Insulating improper ferroelectric domain walls as robust barrier layer capacitors

We report the dielectric properties of improper ferroelectric h-ErMnO$_3$. From the bulk characterisation we observe a temperature and frequency range with two distinct relaxation-like features, leading to high and even colossal values for the dielectric permittivity. One feature trivially originates from the formation of a Schottky barrier at the electrode-sample interface, whereas the second one relates to an internal barrier layer capacitance (BLC). The calculated volume fraction of the internal BLC (of 8 %) is in good agreement with the observed volume fraction of insulating domain walls (DWs). While it is established that insulating DWs can give rise to high dielectric constants, studies typically focused on proper ferroelectrics where electric fields can remove the DWs. In h-ErMnO$_3$, by contrast, the insulating DWs are topologically protected, facilitating operation under substantially higher electric fields. Our findings provide the basis for a conceptually new approach to engineer materials exhibiting colossal dielectric permittivities using domain walls in improper ferroelecctrics with potential applications in electroceramic capacitors.