  The Jahn-Teller effect refers to the symmetry-lowering geometrical distortion
in a crystal (or non-linear molecule) due to the presence of a degenerate
electronic state. Usually, the Jahn-Teller distortion is not polar. Recently,
GaV4S8 with the lacunar spinel structure was found to undergoes a Jahn-Teller
distortion from cubic to ferroelectric rhombohedral structure at TJT = 38K. In
this work, we carry out a general group theory analysis to show how and when
the Jahn-Teller effect gives rise to ferroelectricity. On the basis of this
theory, we find that the ferroelectric Jahn-Teller distort in GaV4S8 is due to
the non-centrosymmetric nature of the parent phase and strong electron-phonon
interaction related to two low-energy T2 phonon modes. Interestingly, GaV4S8 is
not only ferroelectric, but also ferromagnetic with the magnetic easy axis
along the ferroelectric direction. This suggests that GaV4S8 is a multiferroic
in which an external electric field may control its magnetization direction.
Our study not only explains the Jahn-Teller physics in GaV4S8, but also paves a
new way for searching and designing new ferroelectrics and multiferroics.
