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Role of spin-orbit coupling on crystal-field splitting and phase-stability of rare-earth based layered intermetallic

Layered and incommensurate heterostructures have attracted much attention for the occurrence of superconductivity and charge density waves with the possibility of intercalating foreign atoms. However, lanthanide-based heterostructures where (Eu x Sm 1-x )S and TaS 2 are alternatively stacked have been scarcely investigated. In this work, we performed phase stability, bonding behavior and electronic-structure analysis of (Eu x Sm 1-x )TaS 3 using first-principles density-functional theory methods. Our phase stability analysis suggests 50 at.% solubility of Eu in (Eu x Sm 1-x )TaS 3 compared to Eu solubility in all proportions in cubic SmS. The instability of Eu beyond 50 at.% in (Eu x Sm 1-x )TaS 3 was attributed to higher density of Eu-4f states at the Fermi-level. Based on band position calculated from spin-orbit coupling effect, we constructed a qualitative schematic of possible crystal-field analysis. The local change in bond-length and bond-angle around Eu-S in (Eu x Sm 1-x )TaS 3 correlate well with our crystal-field analysis. We believe that quantum mechanical insights provided in this work will be useful to understand other complex heterostructures.

36 MATERIALS SCIENCE↗

Materials Data on EuS by Materials Project

EuS is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Eu2+ is bonded to six equivalent S2- atoms to form a mixture of edge and corner-sharing EuS6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Eu–S bond lengths are 2.92 Å. S2- is bonded to six equivalent Eu2+ atoms to form a mixture of edge and corner-sharing SEu6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

Materials Data on EuS by Materials Project

EuS is Tetraauricupride structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Eu2+ is bonded in a body-centered cubic geometry to eight equivalent S2- atoms. All Eu–S bond lengths are 3.08 Å. S2- is bonded in a body-centered cubic geometry to eight equivalent Eu2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on EuS3 by Materials Project

EuS3 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Eu2+ is bonded to twelve S+0.67- atoms to form distorted EuS12 cuboctahedra that share corners with four equivalent EuS12 cuboctahedra, edges with eight equivalent EuS12 cuboctahedra, edges with sixteen equivalent SEu4S8 cuboctahedra, faces with four equivalent EuS12 cuboctahedra, and faces with eight equivalent SEu4S8 cuboctahedra. There are four shorter (2.77 Å) and eight longer (3.20 Å) Eu–S bond lengths. There are two inequivalent S+0.67- sites. In the first S+0.67- site, S+0.67- is bonded to four equivalent Eu2+ and eight S+0.67- atoms to form distorted SEu4S8 cuboctahedra that share corners with twelve equivalent SEu4S8 cuboctahedra, edges with eight equivalent EuS12 cuboctahedra, edges with eight equivalent SEu4S8 cuboctahedra, faces with four equivalent EuS12 cuboctahedra, and faces with ten equivalent SEu4S8 cuboctahedra. There are four shorter (2.77 Å) and four longer (3.20 Å) S–S bond lengths. In the second S+0.67- site, S+0.67- is bonded in a square co-planar geometry to four equivalent Eu2+ and eight equivalent S+0.67- atoms.

36 MATERIALS SCIENCE↗

Materials Data on Eu3S by Materials Project

Eu3S crystallizes in the hexagonal P6_3/mmc space group. The structure is one-dimensional and consists of two Eu3S ribbons oriented in the (0, 0, 1) direction. Eu is bonded in a distorted L-shaped geometry to two equivalent S atoms. Both Eu–S bond lengths are 2.95 Å. S is bonded to six equivalent Eu atoms to form distorted face-sharing SEu6 pentagonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on EuS2 by Materials Project

EuS2 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two inequivalent Eu3+ sites. In the first Eu3+ site, Eu3+ is bonded in a 9-coordinate geometry to nine S+1.50- atoms. There are a spread of Eu–S bond distances ranging from 2.83–3.32 Å. In the second Eu3+ site, Eu3+ is bonded in a 9-coordinate geometry to nine S+1.50- atoms. There are a spread of Eu–S bond distances ranging from 2.84–3.32 Å. There are four inequivalent S+1.50- sites. In the first S+1.50- site, S+1.50- is bonded in a 5-coordinate geometry to four Eu3+ and one S+1.50- atom. The S–S bond length is 2.08 Å. In the second S+1.50- site, S+1.50- is bonded in a 5-coordinate geometry to four Eu3+ and one S+1.50- atom. The S–S bond length is 2.08 Å. In the third S+1.50- site, S+1.50- is bonded to five Eu3+ atoms to form a mixture of distorted corner and edge-sharing SEu5 trigonal bipyramids. In the fourth S+1.50- site, S+1.50- is bonded to five Eu3+ atoms to form a mixture of distorted corner and edge-sharing SEu5 trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on Eu2S3 by Materials Project

Eu2S3 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Eu3+ sites. In the first Eu3+ site, Eu3+ is bonded to seven S2- atoms to form distorted edge-sharing EuS7 pentagonal bipyramids. There are a spread of Eu–S bond distances ranging from 2.81–2.98 Å. In the second Eu3+ site, Eu3+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Eu–S bond distances ranging from 2.83–3.09 Å. There are three inequivalent S2- sites. In the first S2- site, S2- is bonded to five Eu3+ atoms to form a mixture of distorted edge and corner-sharing SEu5 trigonal bipyramids. In the second S2- site, S2- is bonded to five Eu3+ atoms to form a mixture of distorted edge and corner-sharing SEu5 square pyramids. In the third S2- site, S2- is bonded in a 5-coordinate geometry to five Eu3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on EuS2 by Materials Project

EuS2 crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. Eu3+ is bonded in a 9-coordinate geometry to nine S+1.50- atoms. There are a spread of Eu–S bond distances ranging from 2.84–3.14 Å. There are two inequivalent S+1.50- sites. In the first S+1.50- site, S+1.50- is bonded in a 8-coordinate geometry to four equivalent Eu3+ and four equivalent S+1.50- atoms. All S–S bond lengths are 2.76 Å. In the second S+1.50- site, S+1.50- is bonded to five equivalent Eu3+ atoms to form a mixture of distorted corner and edge-sharing SEu5 trigonal bipyramids.

36 MATERIALS SCIENCE↗