Possibility of Type-III Multiferroics Hosting d^{0} Ferroelectricity and d^{0} Ferromagnetism

Multiferroics are known to be classified into two types. However, type I lacks sufficient magnetoelectric coupling and type II lacks sufficient electric polarization, making both practically difficult. In this Letter, we explore the possibility of type-III multiferroics, where the origins of ferroelectricity and magnetism are highly intertwined but not causally related, with a combination of strong magnetoelectric coupling and large polarization. Our first-principles calculations predict that monolayer TiCdO_{4} is such a type-III ferroelectric-ferromagnetic multiferroic with both electronic and magnetic orders originating from competing electron populations on oxygen atoms. It shows an electric polarization of 50  μC/cm^{2}, while the maximum linear and quadratic magnetoelectric response are as high as 35 000  ps/m and 1.59×10^{-14} s/A, respectively. Our Letter opens up new perspectives for the discovery and design of much-anticipated multiferroics that can be used for cross-modulation.