Multiferroic VHfO₄ with Strain-Tunable Magnetism

The coexistence of ferroelectricity and magnetism in a single-phase oxide is rare because the electronic requirements for these two orders are often incompatible. Here, using first-principles calculations and parallel-tempering Monte Carlo simulations, we propose stoichiometric VHfO$_4$ as a hafnia-derived multiferroic that overcomes this constraint through ordered cation design rather than dilute magnetic doping. We found that VHfO$_4$ could stabilize in a polar \(Pca2_1\)-like structure with layered V/Hf ordering, remains dynamically stable, and preserves switchable ferroelectricity with a large spontaneous polarization. The ordered V sublattice introduces competing exchange interactions that favor an antiferromagnetic ground state at zero strain. Epitaxial strain further drives transitions into additional phases, including a noncollinear spiral-like state and a predominantly in-plane antiferromagnetic state. We also find that out-of-plane lattice distortions along the polar axis strongly modify the exchange interactions and magnetic phase stability, indicating a strain-mediated pathway for electric-field control of magnetism. These results establish VHfO$_4$ as a promising platform for exploring multiferroicity and magnetoelectric coupling in hafnia-based oxides.