  The zero-temperature limit of a continuous phase transition is marked by a
quantum critical point, which can generate exotic physics that extends to
elevated temperatures. Magnetic quantum criticality is now well known, and has
been explored in systems ranging from heavy fermion metals to quantum Ising
materials. Ferroelectric quantum critical behaviour has also been recently
established, motivating a flurry of research investigating its consequences.
Here, we introduce the concept of multiferroic quantum criticality, in which
both magnetic and ferroelectric quantum criticality occur in the same system.
We develop the phenomenology of multiferroic quantum critical behaviour,
describe the associated experimental signatures, and propose material systems
and schemes to realize it.
