Domain walls in hybrid improper ferroelectric Ca$_3$Ti$_2$O$_7$

Coupling or competition between spin, charge, orbital, and structural order parameters can lead to novel properties and functionality in materials. For example, ferroelectrics that allow a coupling between the polarization and another order parameter can enable electric-field control of non-polar order parameters. This talk will focus on a recently discovered type of ferroelectricity (‘hybrid improper’ ferroelectricity) in the Ruddlesden-Popper compound Ca$_3$Ti$_2$O$_7$ , where the polarization is induced via a trilinear coupling to two octahedral rotation distortions of different symmetry. This octahedral rotation-polarization coupling also leads to a complex structure of coupled domain walls. Using a combination of group theoretic analysis and density functional theory calculations, I will present scenarios for domain wall structures in Ca$_3$Ti$_2$O$_7$ and related materials.