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Electric polarization in conventional ferroelectric oxides usually involvesnonmagnetic transition-metal ions with an empty d shell (the d$^0$ rule). Herewe unravel a new mechanism for local electric dipoles based on magneticFe$^{3+}$ (3d$^5$) ion violating the d$^0$ rule. The competition between thelong-range Coulomb interaction and short-range Pauli repulsion in a FeO$_5$bipyramid with proper lattice parameters would favor an off-center displacementof Fe$^{3+}$ that induces a local electric dipole. The manipulation of thiskind of non-d$^0$ electric dipoles opens up a new route for generatingunconventional dielectrics, ferroelectrics, and multiferroics. As a prototypeexample, we show that the non-d$^0$ electric dipoles in ferrimagnetichexaferrites (Ba,Sr)Fe$_{12}$O$_{19}$ lead to a new family of magnetic quantumparaelectrics.

Non-d$^0$ Electric Dipole in FeO$_5$ bipyramid: a New Resource for Quantum Paraelectrics, Ferroelectrics and Multiferroics