfide chromium spinel exhibits a Yafet-Kittel type canted spin structure at low temperatures. As function of external magnetic field, the manganese spins undergo a sequence of ordering patterns of the transverse and longitudinal spin components, which can be mapped onto phases as predicted by lattice-gas models including solid, liquid, super-fluid, and supersolid phases. By detailed dielectric and pyrocurrent measurements, we document a zoo of multiferroic phases with sizable ferroelectric polarization strongly varying from phase to phase. Using lattice-gas terminology, the title compound reveals multiferroic spin-superfluid and spin-supersolid phases, while the antiferromagnetic solid is paraelectric.
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