Ab initio study of doping effects in the 42214 compounds: A new family of layered iron-based superconductors

We present a systematic DFT-GGA theoretical characterization of the ${\mathrm{RE}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_{4-y}{\mathrm{F}}_y$ family of compounds (conventionally called 42214) as a function of a set of key tuning parameters: rare earth (RE = Pr, Sm, and Gd), Te content, oxygen $\to$ fluorine substitutional doping, and external pressure. We focus our discussion on the effect of these parameters on magnetic stability and on the nonmagnetic electronic structure, as most relevant aspects related to the occurrence of superconductivity. To uncover the complexity of the 42214 crystal structure, the electronic analysis is based on an unfolding procedure that allows us to observe the behavior of the hole and electron pockets of the Fermi surface and of the nesting function. We complete the present study with the characterization of a related hypothetical compound having Se substituting for Te. Our results show that this peculiar compound family offers very good opportunities to properly harness material properties; based on our results, we infer that suitably tuning a variety of parameters, as those examined here, improved superconducting properties could be achieved.

Figure 1

Left: Crystal structure of the 42214 compounds: 3D view of the tetragonal cell. Here red, green, yellow, blue, and purple circles represent Fe, As, RE, O, and Te atoms, respectively. Right: (a) Stability of the AFM2 ground state phase and (b) relative magnetic moment ${\mu }_{\text{Fe}}$ as a function of the RE covalent radius (R = 1.61, 1.62, 1.65 Å for Gd, Sm, and Pr, respectively) and at different Te content ($1-x=50\%$, 75%, and 100%). (c) Dependence of the Fe-magnetic moment (${\mu }_{\text{Fe}}$) on the As height ($h_{\text{As}}$),

Figure 2

(a) Band structure projected on the $p$ orbitals of Te calculated for ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{TeO}}_4$ in the nonmagnetic state. (b)–(d) Density of electronic states for ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$, respectively, for $1-x=100\%$, 75%, and 50%, respectively. The shaded area (red, green, and blue) is the total density of states. Black and dashed-gray lines are the 1-Te projected density of states. Black is used for Te atoms belonging to a fully occupied Te layer; dashed gray for Te atoms in a layer with Te vacancies (50%). All 1-Te projections are multiplied by a factor of 20 for plotting convenience.

Figure 3

Band structures projected on the basal plane of the 1Fe bct unit cell for the ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$ ($1-x=100\%$, 75%, and 50% from top to bottom panels, respectively) calculated in the nonmagnetic state and at their respective equilibrium structure.

Figure 4

Fermi surface (top panels) and nesting function (bottom panels) projected on the basal plane of the 1Fe bct unit cell for ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$ ($1-x=100\%$, 75%, and 50%, panels from left to right, respectively) at their respective equilibrium structure. The color intensity is proportional to the value of the nesting function normalized to its value at the zone center.

Figure 5

Structural orthorhombic in-plane parameters ($a,b$) of ${\mathrm{Sm}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$ compounds as a function of external hydrostatic pressure at different Te concentrations ($1-x=50\%$, 75%. and 100%).

Figure 6

Pressure dependence of the structural and magnetic properties of ${\mathrm{Sm}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$ compounds at different Te contents ($1-x=50\%$ red, 75% green, and 100% blue). (a) Stability of the AFM solution as compared to the nonmagnetic calculation; (b) lattice structural $c$ parameter; (c) average magnetic moment at the iron site ${\mu }_{\text{Fe}}$; and(d) average height of the As atom with respect to the iron plane.

Figure 7

Top panel: Stability of the magnetic ground state (AFM2) for the ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_{4-y}{\mathrm{F}}_y$ as a function of F concentration ($y$) at different Te contents ($1-x=100\%$, 75%, and 50%). Multiple data at fixed concentration indicate results for different relative position of dopants. Lines are guide to the eye.

Central panels: Fermi surfaces at 25% of F doping and different Te contents ($1-x=100\%$, 75%, and 50% panels from left to right). Bottom panels: Corresponding nesting function.

Figure 8

(a) As height, (b) Fe magnetic moment, and (c) stability of the AFM2 ground state phase with respect to the nonmagnetic one, as a function of Se concentration (dashed line) in the ${\mathrm{RE}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Se}}_{1-x}{\mathrm{O}}_4$ (RE = Pr, Sm, and Gd) compounds. The same physical quantities in ${\mathrm{RE}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{1-x}{\mathrm{O}}_4$ (RE = Pr, Sm, and Gd) materials are reported as a function of the Te concentration (solid lines), for comparison.

Figure 9

Band structure projected on Fe atoms of the 1Fe bct unit cell for the ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Se}}_{1-x}{\mathrm{O}}_4$ at different Se content ($1-x=100\%$, 75%, and 50%, top, central, and bottom panels, respectively) calculated in the nonmagnetic state and at their respective equilibrium structure.

Figure 10

Fermi surface (top panels) and nesting function (bottom panels) projected on the basal plane of the 1Fe bct unit cell for ${\mathrm{Gd}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Se}}_{1-x}{\mathrm{O}}_4$ for different Se content ($1-x=100\%$, 75%, and 50%, from left to right panels, respectively) at their respective equilibrium structure. The color intensity is proportional to the value of the nesting function normalized to its value at the zone center.