Magnetic hybrid-improper ferroelectrics show potential for multiferroicity that is mediated by nonpolar structural distortions that give rise to both ferroelectricity and a net-magnetic spin canting. Here, we report on a pronounced magnetoelectric response of the ferroelectric state to the intrinsic magnetic ordering and to external magnetic fields in $\mathrm{Ca}{}_3{\mathrm{Mn}}_{1.9}{\mathrm{Ti}}_{0.1}\mathrm{O}{}_7$, a layered perovskite-type system. We observe a sixfold increase in the temperature-dependent response of the polarization-induced optical second-harmonic-generation (SHG) signal to the magnetic order that we explain as a magnetically triggered interlayer coupling of the polar order. Furthermore, an applied magnetic field up to 3 T along the direction of the net magnetization enhances the polarization-induced SHG signal by about 30%. We interpret this as magnetic-field-induced spin canting, which possibly affects the Mn-O bonds and hence the polarization. Optical SHG is of particular advantage to this study as it provides access to the electric polarization with spatial resolution of its domains, unobstructed by the leakage currents that impede contact-based measurements. Our investigations advance the understanding and potential of a highly promising new category of multiferroic materials for magnetoelectric cross control and functionalization.

• Received 19 November 2023
• Revised 4 March 2024
• Accepted 7 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184417