  The influence of rotomagnetic (RM), rotoelectric (RE) and magnetoelectric
(ME) coupling on phase diagram and properties of antiferrodistortive (AFD)
perovskite oxides was reviewed. The main examples we consider in the review are
typical AFD perovkites, such as incipient ferroelectrics EuTiO3, SrTiO3,
EuxSr1-xTiO3, multiferroic BiFeO3 and Bi1-xRxFeO3 (x = La, Nd). The strong
influence of RM, RE and ME couplings on the physical properties and phase
diagrams including antiferromagnetic (AFM), ferroelectric (FE) and structural
AFD phases has been revealed in the framework of Landau-Ginzburg-Devonshire
(LGD) theory, as well as the prediction of novel (double and triple)
multiferroic phases has been demonstrated.
  In the review we are especially focused on (a) the possibility to induce FM
(FE) phase in EuTiO3 (as well as in other paraelectric AFM oxides) by the
application of an electric (magnetic) field due to the ME coupling; (b) the
analysis of the size effects and novel phases in EuxSr1-xTiO3 nanosystems,
where the LGD predicts the presence of the triple AFD-FE-FM(AFM) phase at low
temperatures; (c) the appearance of improper spontaneous polarization and
pyroelectricity in the vicinity of antiphase domain boundaries, structural twin
walls, surfaces and interphases in the AFD phase of non-ferroelectric SrTiO3
induced by the flexoelectricity and rotostriction; (d) the occurrence of low
symmetry monoclinic phase with in-plane FE polarization in thin strained
EuxSr1-xTiO3 films and its stabilization over wide temperature range by AFD
oxygen octahedron tilts due to flexoelectric and rotostriction coupling; (e)
discussion of a surprisingly strong size-induced increase of AFM transition
temperature caused by the joint action of RM coupling with elastic stress
accumulated in the intergrain spaces of BiFeO3 dense ceramics.
