Copper-based charge transfer multiferroics with a $d^9$ configuration

Multiferroics are materials with a coexistence of magnetic and ferroelectric order allowing the manipulation of magnetism by applications of an electric field through magnetoelectric coupling effects. Here we propose an idea to design a class of multiferroics with a $d^9$ configuration using the magnetic order in copper-oxygen layers appearing in copper oxide high-temperature superconductors by inducing ferroelectricity. Copper-based charge transfer multiferroics SnCuO2 and PbCuO2 having the inversion symmetry breaking $P4mm$ polar space group are predicted to be such materials. The active inner s electrons in Sn and Pb hybridize with O $2p$ states leading the buckling in copper-oxygen layers and thus induces ferroelectricity, which is known as the lone pair mechanism. As a result of the $d^9$ configuration, SnCuO2 and PbCuO2 are charge transfer insulators with the antiferromagnetic ground state of the moment on Cu retaining some strongly correlated physical properties of parent compounds of copper oxide high-temperature superconductors. Our work reveals the possibility of designing multiferroics based on copper oxide high-temperature superconductors.