Discovery of Ordered Vortex Phase in Multiferroic Oxide Superlattices.

Ferroics, characterized by a broken symmetry state with nonzero elastic, polar, or magnetic order parameters $\vec{u}$, are recognized platforms for staging and manipulating topologically-protected structures as well as for detecting unconventional topological phenomena. The unrealized possibility of producing ordered topological phases in magnetoelectric multiferroics, exhibiting coupled magnetic and polar order parameters, is anticipated to engender novel functionality and open avenues for manipulating topological features. Here, we report the discovery of an ordered $\pi_1$-$S_\infty$ vortex phase within single-phase magnetoelectric multiferroic BiFeO$_3$. The phase, characterized by positive topological charge and chiral staggering, is realized in coherent TbScO$_3$ and BiFeO$_3$ superlattices and established via the combination of direct- and Fourier-space analyses. Observed order-parameter morphologies are reproduced with a field model describing the local order-parameter stiffness and competing non-local dipole-dipole interactions. Anisotropies canting the order parameter towards $\left $ suppress chiral staggering and produced a competing $\pi_1$-$C_{\infty v}$ vortex phase in which cores are centered.