Modeling the role of the fluorine dopant in the magnetic phase diagram of LaFeAsO${}_{1-x}$F${}_x$ superconductors

By using first-principles calculations we clarify the origin of the doping-induced transition from a stripe-antiferromagnetic phase to a nonmagnetic phase in LaFeAsO${}_{1-x}$F${}_x$. The explicit description of the F atoms in the calculations is found to be essential for reproducing the observed phase transition. Our study shows that the concerted effects of lattice distortion and band filling arising from the dopants act to lower the energy of an unoccupied band of predominant Fe $d_{yz}$ character, until it crosses the Fermi level and the Fe magnetic moment is quenched.

Figure 1

Ball-and-stick representation of LaFeAsO${}_{1-x}$F${}_x$. (a) Top view of the Fe-As layer in the $2\sqrt{2}\times 2\sqrt{2}$ unit cell, containing 16 FeAs units [Fe and As atoms in red (dark gray) and yellow (light gray), respectively]. The stripe-antiferromagnetic spin texture of the Fe atoms in pristine LaFeAsO is shown schematically. (b) Top view of the LaO layer [La and O atoms in silver (white) and blue (black), respectively], with one O atom replaced by F [green (gray)]. In this model corresponding to $x=0.0625$ the nearest-neighbor distance between F dopants is 11.3 Å. (c) Lateral view of LaFeAsO${}_{1-x}$F${}_x$ with $x=0.5$ and the F atoms in the most symmetric arrangement. The unit cell contains 64 atoms.

Figure 2

(a) Calculated magnetic moment per Fe atom in LaFeAsO${}_{1-x}$F${}_x$ as a function of F content $x$. The red disks correspond to the explicit doping model (EDM), the open blue squares correspond to the jellium model (JM), and the black circles are for the virtual-crystal approximation (VCA). The lines are guides to the eye. A magnetic-nonmagnetic phase transition is obtained only within the EDM. (b) Variation of the As height in LaFeAsO${}_{1-x}$F${}_x$ as a function of F content $x$. The red disks, blue squares, and black circles refer to the EDM, JM, and VCA calculations, respectively, and the lines are guides to the eye. The JM and VCA calculations yield incorrect structural trends. The EDM calculations reveal a compression of the Fe-As layer upon doping.

Figure 3

Calculated magnetic moment per Fe atom in LaFeAsO${}_{1-x}$F${}_x$ vs average Fe-As layer separation in the optimized ground-state geometry (blue disks), as obtained within the explicit doping model (EDM). The dashed line is a guide to the eye. Inset: Calculated magnetic moment per Fe atom vs Fe-As layer separation for the two cases of undoped LaFeAsO (open red squares) and of LaFeAsO with additional 0.5 electrons per Fe atoms (c-JM model for $x=0.5,$ blue filled squares). The lines are guides to the eye. The calculations in the main panel and in the inset correspond to the $2\sqrt{2}\times 2\sqrt{2}$ and the $\sqrt{2}\times \sqrt{2}$ unit cells, respectively.

Figure 4

Charge density isosurfaces of doped electronic charge in LaFeAsO${}_{1-x}$F${}_x$ at $x=0.5$. Excess (defect) electronic charge is represented in black [orange (gray)]. The color code for the ball-and-stick representations is the same as in Fig. 1. (a) Jellium model (JM) with the structure of pristine LaFeAsO (Fe-As layer separation 1.35 Å). The doped electrons incorrectly fill Fe $d_{yz}$ states only. (b) Explicit doping model (EDM). In this case the optimized Fe-As layer separation is 1.20 Å. The doped electrons fill the Fe $d_{xy}$ and $d_{yz}$ states, and vacate the $d_{x^2-y^2}$ states. Additional charge rearrangement takes place in the F-doped LaO layer. (c) Simplified c-JM model where the Fe-As layer is compressed as in the EDM (separation: 1.22 Å), and extra electrons are added. The charge rearrangement in this case is very similar to the more sophisticated EDM calculation in (b).

Figure 5

Band structures of LaFeAsO${}_{1-x}$F${}_x$ within the $\sqrt{2}\times \sqrt{2}$ unit cell. The Fermi level is indicated by the blue dashed line. The unoccupied band of predominantly Fe $d_{yz}$ character discussed in the main text is highlighted in red (dotted line). (a) Pristine LaFeAsO. (b) Undoped LaFeAsO with compressed Fe-As layer. (c) c-JM model of LaFeAsO${}_{1-x}$F${}_x$ at $x=0.5$. The band dispersing upward from $\Gamma$ near the Fermi level in (a) and (b) has also $d_{yz}$ character and merges into the red dotted curve in (c) upon suppression of the magnetic order. This is the only band which is filled upon doping in the JM model, as shown in Fig. 4a.