Vanadium-doped HfO$_2$, multiferroic uncompromised

TL;DR

This work addresses the challenge of achieving robust multiferroicity by doping ferroelectric hafnia with vanadium. Using comprehensive density-functional theory, the authors model the solid solution $Hf_{1-x}V_xO_2$ up to $x\approx0.37$, finding that a majority-spin gap of about $1$ eV persists, the polarization remains substantial (around 70% of pristine hafnia), and magnetization grows approximately linearly with $x$. Thermodynamic analysis via mixing free energy shows stability against phase separation up to $x\approx0.16$ at a typical growth temperature, with the stability window expanding modestly at higher temperatures. The results, including detailed DOS and structural patterns, align with recent vhfo2 experiments and point to a feasible, device-relevant ferromagnetic multiferroic in the hafnia family, with data openly available for reuse.

Abstract

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 two-thirds the hafnia value. Ferromagnetic 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.

Figures (12)

• Figure 1: Volume (top) and formation energy per V atom (bottom) of (Hf,V)O$_2$ vs concentration.
• Figure 2: F$_{\rm mix}$ (bottom) and F$_{\rm mix}$/$x$ (top) vs concentration at two temperatures. Error bars, not shown for clarity, are of order 10%.
• Figure 3: Modulus of polarization (top) and magnetization (bottom) vs concentration.
• Figure 4: Projection of the polarization versor on the Cartesian axes. The average projection corresponds roughly to a [111] direction.
• Figure 5: Schematic of the majority-channel density of states vs $x$. Dotted vertical line is the Fermi energy. Arrows sketch the evolution of the V occupied states. Here $x$=1 corresponds to VO$_2$ in its own $C 2/m$ structure.