Mode sequence, frequency change of nonsoft phonons, and LO-TO splitting in strained tetragonalBaTiO3

Abstract

Ultraviolet Raman spectroscopy revealed the existence of an unusual large frequency shift occurring to a non-soft mode of E(TO4) when BaTiO3 is strained to a SrTiO3 substrate [D. Tenne et al., Science 313, 1614]. It raised two interesting questions: (i) whether there are other non-soft modes that possess similar or even larger strain-induced frequency shifts; (ii) how the mode sequence is altered by these shifts in frequency. Note that mode sequence is also pivotal in correctly indexing and assigning the spectroscopy peaks observed in all Raman experiments. By mapping out the evolutions of individual phonon modes as a function of strain using first-principles density functional perturbation calculations, we determine the mode sequence and strain-induced phonon frequency shifts in prototypical BaTiO3. Our study reveals that the mode sequence is drastically different when BaTiO3 is strained to SrTiO3 as compared to that in the unstrained structure, caused by multiple mode crossings. Furthermore, we predict that three other non-soft modes-A1(TO2), E(LO4), and A1(TO3)-display even larger strain-induced frequency shifts than E(TO4). The strain responses of individual modes are found to be highly mode specific, and a mechanism that regulates the magnitude of the frequency shift is provided. As another key outcome of this study, we tackle a long-standing problem of LO-TO splitting in ferroelectrics. A rigorous definition for the LO-TO splitting is formulated, which allows this critical quantity to be calculated quantitatively. The definition immediately reveals a new finding, that is, a large LO-TO splitting not only exists for E(LO4), which is previously known and originates from a soft mode, it also occurs to a non-soft A1(LO3) mode. The LO-TO splitting is shown to decrease drastically with compressive strain, and this decrease cannot be explained by the Born effective charges and high-frequency dielectric constants.

Ferromagnetism in ferroelectric BaTiO3 induced by vacancies: Sensitive dependence on charge state, origin of magnetism, and temperature range of existence

“…Furthermore, the theoretical strain-induced frequency shifts of non-soft phonon modes are in excellent agreement with experiments. 64 A large energy cutoff of 80 Ryd is used for all supercell calculations with vacancies, which provides sufficient convergence.…”

Persistence of strong and switchable ferroelectricity despite vacancies

“…Norm-conserving pseudopotentials54 are used to describe the interaction between core and valence electrons. Ti 3 s and 3 p semi-core orbitals are treated as valence states; quality of our pseudopotentials is good55. The energy cutoff for plane-wave expansion of wavefunction is 90 Ry, which is sufficient.…”

Revisiting eigen displacements of tetragonal BaTiO3: Combined first principle and experimental investigation

“…The classification by Hermet and Raeliarijaona et al [14,15] differed from Freire and Katiyar and termed E(TO1)/A(TO2) modes occurring at 38, 270 cm -1 as (Ti-O) Slater type vibrations, E(TO2)/A(TO1) modes at 180 cm -1 as (Ba-TiO3) Last type vibrations and E(TO4)/A(TO3) at 490 and 520 as Axe (Ti-O6) type vibrations. Ghosez and I. Ponomareva et al [16,17] defined E(TO1) mode as Slater type displacement while in the Zr doped BaTiO3, Dobal et al [18] associated A(TO1) mode with the Ti atomic vibrations i.e.…”