We use resonant and non-resonant X-ray diffraction measurements in combination with firstprinciples electronic structure calculations and Monte Carlo simulations to study the relationship between crystal structure and multiferroic orders in the orthorhombic perovskite manganites, o-RMnO3 (R is a rare-earth cation or Y). In particular, we focus on how the internal lattice parameters (Mn-O bond lengths and Mn-O-Mn bond angles) evolve under chemical pressure and epitaxial strain, and the effect of these structural variations on the microscopic exchange interactions and long-range magnetic order. We show that chemical pressure and epitaxial strain are accommodated differently by the crystal lattice of o-RMnO3, which is key for understanding the difference in magnetic properties between bulk samples and strained films. Finally, we discuss the effects of these differences in the magnetism on the electric polarization in o-RMnO3. * natalya.fedorova@mat.ethz.ch † nicola.spaldin@mat.ethz.ch 1 N. A. Spaldin and M. Fiebig, Science 309, 391 (2005).

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Magnetically induced ferroelectrics exhibit rigidly coupled magnetic and electric order. The ordering temperatures and spontaneous polarization of these multiferroics are notoriously low, however. Both properties can be much larger if magnetic and ferroelectric order occur independently, but the cost of this independence is that pronounced magnetoelectric interaction is no longer obvious. Using spatially resolved images of domains and density-functional theory, we show that in multiferroics with separately emerging magnetic and ferroelectric order, the microscopic magnetoelectric coupling can be intrinsically strong even though the macroscopic leading-order magnetoelectric effect is forbidden by symmetry. We show, taking hexagonal ErMnO3 as an example, that a strong bulk coupling between the ferroelectric and antiferromagnetic order is realized because the structural distortions that lead to the ferroelectric polarization also break the balance of the competing superexchange contributions. We observe the manifestation of this coupling in uncommon types of topological defects like magnetoelectric domain walls and vortex-like singularities.

An exotic coexistence of polar states is known to occur in ferroelectric|dielectric PbTiO 3 |SrTiO 3 (PTO|STO) heterostructures. In the PTO layers with a thickness of 10-20 unit cells, in-plane-polarized regions order alongside the so-called vortex phase with a whirl-like arrangement of electric dipoles. We investigate the optical signature of these polar phases noninvasively using optical second harmonic generation (SHG) on PTO|STO-based heterostructures. We identify the phase coexistence down to a single PTO|STO bilayer. By comparing the SHG yield in dependence of the number of PTO layers, we further find that interlayer coupling plays an important role in setting the final polarization state. Our nonlinear optical experiments demonstrate the potential of this noninvasive approach for the identification and understanding of complex noncollinear ordering of dipole moments in oxide heterostructures and lays the groundwork for their operando investigation.

Systems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy0.7Tb0.3FeO3 domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.