  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.
