  Polar skyrmions are predicted to emerge from the interplay of elastic,
electrostatic and gradient energies, in contrast to the key role of the
anti-symmetric Dzyalozhinskii-Moriya interaction in magnetic skyrmions. With
the discovery of topologically-stable polar skyrmions, it is of both
fundamental and practical interest to understand the microscopic nature and the
possibility of temperature- and strain-driven phase transitions in ensembles of
such polar skyrmions. Here, we explore the reversible transition from a
skyrmion state (topological charge of -1) to a two-dimensional, tetratic
lattice of merons (with topological charge of -1/2) upon varying the
temperature and elastic boundary conditions in [(PbTiO3)16/(SrTiO3)16]8
lifted-off membranes. This topological phase transition is accompanied by a
change in chirality, from zero-net chirality (in meronic phase) to
net-handedness (in skyrmionic phase). To map these changes microscopically
required developing new imaging methods. We show how scanning convergent beam
electron diffraction provides a robust measure of the local polarization
simultaneously with the strain state at sub-nm resolution, while also directly
mapping the chirality of each skyrmion. Using this, we demonstrate strain as a
crucial order parameter to drive isotropic-to-anisotropic structural
transitions of chiral polar skyrmions to non-chiral merons, validated with
X-ray reciprocal space mapping and theoretical phase-field simulations. These
results revealed by our new measurement methods provide the first illustration
of systematic control of rich variety of topological dipole textures by
altering the mechanical boundary conditions, which may offer a promising way to
control their functionalities in ferroelectric nanodevices using the local and
spatial distribution of chirality and order.
