Ferromagnetism induced by entangled charge and orbital orderings in ferroelectric titanate perovskites

In magnetic materials, the Pauli exclusion principle typically drives anti-alignment between electron spins on neighbouring species resulting in antiferromagnetic behaviour. Ferromagnetism exhibiting spontaneous spin alignment is a fairly rare behaviour, but once materialized is often associated with itinerant electrons in metals. Here we predict and rationalize robust ferromagnetism in an insulating oxide perovskite structure based on the popular titanate series. In half-doped layered titanates, the combination of Jahn-Teller and oxygen breathing motions opens a band gap and creates an unusual charge and orbital ordering of the Ti d electrons. It is argued that this intriguingly intricate electronic network favours the elusive inter-site ferromagnetic (FM) ordering, on the basis of intra-site Hund's rules. Finally, we find that the layered oxides are also ferroelectric with a spontaneous polarization approaching that of BaTiO3. The concepts are general and design principles of the technologically desirable FM ferroelectric multiferroics are presented.