Competing Multipolar Orders and Field-induced Kitaev Multipolar Liquid in d² Mott Insulators

In 5d² Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. After a quick review on a microscopic model for various lattices with an edge-sharing octahedra geometry, featuring Ising octupolar and bond-dependent quadrupolar interactions, we present a way to reveal an octupolar order in the osmium double perovskites, Ba₂BOsO₆ (B=Mg,Cd, and Ca). We also discuss a model for these systems under an external magnetic field, which generates highly anisotropic, bond-dependent exchange interactions that depend on the field angle. The external field allows for quadrupole-octupole interactions, once forbidden by symmetry, via mixing with the excited triplet states and provides a microscopic route to uncover a Kitaev multipolar liquid.