Order-parameter-mediated stabilization of the ferroelectric orthorhombic phase in HfO2 by oxygen-vacancy-induced internal stress

Ferroelectricity in HfO2 originates from the formation of a metastable orthorhombic phase (Pca21), yet the microscopic mechanism stabilizing this phase, particularly the role of oxygen vacancies, remains under debate. Here, we investigate internal stress tensors induced by oxygen vacancies and their impact on the relative stability of the orthorhombic (O) and monoclinic (M) phases using first-principles calculations. By evaluating vacancy-induced internal stresses under fixed-lattice conditions, we find that oxygen vacancies generate shear stresses of comparable magnitude in both phases, while the energy difference between them, ΔEO−M, is consistently reduced. Analysis of the stress-order-parameter coupling suggests that, in the M phase, shear stress can couple linearly to the monoclinic distortion order parameter, whereas such linear coupling is symmetry-forbidden in the O phase. Consistent with this picture, oxygen vacancies are expected to affect the M phase more strongly through symmetry-allowed coupling to internal shear stress, thereby reducing ΔEO−M and relatively favoring the ferroelectric O phase.