Ferroelectric materials exhibit a spontaneous electric polarization that can be reversed by an electric field1, a property central to non-volatile memories2,3, sensors4 and actuators5,6. In most conventional ferroelectrics, the polarization originates from a softening of a polar mode7. The amplitude of the mode along a given direction couples with the applied field along the same direction8. Ferroelectrics with a predominant in-plane polarization are harder to use in standard device geometries and therefore the field has mostly focused on out-of-plane ferroelectrics. Developing approaches that enable manipulation of the in-plane polarization component with an out-of-plane field would therefore provide new opportunities for device design and functionality. Here we have discovered that a trilinear coupling between the in-plane and out-of-plane polarization, mediated by means of the octahedral tilts and rotations in the layered ferroelectric Bi4Ti3O12, naturally fulfils this challenge and enables perpendicular switching of the polarization state. In its bulk monoclinic phase, this material hosts a large in-plane polarization (about 50 μC cm−2) driven by a proper ferroelectric instability, together with smaller out-of-plane polarization (about 5 μC cm−2) of improper origin, induced by oxygen octahedral distortions. We demonstrate that, in c-axis-oriented epitaxial films, the in-plane polarization switches deterministically under an out-of-plane electric field. This cross-coupling between orthogonal polarization components provides a route to transverse manipulation of ferroic order parameters and establishes layered ferroelectrics as a platform for capacitive computing concepts.
