DFT + U study of the structural and electronic properties of the ferromagnetic and antiferromagnetic ordering in the PbS-based ternary alloys Pb1−xEuxS (x = 0.25, 0.50, 0.75 and 1)

We use first-principles full-potential method to study the structural and electronic properties of the ferromagnetic (FM) and antiferromagnetic (AF) ordering in the PbS-based ternary alloys Pb1−xEuxS (0 ≤ x ≤ 1). It is shown that the generalized gradient approximation (GGA) functional of DFT in its standard form is not sufficient for obtaining the correct physical interpretation of the binary PbS and EuS compounds and, therefore, the calculations have been extended by considering spin-orbit coupling (SOC) in the Pb atoms and by treating strongly localized f electrons of Eu by the self-interaction correction (SIC) scheme. The Wu and Cohen (WC) generalized gradient approximation (GGA) functional has been used for structural optimization, whereas the GGA parameterization scheme formulated by Engel and Vosko (EV) has also been utilized for calculating the electronic properties of all the compounds. The experimental value of Coulomb parameter (Uf-expt.) within the SIC provide good description for the structural properties of all compounds but fails to predict an accurate EuS energy band structure. A comparison of the results obtained using the WC GGA + SOC + U and EV GGA + SOC + U shows that the later deliver much better band structure profiles of the ferromagnetic EuS and non-magnetic PbS. The ternary alloys constructed by substituting Eu for the Pb atoms in the rocksalt PbS have been used for computing the structural and electronic properties of FM and AF ordering in the Pb1−xEuxS. The stability of the alloys with respect to two magnetic orders has been analyzed and the effect of FM and AF coupling on the electronic properties of the alloys are carefully studied. In particular, the variation of the degree of contribution from the various electronic energy states from the different elements in the alloys has been elucidated in terms of the total and partial density of states for all the composition ranges. Importantly, our results predict that the ternary Pb1−xEuxS alloys have a direct band gap nature and AF is the preferred magnetic order.

Electronic band structures of antiferromagnetic Pb1−xEuxS (0.25 ≤ x ≤ 0.75 alloys:Figure optionsDownload as PowerPoint slideHighlights
► Structural properties of Pb1−xEuxS in the FM and AF magnetic ordering are computed.
► Shortcomings in standard DFT simulations for PbS and EuS are analyzed and overcome.
► Electronic properties of Pb1−xEuxS alloys estimated using appropriate GGA schemes.
► Performance of simple and extended GGA functional is compared.
► Stability in FM and AF ordering and effects on band structure and DOS predicted.