Unusual ferroelectricity induced by the Jahn-Teller effect: A case study on lacunar spinel compounds

The Jahn-Teller effect refers to the symmetry-lowering geometrical distortion in a crystal (or nonlinear molecule) due to the presence of a degenerate electronic state. Usually, the Jahn-Teller distortion is not polar. Recently, GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ with a lacunar spinel structure was found to undergo a Jahn-Teller distortion from a cubic to ferroelectric rhombohedral structure at T$_{\mathrm{JT}} \quad =$ 38 K. Here, 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 ?nd that the ferroelectric Jahn-Teller distortion in GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ is due to the noncentrosymmetric nature of the parent phase and a strong electron-phonon interaction related to two low-energy T$_{\mathrm{2}}$ phonon modes. Interestingly, GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ is not only ferroelectric, but also ferromagnetic with a magnetic easy axis along the ferroelectric direction. This suggests that GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ is a multiferroic material in which an external electric ?eld may control its magnetization direction. Our study not only explains the Jahn-Teller physics in GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$, but also paves a way for searching and designing different ferroelectrics and multiferroics.