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Multipolar Magnetism: A Detective Story

It has been postulated that d-orbital systems with large spin-orbit coupling are able to host multipolar ordered phases. Motivated by recent experiments done with cubic double perovskites, we carried out an exact diagonalization study, where it was argued that a ferro-octupolar ordered phase could be stabilized via the splitting of a five-fold J=2 multiplet. The splitting may be attributed to a combination of t 2g -e g mixing, as well as a deviation from spherically symmetric interactions. We also show that such a splitting would explain semi-quantitatively, the experimental observations. My goal with this colloquium is not only to share this work, but give some insight into the general methodology and philosophy of solving problems motivated by puzzling experiments in the field.