  Skyrmions are whirl like topological spin objects with high potential for
future magnetic data storage. It is a fundamental question, relevant for both
basic research and application, if a ferroelectric (FE) polarization can be
associated with their magnetic texture and if these objects can be manipulated
by electric fields. Here, we study the interplay between magnetism and electric
polarization in the lacunar spinel GaV4S8, which undergoes a structural
transition associated with orbital ordering at 44 K and reveals a complex
magnetic phase diagram below 13 K, including a ferromagnetic (FM), cycloidal,
and N\'eel-type skyrmion lattice (SkL) phase. We found that the orbitally
ordered phase of GaV4S8 is FE with a sizable polarization of ~1 {\mu}C/cm2.
Moreover, we observed spin-driven excess polarizations in all magnetic phases
and, hence, GaV4S8 hosts three different multiferroic phases with coexisting
polar and magnetic order. These include the SkL phase where we predict a strong
spatial modulation of the FE polarization close to the skyrmion cores. By
taking into account the crystal symmetry and spin patterns of the magnetically
ordered phases, we identify the exchange striction as the main microscopic
mechanism behind the spin-driven FE polarization in each multiferroic phase.
Since GaV4S8 is unique among the known SkL host materials due to its polar
crystal structure and the observed strong magnetoelectric effect, this study is
an important step towards the non-dissipative electric-field control of
skyrmions.
