Hidden magnetoelectric multipoles in complex oxides

Most magnetic materials, phenomena and devices are well described in terms of magnetic dipoles of either spin or orbital origin. There is mounting evidence, however, that higher-than-dipolar order multipoles both exist (often in hiding) and lead to intriguing magnetic behaviors.  In this talk I will discuss the relevance of the so-called magnetoelectric multipoles, which form the next-order term, after the magnetic dipole, in the multipolar expansion of the magnetization density in a magnetic field.  First, I will describe how magnetoelectric multipoles underlie multiferroic behavior and in particular how they determine the magnetic response to applied electric fields. Then I will discuss signatures of hidden magnetoelectric multipolar order, how it can be unearthed using electronic-structure calculations and possibilities for its direct measurement.