Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

TL;DR

This paper demonstrates the physical realization of the topological Roman surface through spin-induced ferroelectric polarization in cubic perovskite oxides, revealing a novel non-orientable topological state with path-dependent magnetoelectric effects.

Contribution

It introduces the first physical realization of the Roman surface as a topological state in a material, linking complex mathematical topology with spin-induced ferroelectric polarization.

Findings

Polarization resides on the Roman surface in certain oxides.

Polarization path depends on magnetic field evolution.

Experimental periodicity matches theoretical topological predictions.

Abstract

Topology, a mathematical concept in geometry, has become an ideal theoretical tool for describing topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological/geometrical invariants, which are usually defined on orientable surfaces such as torus and sphere. It is natural to quest whether it is possible to find the physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) resides on the topological Roman surface, a non-orientable two-dimensional manifold formed by sewing a Mobius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Mobius strip or orientable disc depending on how the spin evolves as controlled by external magnetic field. Experimentally, the periodicity of polarization can be the same or the twice of the rotating magnetic field, being well consistent with the orientability of disc and Mobius strip, respectively. This path dependent topological magnetoelectric effect presents a way to detect the global geometry of the surface and deepens our understanding of topology in both mathematics and physics