Three-dimensional imaging of topologically protected strings in a multiferroic nanocrystal

Multiferroic materials can host a plethora of intriguing phenomena due to the presence of multiple ferroic properties that break both spatial inversion symmetry and time reversal symmetry at an observable scale. Hexagonal manganite multiferroics are of particular interest as the properties of their symmetry-lowering phase transition can be described by a Mexican-hat-like potential energy surface. The early universe is proposed to have undergone a symmetry-lowering phase transition that is described by a similar Mexican-hat-like potential that gives rise to the formation of one-dimensional topologically protected defects known as cosmic strings. According to the Kibble-Zurek mechanism, hexagonal manganite multiferroics can host the crystallographic equivalent of cosmic strings and can therefore serve as a testing ground for exploration of concepts in cosmology. To date, however, direct imaging of 1D topological defects in a condensed matter material system has not been achieved. Here we report on robust three-dimensional imaging of topologically protected strings in a single hexagonal manganite nanocrystal, enabled by advances in experimental techniques. Our findings reveal multiferroic strings with a preferred phase vortex winding direction and average separation of similar to 93 nm.