First-principles calculations of Raman and infrared spectroscopy for phase identification and strain calibration of hafnia

Abstract

Using density functional perturbation theory, we computed the phonon frequencies and Raman and IR activities of hafnia polymorphs (P42nmc, Pca21, Pmn21, Pbca OI, brookite, and baddeleyite) for phase identification. We investigated the evolution of Raman and IR activities with respect to epitaxial strain and provide plots of frequency differences as a function of strain for experimental calibration and identification of the strain state of the sample. We found Raman signatures of different hafnia polymorphs: [Formula: see text] cm−1 for P42nmc, [Formula: see text] cm−1 for Pca21, [Formula: see text] cm−1 for Pmn21, [Formula: see text] cm−1 for Pbca (OI), [Formula: see text] cm−1 for brookite, and [Formula: see text] cm−1 for baddeleyite. We also identified the Raman [Formula: see text] mode, an anti-phase vibration of dipole moments [[Formula: see text] cm−1 for OI and [Formula: see text] cm−1 for brookite], as the Raman signature of antipolar Pbca structures. We calculated a large splitting between the longitudinal optical and transverse optical modes [[Formula: see text] cm−1 in Pca21 and [Formula: see text] cm−1 in Pmn21] to the same order as those observed in perovskite ferroelectrics and related them to the anomalously large Born effective charges of Hf atoms [[Formula: see text]].