Abstract
Topological defects in matter behave collectively to form highly non-trivial structures called topological textures that are characterised by conserved quantities such as the winding number. Here we show that an epitaxial ferroelectric square nanoplate of bismuth ferrite subjected to a large strain gradient (as much as 10(5) m(-1)) associated with misfit strain relaxation enables five discrete levels for the ferroelectric topological invariant of the entire system because of its peculiar radial quadrant domain texture and its inherent domain wall chirality. The total winding number of the topological texture can be configured from - 1 to 3 by selective non-local electric switching of the quadrant domains. By using angle-resolved piezoresponse force microscopy in conjunction with local winding number analysis, we directly identify the existence of vortices and anti-vortices, observe pair creation and annihilation and manipulate the net number of vortices. Our findings offer a useful concept for multi-level topological defect memory.