X-ray diffraction experiments, luminescence measurements and first-principles GGA + U calculations on YTaO₄

Highlights

• GGA + U calculation shows that a band gap of 5.1 eV of the host lattice can be accommodated.

• The composition and structure of the valence and conduction bands of the tantalate system are calculated.

• The calculated DOS compared well with the excitation spectra.

Abstract

The structural and electronic properties of yttrium tantalate (YTaO₄) crystal are studied using experimental and first-principles total energy calculations. The band gap of the host lattice from absorption and luminescence experiment is measured to be 5.1 eV. This is close to 5.14 eV reproduced by means of GGA + U approach. In our calculation, we tune both the Hubbard energy U and the exchange parameter J to reproduce the energy gap measured experimentally. It is found that the Hubbard energy U plays a major role in reproducing the experimentally measured energy gap but the exchange parameter J does not. We also calculate the density of states (DOS) using the optimized U to interpret the experimentally measured luminescence spectra. Both the experimental and DOS calculation show that the valence band of tantalate (Ta) system is mainly composed of oxygen (O) 2p states. The lower conduction band is mainly composed of Ta 5d states, while the upper conduction band involves contribution mainly from yttrium (Y) 4d states, with the middle conduction band mainly a mixture of Ta and Y states.

Introduction

Undoped YTaO₄ is well known as a self-activated phosphor. Historically, Ferguson [1] in 1957 was the first to describe both natural fergusonite (a yttrium niobium-tantalate) and synthetic YTaO₄ correctly, where they crystallized in monoclinic symmetry with the space group 15 (I2/a). YTaO₄ exhibits three crystal structures. At high temperature the tetragonal form (T, space group 88) with scheelite structure distorts via a second-order phase transition to monoclinic (M, space group 15) structure having the fergusonite structure. Another monoclinic structure, called M′ (space group 13), can be synthesized directly at lower temperatures (below 1400 °C). M′ transforms to T at approximately 1450 °C and then to M upon cooling.

As we all know, performances of phosphors and luminescence properties strongly depend on their crystal and electronic structures which can be understood via quantum mechanical calculations. Two main issues pertaining to the atomistic calculation of YTaO₄ are the emission spectrum of the host lattice and charge transfer transitions [2], [3]. Despite the fact that YTaO₄ has seen much potential commercial values, there is relatively little calculation work done on the host material, not to mention the activator-doped lattice as a whole. Some fundamental questions concerning host lattice emission and charge transfer transitions in YTaO₄ remain to be answered.

This paper is dedicated to investigate the electronic properties of YTaO₄ through the study of its density of states (DOS) and band structure using experimental and first-principles calculations. To the best of our knowledge, there is no offer of any explanation in the literature to the apparent discrepancy between the experimental spectra and calculated DOS [4], [5], [6], [7]. The experimental spectra recorded a 5.1 eV band gap between conduction band and valence band while the gaps from first-principles calculations are 4.2 eV (without scissor operator) and 4.8 eV (with scissor operator) [3], [4]. Thus, there is a discrepancy of 0.9 eV (without scissor operator) between experiment measurement and first-principles calculation. Scissor operator is applied to include the effects of self-energy and excitonic shift only. Therefore, the band gap issue cannot be resolved even with scissor operator. This further leads to the incapability (by simulation) to reproduce the DOS plot as obtained in experiment. The electron configurations of the host lattice atoms are Y[5s²4d¹], Ta[5d³6s²] and O[2s²2p⁴]. The 2p-orbital from the oxygen contributes to the valence band while Ta and Y atoms have more impact on the conduction band. Ta-5d electrons contribute to the profile of lower conduction band while upper conduction band receives contribution mainly from Y-4d orbitals. However, the total contributions from all these atoms obtained via DOS calculation fail to account for the DOS inferred from the experiments. This provides the ground for us to believe that previous reports might have overlooked the contribution of certain quantum mechanical interactions, specifically those from the d-electrons among the atoms in the host lattice.

Density functional theory (DFT) is a widely used method to calculate the ground state energy of a system by mapping a multiple-electron system into a single electron problem. By incorporating exchange-correlation such as local (spin) density approximation (L(S)DA) and generalized gradient approximations (GGA), DFT has attained much success in deriving the ground state electronic structure properties. However when it comes to systems with highly correlated electrons such as that possess d- or f-electrons, computations with L(S)DA or GGA reveals their insufficiencies. They fail to describe magnetic insulator such as 3d-transition-metal oxides or Mott insulator. Despite being able to reproduce the ground state structures for the magnetic NiO and MnO series, the theory wrongly predicted Mott insulators as metal. In addition, the gaps in NiO and MnO are predicted to be too small in magnitude compared to photoemission experiments [8]. Many attempts have been made to improve the L(S)DA and GGA calculations on systems with d- or f-electrons. One of the most successful improvements is the ‘+U’ approach (i.e., L(S)DA + U and GGA + U). As pointed out by Anisimov et al. [9], [10], the L(S)DA behaves like a weak-coupling mean-field theory. Anisimov et al. generalized the L(S)DA method by proposing the L(S)DA + U approach to strongly correlated systems. In this approach effective on-site interactions are introduced to the existing Hamitonian to better account for the orbital dependence of the Coulomb and exchange interactions of the strongly correlated (i.e., d- and f-) electrons. The basic idea of L(S)DA + U (which also applies to GGA + U) calculation is described as followed [9], [10], [11]: For delocalized s- and p-electrons in the atom, only L(S)DA calculations are involved. For localized d- or f-electrons, on-site d–d column interaction or Hubbard-like term is used instead of the averaged coulomb energy. The d- or f-electron interactions can be calculated via this ‘+U’ approach quite accurately. Many DFT packages, such as WIEN2k [12], provide computational functionality to calculate the ‘+U’ effect conveniently.

The discrepancy between the published experimental results on the energy band gap of YTaO₄ (from luminescence excitation spectra and absorbance data) and the value obtained from DFT are quite significant. One of the main goals of this work is to address this issue by reproducing the experimentally measured energy band gap through GGA + U calculations using the DFT package WIEN2k [12]. To this end, we also prepared YTaO₄ sample and carried out experimental measurements (X-ray diffraction, UV and VUV excitation luminescence) on them. DOS obtained from the GGA + U calculation is then used to provide insight into the origin of the features measured in the excitation spectra. The DOS profile obtained via the scissor operator approach [3], [4], [13], despite being able to reproduce the right band gap, does not match well with the experimentally measured spectrum. On the other hand, in the ‘+U’ approach the band gap is tuned to experimental value, and the resultant DOS profile is found to match well with the UV and VUV spectrum. Essentially, we need to have the right band gap and at the same time the correct DOS profile. The ‘+U’ approach, as exemplified by our work, is a plausible way to achieve just that.

Experimental and first-principles calculation procedures will be explained in Section 2. Section 3 is devoted to the discussion on experimental results, DFT calculations and their complementary interpretations. Short summary is given at the end of this work.