Design of Mott Multiferroic HfO₂ by Inducing Unpaired d States

Single-phase multiferroics are rare due to the incompatibility of the empty d orbitals for ferroelectricity and partially filled d orbitals for magnetism. This study proposes a route to achieve Mott multiferroicity in HfO₂ via Nb and Ta doping, which induces an extra d electron while preserving the oxygen displacement in the polar phase. Density functional theory (DFT) calculations confirm the stability of doped ferroelectric (FE) HfO₂, with FE transition temperatures exceeding room temperature and reduced switching barriers. A significant magnetoelectric coupling is observed where FE switching induces an interchange of magnetic coupling types and a stochastic reorientation of spin ordering. Notably, the ferromagnetic (FM) switching is governed by the intermediate FE switching pathway, not merely the initial and final FE states. This novel coupling magnetoelectric coupling mechanism can be used for ultrafast and energy-efficient probabilistic computation.