Construction of $A-B$ heterolayer intermetallic crystals: Case studies of the 1144-phase TM-phosphides $\mathit{AB}$(TM)${}_4{\mathrm{P}}_4$ (TM=Fe, Ru, Co, Ni)

The discovery of the 1144 phase, e.g., ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, creates opportunities to build novel intermetallics with alternative stacking of two parent compounds. Here we formalize the idea by defining a class of bulk crystalline solids with $A\text{−}B$ stacking (including 1144 phases and beyond), which is a generalization of heterostructures from few-layer or thin-film semiconductors to bulk intermetallics. Theoretically, four families of phosphides $\mathit{AB}$(${\mathrm{TM})}_4{\mathrm{P}}_4$ (TM=Fe, Ru, Co, Ni) are investigated by first-principles calculations, wherein configurational, vibrational, and electronic degrees of freedom are considered. It predicts a variety of stable 1144 phases (especially Ru- and Fe-phosphides). Stability rules are found and structural/electronic properties are discussed. Experimentally, we synthesize high-purity ${\mathrm{CaKRu}}_4{\mathrm{P}}_4$ as a proof of principle example. The synthetic method is simple and easily applied. Moreover, it alludes to a strategy to explore complex multicomponent compounds, facilitated by a phase diagram coordinated by collective descriptors.

Figure 1

(a) The crystal structure of the 1144 phase. If $A$ and $B$ sites are occupied by the same cations, it becomes the 122 phase. (b) Structure parameters with broken glide symmetry. (c) Charge transfer from cation layers to TM layers. (d) Schematic charge distribution of ${\mathrm{KCaRu}}_4{\mathrm{P}}_4$. The layers of ${\mathrm{K}}^{+}$ and ${\mathrm{Ca}}^{2+}$ take positive charges; each TM layer takes $-1.5\mathrm{e}$ per unit cell. Pn stands for pnictogen and TM stands for transition metals

Figure 2

Lattice parameters $a$ (red) and $c$ (blue) of the tetragonal unit of 122 phases. Filled and open points represent experimental and theoretical values. Missing points are unstable or not reported yet. Experimental results are cited from Springer Materials data base.

Figure 3

(a) $\mathrm{\Delta }H$ (proportional to the hexagon size) plotted against two descriptors: $\mathrm{\Delta }a=-\mid a_{122}^A-a_{122}^B\mid , \mathrm{\Delta }c=\mid c_{122}^A-c_{122}^B\mid$, where $a$ and $c$ are lattice parameters of the two parent 122 phases $A{\left(\mathrm{TM}\right)}_2{\mathrm{P}}_2$ and $B{\left(\mathrm{TM}\right)}_2{\mathrm{P}}_2$. The most promising systems are highlighted with solid hexagons and the corresponding cations are denoted. (b) Temperature dependence of free energy $\mathrm{\Delta }G=G_{122\left(s\right)}-G_{1144}$. ($\mathrm{\Delta }G>0$ 1144 phase is stable.) The dashed line only includes $S_{\mathrm{conf}}$. The blue line further includes $S_{\mathrm{vib}}$ and $S_e$.

Figure 4

The formation enthalpy $\mathrm{\Delta }H$ of (a) $\mathit{AB}{\mathrm{Fe}}_4{\mathrm{As}}_4$ with $AB$ being alkali metal (Ai) and alkaline earth (Ae), (b) of $\mathit{AB}{\mathrm{Ru}}_4{\mathrm{P}}_4$. Each spot represents a particular pair of $A\text{−}B$. Color scales represent $\mathrm{\Delta }H$, and red means stable 1144 phase (unit: meV/atom). $\mathrm{I}+\mathrm{II}$ means alkali metal (AI) plus alkaline earth (AII); $\mathrm{II}+\mathrm{II}$ means $\mathrm{AII}+\mathrm{AII}$; $\mathrm{I}+\mathrm{II}$ means $\mathrm{AI}+\mathrm{AII}$. Eu, La, etc., mean the specific rare earth (RE) combined with another AI or AII. The $\mathrm{\Delta }H$ of subgroups (c) $\mathrm{I}+\mathrm{II}$ and (d) $\mathrm{II}+\mathrm{III}$. Other subgroups are shown in [39]. The shapes of points are consistent with the legend in (b). (e)(f) $\mathrm{\Delta }H$ contribution from $\mathrm{\Delta }{H}_a, \mathrm{\Delta }{H}_c$, and $\mathrm{\Delta }{H}_0$. The dashed line represents the magnitude $|\mathrm{\Delta }{H}_0|$. Note that $\mathrm{\Delta }{H}_0$ is positive for (e), but negative for (f).

Figure 5

[(a)–(c)] FS in $k_z=0$ plane (unit for k: $1/a$, orbitals are colored). The main nesting vector is denoted (the nesting vector is from origin to the highest peak of $\chi \left(\mathbf{q}\right)$). [(d)–(f)] Noninteracting electronic susceptibility $\chi \left(\mathbf{q}\right)$ (arbitrary units with $\chi \left(0\right)$ normalized to unity). [(g) and (f)] FS of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ and ${\mathrm{CaFe}}_2{\mathrm{As}}_2$. The BZ is based on the tetragonal cell [Fig. 1], which contains ten atoms. Dashed lines represent an alternative BZ based on primitive cell of 122 phases (containing five atoms) projected to $k_z=0$ plane (octagon), where $\overline{X}$ is equivalent to $M$ point for 1144 phases.

Figure 6

(a) The $c$-lattice parameters (calculation) for various 1144 phases (solid) and its parent phases (hollow). The solid spot is on the average of the two hollow spots. The full list of $AB$ (from left to right): KRb, KCs, RbCs, KCa, RbCa, CsCa, KSr, RbSr, CsSr, CaSr, KBa, RbBa, CsBa, CaBa, SrBa, (K, Rb, Cs, Ca, Sr, Ba)Ln (Ln=La, Ce, Pr, Eu). For brevity, only $B$ is listed on section boundaries. (b) The middle-point rule fails for $a$-lattice parameters, as considerable deviations are observed for CsCa, RbBa, CsBa, etc. (c) Linear fitting of $\mathrm{\Delta }c$ with $\mathrm{\Delta }R$. The slopes of different 1144-systems are quite close: $\mathit{AB}{\mathrm{Fe}}_4{\mathrm{As}}_4$: 4.16, $\mathit{AB}{\mathrm{Ru}}_4{\mathrm{P}}_4$: 4.90, $\mathit{AB}{\mathrm{Fe}}_4{\mathrm{P}}_4$: 4.78, $\mathit{AB}{\mathrm{Co}}_4{\mathrm{P}}_4$: 5.69. The inset shows the fitting with grouping cation combinations, not distinguishing TM. The slopes are 4.91, 5.00, and 4.61 for $\mathrm{I}+\mathrm{II}, \mathrm{I}+\mathrm{III}$, and $\mathrm{II}+\mathrm{III}$ cations, respectively.

Figure 7

[(a) and (b)] Powder XRD pattern and Refinement of ${\mathrm{CaRu}}_2{\mathrm{P}}_2$ and ${\mathrm{KRu}}_2{\mathrm{P}}_2$. (c) PXRD and Rietveld refinement results for the ${\mathrm{CaKRu}}_4{\mathrm{P}}_4$. (003), (005), and (007) peaks are indicated by the red arrows. The observed profile is indicated by red circles and the calculated profile by the solid line. Bragg peak positions are indicated by vertical tics, and the difference diffractogram is in blue.

Figure 8

Examples of constructing heterocrystals. [(a) and (b)] Two types of 12442 phase. Differences: type A: four layers of Fe-As and two layers of composite cation layers ${(\mathrm{Ca}-\mathrm{F})}^{+}$ per unit cell; type B: two layers of Fe-As and four layers of cation layers ${(\mathrm{Pr}-\mathrm{O})}^{+}$ (c) 22241 phase.

Figure 9

(a) Traditional phase diagram with $N=3$ (triangle) and 4 (tetrahedron). The complexity of phase diagram will quickly increase with ingredient number $N$. Stable phases only sparsely distribute, leaving phase separation in most regions. [40] (b) Formation enthalpy of 1144 phases $AB{\mathrm{Ru}}_4{\mathrm{P}}_4, AB{\mathrm{Fe}}_4{\mathrm{P}}_4, AB{\mathrm{Fe}}_4{\mathrm{As}}_4$ (color scales, meV/atom) vs collective descriptors as coordinates, with which the phase diagram could include compounds with flexible compositions and concentrations. It has a clear separation between the stable (red) and the unstable (blue) and is a generalization of phase diagram in Ref. [4].