  Ferroic materials are well known to exhibit heterogeneity in the form of
domain walls. Understanding the properties of these boundaries is crucial for
controlling functionality with external stimuli and for realizing their
potential for ultra-low power memory and logic devices as well as novel
computing architectures. In this work, we employ synchrotron-based near-field
infrared nano-spectroscopy to reveal the vibrational properties of ferroelastic
(90$^\circ$ ferroelectric) domain walls in the hybrid improper ferroelectric
Ca$_3$Ti$_2$O$_7$. By locally mapping the Ti-O stretching and Ti-O-Ti bending
modes, we reveal how structural order parameters rotate across a wall. Thus, we
link observed near-field amplitude changes to underlying structural modulations
and test ferroelectric switching models against real space measurements of
local structure. This initiative opens the door to broadband infrared
nano-imaging of heterogeneity in ferroics.
