Aberration Corrected STEM imaging of ferroelectric domain walls in $\mathbf{Ca_3Ru_{2(1-x)}Ti_xO_7}$*

$\mathrm{Ca_3Ru_2O_7}$ is a layered Ruddlesden-Popper oxide which is a strongly correlated metal at room temperature and undergoes a MIT at 48K. Ti doped $\mathrm{Ca_3Ru_2O_7}$ is a Mott metal at 300K with the Mott transition temperature increasing with Ti concentration (90K at 5\% Ti), but without increase in strain due to the similarity in the size of $\mathrm{Ti^{4+}}$ and $\mathrm{Ru^{4+}}$ cations. The bulk crystals show the presence of domain walls as observed by polarized light microscopy. Aberration-corrected STEM imaging demonstrates the presence of both $\mathrm{90^{\circ}}$ and $\mathrm{180^{\circ}}$ domain walls along with domain junctions. EELS was performed at 300K and 77K to measure the Ru $\mathit{t_{2g}}$ $\longrightarrow$ O $\mathit{2p}$ hybridization in metallic and insulating ground states. The ferroelectric distortions inside the domains were measured to be isostructural to distortions in hybrid improper ferroelectric $\mathrm{Ca_3Ti_2O_7}$. Additionally,as confirmed by STEM imaging the $\mathrm{180^{\circ}}$ domain walls exist in head-to-head, head-to-tail and tail-to-tail configurations, thus leading to the intriguing possibility of competition between local ferroic dipole moments and a global shielding from the metallic ground state at room temperature.