Eur. Phys. J. B (2016) 89: 256
https://doi.org/10.1140/epjb/e2016-70430-x

Regular Article

Electronic and optical properties of β′-Tb₂(MoO₄)₃: DFT+U approach

¹ New Technologies – Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic
² School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis, Malaysia

^a e-mail: maalidph@yahoo.co.uk

Received: 13 July 2016
Received in final form: 31 August 2016
Published online: 28 November 2016

Abstract

The ground state properties of β′-Tb₂(MoO₄)₃ are investigated using the density functional theory plus U-Hubbard Hamiltonian. To ascertain the influence of the spin-polarization on the ground state properties of orthorhombic β′-Tb₂(MoO₄)₃, we have performed spin-polarization calculations and the spin-polarized electronic band structure for spin-up (↑) and spin-down (↓) are calculated. It has been found that for spin-up (↑) and spin-down (↓) the β′-Tb₂(MoO₄)₃ compound possesses indirect energy band gap, as the valence band maximum (VBM) is located at Y point of the Brillouin zone (BZ) and the conduction band minimum (CBM) at the center of the BZ. The calculated value of the band gap is 3.61 eV for spin-up (↑) and spin-down (↓), and it is in close agreement with the measured one (3.76 eV). It is clear that the electronic band structure for spin-up (↑) and spin-down (↓) cases presents identical configuration. Therefore, we can conclude that the spin-polarization has identical influence on the ground state properties of β′-Tb₂(MoO₄)₃. To ascertain this observation, we have presented and explained the necessary ingredients of the calculated total and atom-resolved density of states. It has been noticed that the calculated total density of states (TDOS) for spin-up (↑) and spin-down (↓) cases are identical confirming that the spin-polarization has identical influence on the ground state properties of β′-Tb₂(MoO₄)₃. For more details, in order to have deep insight into the electronic structure, we have presented the atom-resolved density of states which show identical features for spin-up (↑) and spin-down (↓). The angular momentum projected density of states (PDOS) helps to identify the angular momentum character of the various structures. To obtain more details about the electronic structure and, hence, the ground state properties, the complex first-order linear optical dispersion is calculated for spin-up (↑) and spin-down (↓) cases to ascertain the influence of the spin-polarization on the ground state properties.