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TROSCOPY OF CONDENSED MATTER

Phonon Spectrum of Eu2Sn2O7: Ab Initio Calculation V. A. Chernysheva, *, P. A. Agzamovab, and A. V. Arkhipova a Ural

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Federal University, Yekaterinburg, 620075 Russia M.N. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108 Russia *e-mail: [email protected] Received March 28, 2020; revised May 17, 2020; accepted July 3, 2020

Abstract—The crystal structure and phonon spectrum of a Eu2Sn2O7 crystal is studied within the MO– LCAO approach using the hybrid DFT functional, which takes into account the contribution from nonlocal exchange to the Hartree–Fock formalism. Frequencies, types, and intensities of fundamental vibrations, which are active in IR and Raman scattering spectra, are determined. Elastic constants are calculated. The calculations are performed using the CRYSTAL17 program, designed to simulate periodic structures within the MO–LCAO approach. Keywords: rare-earth stannates, phonons, elastic constants, hybrid functionals DOI: 10.1134/S0030400X20110090

INTRODUCTION Rare-earth oxides with a pyrochlore (A2B2O7) structure (A is a rare-earth ion and B is Ti, Ge, Zr, Sn, or Mo) have been of great interest for several decades due to the variety of properties and potential application as phosphors [1–4]. A number of recent studies were devoted to europium stannate Eu2Sn2O7 [5–7]. A Raman spectrum of Eu2Sn2O7 has lately been measured [5]. It appears important to perform ab initio calculations of the Eu2Sn2O7 phonon spectrum. In this study, we perform successive calculation of the crystal structure and phonon spectrum at the Γ point of europium stannate Eu2Sn2O7 within the density functional theory (DFT) with a hybrid functional taking into account the contribution from nonlocal exchange to the Hartree–Fock formalism. The Eu2Sn2O7 elastic constants are also calculated (there are hardly any information about these parameters in publications). Europium stannate has a pyrochlore structure, sp. gr. Fd 3 m (no. 227). Ions occupy the following sites: 16c (0, 0, 0) for Sn, 16d (1/2, 1/2, 1/2) for Eu, 48f (x, 1/8, 1/8) for O1, and 8b (3/8, 3/8, 3/8) for O2. Oxygen occupies two symmetrically nonequivalent sites. CALCULATION METHODS The calculations were performed within the density functional theory (DFT) using the hybrid functionals PBE0 [8] and B3LYP [9], which take into account both the local and nonlocal (within the Hartree–Fock formalism) exchanges. A comparison of different-level functionals [10] showed that PBE0 is characterized by

a small error in reproduction of the electron density and other characteristics with respect to the calculation by the coupled-cluster CCSD method. We also performed calculation with the SVWN functional (Slater exchange, Vosko–Wilk–Nusair correlation). The SVWN functional used for local density approximation (LDA) calculations is a combination of the Slater exchange functional [11] with correlation of a homogeneous electron gas within the Vosko–Wilk– Nusair approximation [12]. The calculations were performed in