Imaging Orientation Dependent Spin Cycloids in BiFeO₃

Materials with multiple order parameters have been one of the major themes in condensed matter research for several decades. Of particular interest is the study of magnetoelectric (ME) multiferroic BiFeO₃, where the coupling between antiferromagnetic and ferroelectric order parameters leads to a plethora of novel functionalities such as electric field controlled antiferromagnetic order, which is crucial for the development of spin-based ultra-low power electronics. The antiferromagnetic order in BiFeO₃ is notably complex, as the inherent ME coupling, along with Dzyaloshinskii–Moriya interaction, results in the formation of spin cycloid. With the recent advent of high-resolution nanoscale imaging techniques, such as scanning nitrogen vacancy magnetometry (SNVM), it is now possible to image these cycloids in real space. This advancement has not only enhanced our understanding of ME coupling but has also been extremely beneficial in analyzing its response to epitaxial constraints and electrostatic/geometrical boundary conditions, which are fundamental to the development of any electronic devices. In this work, we employ high-resolution SNVM to image how spin cycloids evolve with the orientation of thins films grown by sputtering and molecular beam epitaxy. We find that for (111)_pc (pc: pseudo cubic) oriented films where the cycloid propagation vectors lie within the surface of the film, a complete morphogenesis occurs, leading to the formation of Turing patterns. We investigate its response to an external electric field and compare our results with the (100)_pc and (110)_pc films made on substrates of different orientations. These results will lay the foundation for understanding the formation of the spin cycloid vis-à-vis crystal orientation which would be monumental in understanding the spin transport in multiferroics.