Topologically Nontrivial Polar Structures in Ferroic Order Parameter Space

When ferroic materials are explored in three dimensions, they offer a rich playground for fundamental physics. The higher degrees of freedom available in 3D, along with the new topologies and geometries they enable, produce numerous novel effects, including exotic dynamic behaviors and topological textures (see movie 1 and movie 2) on nanometer scales.

Our group conducts experimental studies on three-dimensional multiferroic systems across a range of length scales. We investigate micrometer-sized systems, where topological structures analogous to everyday objects are observed, and nanoscale systems, where controlled growth and lithography allow us to manipulate their properties.

The experimental study of these systems presents significant challenges. Until recently, available techniques were limited to flat surfaces or films, preventing visualization or creation of 3D ferroic structures, such as vortex cores. Consequently, much of our recent work has focused on developing state-of-the-art methods to fabricate and visualize ferroic order in three dimensions. With these advanced experimental capabilities, we now concentrate on studying the physics of 3D ferroic systems while continually enhancing our techniques.

Topologically nontrivial polar structures, such as vortices, skyrmions, and merons, are topologically protected states of matter that can emerge in polar materials. These vortices are analogous to magnetic vortices but involve the polarization of the material instead of magnetic spins. They arise in materials where the polarization field exhibits complex spatial patterns due to competing interactions and asymmetries in the material’s structure or composition. Recent studies by the Fohtung Research Group demonstrated the use of Bragg Coherent Diffraction Imaging (BCDI) to spatially resolve the structural asymmetries in and around topological polar vortex structures. The figure below shows the vortex core and its behavior under different electric fields. Further investigation using BCDI revealed an enhancement in the piezoelectric response of the nanoparticle around the topological polar vortex core. This response was observed to decay away from the vortex core, following a power-law behavior.

BCDI has been instrumental in studying the structural asymmetry of topological vortices. It leverages the high coherence and brilliance of X-rays generated by synchrotrons to spatially resolve the structure of a nanocrystal, achieving angstrom-level resolution for strain and nanometer-level resolution for imaging. BCDI combines the capabilities of high-resolution X-ray diffraction and iterative phase retrieval algorithms to obtain the phase information lost in intensity data.

Figure 1 shows BCDI 3D mapping of nanodomains and vortex dynamics in BTO.

Figure 1 Three-dimensional nanodomain and vortex dynamics in BTO nanoparticle.
Figure 2. Three-dimensional mapping of piezoelectric coefficient d33 in BTO nanoparticle.
  1. Karpov, D., Liu, Z., Rolo, T. et al. Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field. Nat Commun 8, 280 (2017).
  2. Xiaowen Shi, Nimish Prashant Nazirkar, Ravi Kashikar, Dmitry Karpov, Shola Folarin, Zachary Barringer, Skye Williams, Boris Kiefer, Ross Harder, Wonsuk Cha, Ruihao Yuan, Zhen Liu, Dezhen Xue, Turab Lookman, Inna Ponomareva, and Edwin Fohtung. ACS Applied Materials & Interfaces 2024 16 (6), 7522-7530 DOI: 10.1021/acsami.3c06018