Three-dimensional Bragg Coherent x-ray diffraction imaging of multiferroic nanocrystals

Abstract

Bragg Coherent X-ray Diffraction Imaging (BCDI) has emerged as a powerful tool for being anon-destructive and lens-less imaging technique for analysing structures and strain of nano-crystalline materials. It allows for three-dimensional visualisation of crystal defects and is particularly adept at elucidating the intricate dynamics within these materials. BCDI's potential in studying multiferroic materials, specifically for unveiling their domain structure and coupled structural deformations, is rooted in its sub-angstrom sensitivity to atomic displacements. Multiferroics are materials that simultaneously exhibit more than one ferroic property, including ferromagnetism, ferroelectricity, ferroelasticity, or ferrotoroidicity, and more recently, the definition has extended to include anti ferroic orders. They have been a focus of research due to their wide range of potential applications brought about by their complex interplay between magnetic, electric and structural orderings. The domain structure can be particularly complex in improper ferroelectrics such as the hexagonal manganites since the polarization is a slave to a non-ferroelectric primary order parameter that drives the domain formation. In antiferromagnetic YMnO₃, for example, this leads to an unusual hexagonal vortex domain pattern with topologically protected domain walls which have been shown to exhibit electrical conductivity and a net magnetic dipole moment at the sample surface. Characterizing the three-dimensional structure of these domains and domain walls has been elusive, however, due to a lack of suitable imaging techniques. This thesis advances the study of multiferroic materials by incorporating the three-dimensional BCDI for unveiling the intricate structural dynamics. Motivated by unveiling these phenomena, supporting tools for BCDI are developed and enhanced, which facilitate uncovering the underlying physical phenomena in these materials. Here we report a multi-peak BCDI determination of the domain walls and domain types in a single YMnO₃ nanocrystal. By reconstructing high-resolution, three-dimensional images of the structure and the full strain tensor field, two ferroelectric domains are observed separated by a domain wall and confirm that the primary atomic displacements occur along the crystallographic c-axis throughout the nanocrystal. By correlating the BCDI experiment with atomistic simulation, the Mexican hat symmetry model of domain formation was verified in the hexagonal manganites, and the two domains are established to correspond to adjacent minima in the Mexican hat with opposite ferroelectric polarization and adjacent trimerization domains. Finally, using a circular mean comparison we show that for this sample the two domains correspond to a clockwise winding around the brim of the hat. Furthermore, the exploration of multi ferroic materials and their interaction with light at the nanoscale presents a captivating frontier in materials science. Of particular interest is the phenomenon of photostriction in Bismuth Ferrite (BiFeO₃), the light-induced deformation of crystal structures, which enhances the prospect for device functionality based on these materials. Understanding and harnessing multiferroic phenomena holds significant promise in various technological applications, from optoelectronics to energy storage. The orientation of the ferroelectric axis, therefore, is an important design parameter for devices formed from multiferroic materials. Determining its orientation in the laboratory frame of reference usually requires knowing multiple wavevector transfer (Q-Vector) directions, which can be challenging to establish due to the need for extensive reciprocal-space searches. Our study advances the understanding of the photostriction effect in a single nanocrystal by observing laser polarisation-dependent photostriction and quantitatively characterising its surface nature. We demonstrate a method to pinpoint the ferroelectric axis of a single multiferroic nanocrystal in the laboratory frame of reference using a single Q-vector directly from phase information. This technique is particularly valuable as BCDI evolves towards in-operando imaging of nanocrystals in devices, where knowing the crystal orientation is critical. Our approach significantly simplifies the otherwise daunting task of extensive reciprocal space exploration for a single nanocrystal.

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