“…Lacunar spinel compounds GaM 4 X 8 (M = V, Nb, Mo, Ta, and X = S, Se) are Mott insulator systems that exhibit various electronic and magnetic properties, such as pressure-induced superconductivity, − negative colossal magnetoresistance, spin-singlet state, , spin–orbit entangled molecular J eff state, − and magnetic skyrmions. − Since the formal valence of M is 3.25+, the average number of d electrons are 7/4 and 11/4 for group V (M = V, Nb, Ta) and group VI (M = Mo) transition metals, respectively. Since only half of the tetrahedral sites are occupied by Ga atoms, the pyrochlore network of M atoms takes on a breathing-type structure, resulting in M 4 tetrahedral clusters.…”