Hidden, Entangled and Resonating Orders

The concept of magnetic dipolar order -- for example ferro, ferri or antiferromagnetic -- is at the core of our understanding of the behavior of magnetic materials, and is invaluable in selecting and tailoring them for applications. Sometimes, however, magnetic materials surprise us, and behave in ways that can not be captured within our established paradigms, suggesting additional kinds of order that are not yet identified. The indicators and implications of such ``hidden order'' are the subject of this talk. Using multiferroic composite order consisting of coupled electric and magnetic dipoles as a model, I will first discuss hints of static hidden order in existing materials, the intriguing behaviors that such hidden order causes, and experimental efforts that could unambiguously reveal it. Next, I will describe new physics that can emerge when the order is explicitly quantum mechanical, specifically the occurrence and signatures of multiferroic quantum criticality. Finally, I will explore dynamical order, in which thermal effects or an external drive cause a time evolution of the coupled quantum mechanical wavefunctions. I will outline promising future directions in the heroic effort to unearth, explain and exploit these hidden, entangled and resonating orders, which will doubtless keep us entertained for many years to come.