First-principles Calculations of Raman and Infrared Spectroscopy for Phase Identification and Strain Calibration of Hafnia

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: ω(A1g)=300 cm−1 for P42nmc, ω(A1)=343 cm−1 for Pca21, ω(B2)=693 cm−1 for Pmn21, ω(Ag)=513 cm−1 for Pbca (OI), ω(Ag)=384 cm−1 for brookite, and ω(Ag)=496 cm−1 for baddeleyite. We also identified the Raman B1g mode, an anti-phase vibration of dipole moments [ω(B1g)=758 cm−1 for OI and ω(B1g)=784 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 [ΔωLO−TO(A1z)=255 cm−1 in Pca21 and ΔωLO−TO(A1)=263 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 [Z*(Hf)=5.54].