Coexistence of ferroelectricity and ferromagnetism in vanadium-doped HfO2

Ab initio density-functional calculations show that orthorhombic Pca21 hafnia HfO2 mixed with vanadium at low concentration is a ferroelectric and ferromagnetic insulator. The multiorbital degeneracy of singly-occupied V states in the nominally 4+ ionic state is broken by magnetism, reduced symmetry, and local distortion, causing a single one-electron majority state per V atom to be occupied. A gap of order 1 eV thus survives at all V concentrations, and intrinsic polarization is preserved at the level of 60–70% of the undoped-HfO2 value. Magnetization is found to increase linearly with V content, with values of 30–40 emu/cm3 at concentrations near the end of the stability range (∼16% V).