Hidden order in the osmates: Microscopic theory and phenomenology

Phases associated with multipolar broken symmetries are often termed 'hidden orders' since they elude conventional experimental probes. Understanding the origin of the multipolar degrees of freedom, and their exotic ordering has been a subject of intense interest over the past decade. While much of the initial work on the subject was done in the context of f-electron heavy fermion systems, recent experiments have put the spotlight on d-orbital systems as a rich playground for exploring these multipolar orders. In particular, heavy d-orbital spin-orbit coupled Mott insulators provide a very natural way to stabilize ground states with multipolar moments. In this talk, I will review the advancements in our theoretical understanding of a class of osmates, and various proposals for their multipolar ordering. I will present ideas both from a phenomenological point of view, inspired by experimental evidence, as well as from microscopic calculations, which have given us insight into not only the rich phases that can be exhibited in these compounds, but also into limitations of existing perturbative techniques used to study "standard" Mott insulators. I will conclude with our understanding of recent NMR experiments that have provided a further peek into these complex orders.