Magnetoelectric correlations in multiferroics at the nanoscale

Magnetoelectric coupling phenomena in multiferroics were initially treated almost exclusively as bulk effects exhibited by homogeneous materials. In recent years, however, attention has moved to the nanoscale. On the one hand, magnetoelectric phase control ultimately happens on the level of the mostly sub-micrometer-sized domains. On the other hand, domain walls, interfaces and thin films are nanoscale objects that have been proving to be the source of intriguing magnetoelectric coupling effects. In my talk, I will therefore explore the fascinating world of magnetoelectric correlations at the nanoscale in a number of examples, the diversity of which is intended to demonstrate the enormous potential of the nanoscale perspective on multiferroics. Among the examples I may discuss are: [1] a seemingly contradictory coexistence of strong local and forbidden global magnetoelectric coupling in multiferroics with separately emerging magnetic and ferroelectric order (type I); [2] conversion of a multiferroic bulk state into a multiferroic domain wall in a non-multiferroic environment; [3] the evolution of the improper ferroelectric state in a type-I multiferroic towards the thin-film limit of a single monolayer; [4] a giant net-polarization enhancement in low-voltage-switchable La-substituted BiFeO₃ heterostructures by electric-field training.