Is it possible to stabilize the 1144-phase pnictides with tri-valence cations?

A lately discovered 1144 phase has generated significant interest for its high superconducting temperatures, disorder-free doping, and various chemical substitutions. However, it has only been found in iron arsenides ($AB{\mathrm{Fe}}_4{\mathrm{As}}_4$), and cations are limited to +1 or +2 valence states (e.g., alkali metals, alkaline earth elements, and Eu). Whether more 1144 phases could be stabilized and whether intriguing properties exist are questions of general interest. In this work, we investigate 1144 iron and cobalt arsenides with tri-valence cations (La, Y, In, Tl, Sm, Gd). We study phase stability among other competing phases: 122 solution phase and phase decomposition. With La as the cation, we predict room-temperature stable 1144 structures: $\mathrm{La}A{\mathrm{Fe}}_4{\mathrm{As}}_4$ ($A=\mathrm{K}$, Rb, and Cs). Other La-contained 1144 structures tend to form solution phase. The solubility of La is estimated and compared with the experiment. By contrast, we do not find stable 1144 structures with Y as the cation. For In and Tl as cations, two 122-phase compounds are remarkably stable: ${\mathrm{InCo}}_2{\mathrm{As}}_2$ and ${\mathrm{TlCo}}_2{\mathrm{As}}_2$, which adds to our knowledge about the In(Tl)-Co-As phase diagram. Stable 1144 phases are found in ${\mathrm{InKCo}}_4{\mathrm{As}}_4$ and ${\mathrm{InRbCo}}_4{\mathrm{As}}_4$. With Sm and Gd as cations, 1144- or 122-phase iron arsenides are generally unstable. Among structures investigated, we recognize two critical factors for 1144-phase stability: size effect and charge balance, which yields a merging picture with the rule found in previous 1144 systems. Moreover, $\mathrm{La}A{\mathrm{Fe}}_4{\mathrm{As}}_4$ ($A=\mathrm{K}$, Rb, and Cs), ${\mathrm{InCo}}_2{\mathrm{As}}_2$, and ${\mathrm{TlCo}}_2{\mathrm{As}}_2$ are exhibiting semimetal features and a two-dimensional Fermi surface, similar to iron superconductors.

Figure 1

Crystal structures involved in this work. (a) The 122/1144 phase. The 122 phase with $XY$ sites being occupied by the same cation. 1144 phase with $X$ and $Y$ being occupied by different cations. (b) InAs; (c) XAs ($X=\mathrm{La}$, Y, Gd, Sm); (d) $\alpha$ phase of Tl or Co; (e) CoAs; (f) ${\mathrm{Fe}}_2\mathrm{As}$. The space group is labeled for each structure.

Figure 2

The phase diagram of ternary alloys. (a) X-Fe-As ($X=La$, Y, Sm, and Gd); (b) In-Co-As; (c) Tl-Co-As. The known thermodynamically stable phase is denoted by blue dots on the graph. The 122 phase is designated as the orange dot.

Figure 3

$\mathrm{\Delta }H$ dependence on atomic radius of cations in several La- and Y-contained 1144 structures. Positive $\mathrm{\Delta }H$ favors phase decomposition, colored in blue, while negative $\mathrm{\Delta }H$ favors 1144 phase, colored in red. Evidently, $\mathrm{\Delta }H$ decreases as the cation radius increases. Thus, the 1144 phase is better stabilized with larger cations.

Figure 4

(a) Band structure of ${\mathrm{LaRbFe}}_4{\mathrm{As}}_4$. (b) Zoom-in of (a), in which the inset shows the primitive tetragonal B.Z. In (a) and (b), there are six bands crossing the Fermi level near the $\mathrm{\Gamma }$ point and four bands near the M point. (c) and (d) The band structures of ${\mathrm{LaKFe}}_4{\mathrm{As}}_4$ and ${\mathrm{LaCsFe}}_4{\mathrm{As}}_4$.

Figure 5

(a)–(c) Fermi surface (shown as the black color) in the $k_z=0$ plane for ${\mathrm{LaKFe}}_4{\mathrm{As}}_4$, ${\mathrm{LaRbFe}}_4{\mathrm{As}}_4$, and ${\mathrm{LaCsFe}}_4{\mathrm{As}}_4$. The color scale represents the energy difference between the nearest band to the Fermi level. (d)–(f) Fermi surface of the three systems in the $k_x=0$ plane. (g)–(i) Fermi surface of ${\mathrm{RbFe}}_2{\mathrm{As}}_2$, ${\mathrm{CaRbFe}}_4{\mathrm{As}}_4$, and ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ in the $k_z=0$ plane. The color bar is interpolated linearly in energy.

Figure 6

DOS and projected DOS of (a) ${\mathrm{InCo}}_2{\mathrm{As}}_2$, (b) ${\mathrm{TlCo}}_2{\mathrm{As}}_2$, (c) ${\mathrm{RbFe}}_2{\mathrm{As}}_2$, and (d) ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. The band structure of (e) ${\mathrm{InCo}}_2{\mathrm{As}}_2$ and (f) ${\mathrm{KInCo}}_4{\mathrm{As}}_4$.

Figure 7

The Fermi surface of ${\mathrm{InCo}}_2{\mathrm{As}}_2$ [(a), (c), and (e)] and ${\mathrm{TlCo}}_2{\mathrm{As}}_2$ [(b), (d), and (f)] in the $k_z=0$, $k_y=0$, and $k_y=0.5$ plane. The color scale represents the energy difference between the nearest band to Fermi level. In calculating these Co arsenides, we have adopted the same supercell of $2\times 2\times 1$ as Fe arsenides.