Magnetic Field Induced Quantum Phase Transition in Multiferroic Vanadium Spinels

Vanadium spinels with the formula AV2O4 (A $=$ Cd, Mg, Zn, etc) show strong magnetic frustration due to a structure of corner-sharing tetrahedra. A tetragonal structural distortion and an ``up up down down'' magnetic ordering along diagonal chains result at low temperatures, which breaks spatial-inversion symmetry. CdV2O4 is insulating enough that this magnetic order produces ferroelectricity. Here we present data on CdV2O4 and MgV2O4, showing a field-induced quantum phase transition near 40 Tesla, which is a very small energy scale compared to the dominant magnetic exchange interactions. This transition suppresses ferroelectricity and produces a magnetization jump. We show that this transition can be explained by a model that includes spin-orbit coupling effects, and also a trigonal structural distortion at zero and applied magnetic fields.