  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.
