Optical, dielectric, and magnetoelectric properties of ferroelectric and antiferroelectric lacunar spinels

Lacunar spinels with a chemical formula of $AM_4X_8$ form a populous family of narrow-gap semiconductors, which offer a fertile ground to explore correlation and quantum phenomena, including transition between Mott and spin-orbit insulator states, ferro/antiferroelectricity driven by cluster Jahn-Teller effect, and magnetoelectric response of magnetic skyrmions with polar dressing. The electronic and magnetic properties of lacunar spinels are determined to a large extent by their molecular-crystal-like structure. The interplay of electronic correlations with spin-orbit and vibronic couplings leads to a complex electronic structure already on the single-cluster level, which -- together with weaker inter-cluster interactions -- gives rise to a plethora of unconventional correlated states. This review primarily focuses on recent progresses in the field of optical, dielectric, and magnetoelectric properties on lacunar spinels. After introducing the main structural aspects, lattice dynamics and electronic structure of these compounds are discussed on the basis of optical spectroscopy measurements. Dielectric and polarization studies reveal the main characteristics of their low-temperature ferro- or antiferroelectric phases as well as orbital fluctuations in their high-temperature cubic state. Strong couplings between spin, lattice, and orbital degrees of freedom are manifested in singlet formation upon magnetostructural transitions, the emergence of various multiferroic phases, and exotic domain-wall functionalities.