Broken symmetry, strong correlation, and splitting between longitudinal and transverse optical phonons of MnO and NiO from first principles

Abstract

We propose a first-principles scheme, using the distorted structure, to obtain the phonons of the undistorted parent structure for systems with both broken symmetry as well as the splitting between longitudinal optical and transverse optical ͑TO͒ phonon modes due to long-range dipole-dipole interactions. Broken symmetry may result from antiferromagnetic ordering or structural distortion. Applications to the calculations of the phonon dispersions of NiO and MnO, the two benchmark Mott-Hubbard systems with the TO mode splitting for MnO, show remarkable accuracy.With advances in calculating atomic force constants within the framework of density-functional perturbation theory 1 and density-functional theory, 2 first-principles calculations can now predict electronic and vibrational properties for many classes of materials, including simple metals, transition metals, intermetallics, semiconductors, hydrides, and earth materials with exceptional accuracy. 3 However, it has been difficult to predict the lattice dynamics for strongly correlated electronic systems, particularly Mott-Hubbard insulators. These include materials such as NiO and MnO, 4-8 the La 2 CuO 4 -based cuprate superconductors, 9 and the LaMnO 3 -based colossal magnetoresistance manganites. 10 Experimental measurements also yielded inconsistent results on the frequency values of the optical phonons for both MnO ͑Refs. 6 and 8͒ and NiO. 5,7 The specific difficulties 11-15 in predicting the lattice dynamics of Mott-Hubbard insulators are: ͑i͒ the highly correlated nature of electronic states in these materials and ͑ii͒ the slight lowering of crystal symmetry as a result of antiferromagnetic ordering ͑ϳ0.6°for MnO and ϳ0.07°for NiO away from cubic 16 ͒.In this work, we report a scheme to accurately compute phonon dispersions of Mott-Hubbard systems such as MnO and NiO. This involves a combination of a method for recovering the ideal cubic symmetry from the slightly distorted structure, the mixed-space approach 17 for treating the splitting between longitudinal optical ͑LO͒ and transverse optical ͑TO͒ phonon modes, and the density-functional theory ͑DFT͒ plus U method for accounting for the strong electron correlation. 18 In applying the direct approach to predict the phonon dispersions of polar materials, a lot of effort 19-23 has been made to treat the contribution of the nonanalytical term. The mixed-space approach makes it parameter-free to accurately determine the phonon frequencies using the direct approach for polar materials. 17 In this approach, the force constants are written aswhere ⌽ ␣␤ jk is the interaction force-constant between atom j in the primitive cell M and atom k in the primitive cell P, ␣␤ jk the contribution from short-range interactions, N the number of primitive unit cells in the supercell, and D ␣␤ jk ͑na ; q → 0͒ the contribution from long-range interactions, i.e., the so-called nonanalytical part of the dynamical matrix in the limit of zero wave vector q. According to Cochran and Cowley 24

First-principles calculations of lattice dynamics and thermal properties of polar solids

“…It was seen that the spurious imaginary phonon frequencies in SrTiO 3 and EuTiO 3 disappear, resulting in a remarkably good agreement with experiments. A similar idea was used for Mott-Hubbard insulators MnO and NiO, 66 i.e., the dynamic matrices with the ideal cubic symmetry recovered from the distorted antiferromagnetic structures, the LO-TO splittings estimated using the mixedspace approach, and the strong electron correlations accounted for by the GGA+U method, 59 which produced accurate phonon dispersions for MnO and NiO. For room temperature multiferroic BiFeO 3 , 67 the challenge in calculating its phonon properties is due to the fact that BiFeO 3 is a Mott-Hubbard insulator with band gap 2.5 eV, involving a polar effect and strong correlation among the d electrons of Fe.…”

Phonon dispersion inSr2RuO4studied by a first-principles cumulative force-constant approach

“…In using the finite difference approach or supercell approach, inaccuracies are thought to arise from the truncation of the force constants. 19,20 This is not completely true as demonstrated by our recent works for the calculations of phonon properties for polar materials 14 of ␣-Al 2 O 3 , MgO, c-SiC, and h-BN, and the calculations of the phonon dispersions for Mott-Hubbard insulators 13 of NiO and MnO. At this point, we want to clarify some important aspects of the cumulative force-constant approach.…”

“…In this work, we report the calculated phonon frequencies for Sr 2 RuO 4 using the real-space cumulative force-constant approach, [11][12][13][14] which will be briefed below in Eqs. ͑1͒ and ͑2͒.…”

Spin-phonon coupling in antiferromagnetic nickel oxide

“…The calculated TO mode splitting at the C point of 7 cm À1 depends on the BZ direction, and it is close to literature values. 43,50 The calculated frequencies of the LO 0 and LO modes are at 535 cm À1 and 571 cm À1 , respectively. Three of the calculated C-point phonon energies agree well with the UV Raman peaks, while the TO 0 Raman peak at 413 cm À1 has no corresponding calculated energy at C. A comparison of the calculated LO and TO frequencies in Figs.…”