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 (P4(2)nmc, Pca2(1), Pmn2(1), 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: omega ( A(1g) ) = 300 cm(-1) for P4(2)nmc, omega (A( 1)) = 343 cm(-1) for Pca2(1), omega ( B-2) = 693 cm(-1) for Pmn2(1), omega (A( g)) = 513 cm(-1) for Pbca (OI), omega (A(g)) = 384 cm(-1) for brookite, and omega (A(g)) = 496 cm(-1) for baddeleyite. We also identified the Raman B-1g mode, an anti-phase vibration of dipole moments [omega (B-1g) = 758 cm(-1) for OI and omega ( B-1g ) = 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 [delta omega(LO) - TO ( A(1)(z)) = 255 cm(-1) in Pca2(1) and delta omega( LO) (- TO) ( A 1 ) = 263 cm(-1) in Pmn2(1)] 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]. Published under an exclusive license by AIP Publishing.

Automated summary

Using density functional perturbation theory, this study computed the phonon frequencies and Raman and IR activities of various hafnia polymorphs and investigated their evolution with epitaxial strain. The study identified Raman signatures for different polymorphs and a new Raman signature for antipolar structures. Additionally, a large splitting between the longitudinal optical and transverse optical modes was calculated and related to the anomalously large Born effective charges of Hf atoms.