Endohedral gallide cluster superconductors and ... - PNAS

Endohedral gallide cluster superconductors and superconductivity in ReGa5 Weiwei Xiea, Huixia Luoa, Brendan F. Phelana, Tomasz Klimczukb, Francois Alexandre Cevallosa, and Robert Joseph Cavaa,1 a Department of Chemistry, Princeton University, Princeton, NJ 08540; and bFaculty of Applied Physics and Mathematics, Gdansk University of Technology, 80-233 Gdansk, Poland

Contributed by Robert Joseph Cava, November 11, 2015 (sent for review October 12, 2015; reviewed by Malcolm R. Beasley and Danna Freedman)

We present transition metal-embedded (T@Gan) endohedral Gaclusters as a favorable structural motif for superconductivity and develop empirical, molecule-based, electron counting rules that govern the hierarchical architectures that the clusters assume in binary phases. Among the binary T@Gan endohedral cluster systems, Mo8Ga41, Mo6Ga31, Rh2Ga9, and Ir2Ga9 are all previously known superconductors. The well-known exotic superconductor PuCoGa5 and related phases are also members of this endohedral gallide cluster family. We show that electron-deficient compounds like Mo8Ga41 prefer architectures with vertex-sharing gallium clusters, whereas electron-rich compounds, like PdGa5, prefer edge-sharing cluster architectures. The superconducting transition temperatures are highest for the electron-poor, corner-sharing architectures. Based on this analysis, the previously unknown endohedral cluster compound ReGa5 is postulated to exist at an intermediate electron count and a mix of corner sharing and edge sharing cluster architectures. The empirical prediction is shown to be correct and leads to the discovery of superconductivity in ReGa5. The Fermi levels for endohedral gallide cluster compounds are located in deep pseudogaps in the electronic densities of states, an important factor in determining their chemical stability, while at the same time limiting their superconducting transition temperatures. superconducitivity

| endohedral cluster | solid state chemistry

T

he prediction of new superconductors remains an elusive goal. Although one can analyze the superconductivity, once discovered, through materials physics-based “k-space” pictures based on Fermi surfaces, energy band dispersions, and effective interactions, often it is chemists, whose viewpoint is instead from “real space” rather than k-space, who find such superconductors in the first place (1, 2). Given the difficulty in making extrapolations between the physics of superconductivity and the chemical stability of compounds that will be superconducting, there are as many strategies for finding new superconductors as there are researchers looking for them (3–5). Most such search strategies fail, because the interactions that give rise to superconductivity can also lead to competing electronic states or can be strong enough to tear potential compounds apart (6, 7). One chemical perspective for increasing the odds of finding superconductivity is to postulate that it runs in structural families. The perovskites are a well-known example of this in metal oxides, and in intermetallic compounds, the “122” ThCr2Si2 structure type is a good example (8–10). It is the discovery of these new structural families of superconductors that often leads, sometimes slowly or sometimes quickly, to advances in new superconducting materials. Here we show that a previously unappreciated chemical family, the endohedral gallium cluster phases, is a favored chemical family for superconductivity. Further, we analyze the occurrence and hierarchical structures of such phases from a molecular perspective and then use that perspective to predict the existence and structure of a previously unreported compound, ReGa5. We find that compound and discover it to be superconducting. E7048–E7054 | PNAS | Published online December 7, 2015

Endohedral Gallium Clusters and Superconductivity Elemental gallium, in group 13, is located at the Zintl border in the periodic table and is known in solid state chemistry for its tendency, due to its moderate electronegativity, to form compounds based on gallium clusters (11). (The Zintl border separates groups 13 and 14. In combination with electropositive metals, the elements in group 14 and to the right usually form compounds whose electronic structures are consistent with filled bonding, filled nonbonding, and empty antibonding levels, and therefore are electron precise, which is not generally the case for group 13 and to the left.) Previous investigations of binary alkali metal-Ga (A-Ga) solid state systems have resulted in the discovery of many new Zintl compounds, in which Gan clusters or molecules use the electrons donated from the alkali metals to satisfy their valence requirements (12). The large electronegativity differences between alkali metals and Ga always makes these AmGan Zintl compounds valence-precise semiconductors, i.e., they display a relatively large band gap between occupied and unoccupied states, motivating the investigation of Zintl compounds as good thermoelectric materials above ambient temperature (13). Structurally, the Ga atoms in AmGan systems form icosahedral (Ga12) or octahedral (Ga6) clusters, analogous to those found in borane chemistry (14). The gallium clusters in the Zintl phases are analogs to borane clusters and follow the same rules for the number of skeletal electrons required for stability. When replacing alkali metals with lanthanides or actinides (R) to form Ga-rich RmGan compounds, the electronegativity differences between R and Ga are smaller than those between the alkalis and Ga, and the semiconducting band gap diminishes—sometimes to zero to yield metallic conductivity. The formation of exo-bonds to other clusters in vertex-sharing, edge-sharing, or face-sharing cluster Significance The prediction of new superconductors remains an elusive goal. It is often chemists who find new superconductors, although it is difficult to translate the physics of superconductivity into chemical requirements for discovering new superconducting compounds. There are many strategies for finding new superconductors, one being to postulate that superconductivity runs in structural families. Here we show that a previously unappreciated structural family, the endohedral gallium cluster phases, is favored for superconductivity, and then use the understanding we develop to find a superconductor. More broadly, our work shows that molecule-based electron counting and stability rules can provide a useful chemistry-based design paradigm for finding new superconductors. Using these ideas to search for new superconductors will be of significant future interest. Author contributions: W.X. and R.J.C. designed research; W.X., H.L., and F.A.C. performed research; W.X., T.K., and R.J.C. analyzed data; and W.X., B.F.P., and R.J.C. wrote the paper. Reviewers: M.R.B., Stanford University; and D.F., Northwestern University. The authors declare no conflict of interest. 1

To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1522191112/-/DCSupplemental.

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Table 1. Selected Binary Phases with Endohedral Ga-clusters Binary compounds

Structure type

Pearson symbol

Tc (K)

Reference

V8Ga41 Mo8Ga41 Mo6Ga31 ReGa5 Rh2Ga9 Ir2Ga9 PdGa5

V8Ga41 V8Ga41 Mo6Ga31 ReGa5 Co2Al9 Co2Al9 PdGa5

hR147 hR147 mS148 oS48 mP22 mP22 tI24

— 9.8 8 2.3 2.0 2.3 —

Girgis et al. (36) Yvon (23) Yvon (23) This work Shibayama et al. (22) Shibayama et al. (22) Grin et al. (29)

APPLIED PHYSICAL SCIENCES

hierarchies and the distortion of the clusters away from ideal deltahedral symmetries can also stabilize RmGan compounds (15). Examples of the Ga clusters in these compounds can be seen in Fig. 1A. The introduction of transition metals (T) to the centers of the gallium clusters to create T@Gan endohedral clusters reduces the cluster charge and is an important path to gallide chemical stability. For example, the Ni-centered Ni@Ga10 cluster (Fig. 1A) yields the chemical stability of Na10NiGa10 (11). Of great interest for their electronic properties are the large number of thus-derived ternary A/R-T-Ga (A = alkali or alkali-earth; R = lanthanide or actinide; and T = late transition metal) compounds. An important class of superconductors has been discovered in this group. The actinide-based compound PuCoGa5, for example, is assembled from metal-centered endohedral clusters: Pu-centered Ga cuboctahedra (Pu@Ga12) and Co-centered Ga cubes (Co@Ga8) (Fig. 1 B and C) and displays a very high critical temperature Tc= 18.5 K that increases to 22 K under pressure (16). The Tc= 2.8 K superconductor Sm4Co3Ga16 similarly contains Sm@Ga12 and Co@Ga8 endohedral clusters that are isostructural with the Pu@Ga12 and Co@Ga8 clusters in PuCoGa5; because the clusters are not present in a 1:1 ratio, the hierarchical

Fig. 2. Electronic structures of Ga-cluster–based binary phases from a molecular perspective. (Left) The isolated clusters, showing for each: above, the Gan clusters and then below, the TGan endohedral clusters. (Center) The molecular energy level diagrams for the isolated Ga-clusters and the T-centered endohedral Ga-clusters, obtained using the extended Hückel theory. (Two different minimal basis sets involving Slater-type single-zeta functions for s and p orbitals and double-zeta functions for d orbitals were used.) (Right) The electronic DOS generated by VASP based on the optimized crystal structures of Mo8Ga41, Rh2Ga9, and PdGa5.

Fig. 1. Schematic structural relationships among different kinds of Gacluster compounds. (A) Ga metal reacts with alkali and alkali earth elements to yield Zintl phases such as K3Ga13, which has isolated Ga12 icosahedral clusters, and Ba5Ga6, which has Ga6 octahedral clusters. In Na10NiGa10, a transition metal (Ni)-centered endohedral Ni@Ga10 cluster is found (19). (B) The combination of Ga plus R (R = lanthanide and actinide elements) leads to the formation of polar intermetallics, for example, PuGa6, which contains Pu@Ga12 clusters (15). (C) Centering Ga-clusters with transition metals stabilizes Ga-cluster compounds such as CoGa3, which contains Co@Ga8 square antiprism clusters (38). (D) Combining T-centered and R-centered clusters forms the unconventional superconductor PuCoGa5, in which Pu@Ga12 cuboctahedra share faces with neighboring Pu@Ga12 and Co@Ga8 (cube) clusters (16). (E) Adding more Ga atoms to T-Ga systems forms other Ga-rich compounds, such as the superconductor Mo8Ga41. In this compound, Mo@Ga10 clusters are found (23).

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architecture is more complex in this compound (17). Also important as heavy fermion superconductors are the In analogs of these phases, the CeMIn5 (M = Co, Rh, Ir) family of compounds, which are iso-structural with PuCoGa5; their study has considerably illuminated the understanding of the interplay between superconductivity and magnetism (18). Fig. 1 summarizes the structural relationships described here. The electron transfer between cations and anions in the A-Ga or R-Ga systems is clearly primarily ionic due to the large electronegativity differences (19). It is much less obvious, however, to tell a priori how the electrons are transferred in Ga-rich T-Ga (T = transition metal) binary phases such as Mo 8Ga41 and PdGa5, because the electronegativities for late transition metals and gallium are similar (20, 21). Nonetheless, we can define here a set of electron counting rules and the relationships between electron counting and the hierarchical architectures of the endohedral clusters required for chemical stability through observation of the known phases. Further, we can establish an PNAS | Published online December 7, 2015 | E7049

Fig. 3. Motivation for searching for superconductors in the Re-Ga systems based on electron counting and cluster architectures. Mo8Ga41 contains vertexsharing 10-coordinate Ga-clusters; Rh2Ga9 and PdGa5 contain both vertex-sharing and edge-sharing clusters. Before the current work there were no known compounds in this family with 22 electrons per transition metal.

empirical relationship between electron counting and superconducting transition temperature in these compounds; we find that as the number of electrons per formula unit decreases, the critical temperature for superconductivity first increases and then decreases. Among the previously reported binary endohedral Ga cluster phases, Mo8Ga41 is a superconductor with Tc = 9.8 K (1); Mo6Ga31 is a superconductor with Tc = 8.0 K (1); Rh2Ga9 is a superconductor with Tc = 2.0 K; and Ir2Ga9 is a superconductor with Tc = 2.3 K (22). Based on this understanding, we designed and synthesized the previously unreported binary endohedral cluster compound ReGa5 and found it to be superconducting at a critical temperature T c = 2.3 K. Our electronic structure calculations show that the Fermi level of ReGa5 is located within a pseudogap in density of electronic states (DOS), which, as is seen in the other binary endohedral gallium cluster superconductors, is required for the chemical stability of the compound. Given that superconducting transition temperatures should be higher for materials with a higher density of electronic states and that the location of the Fermi energy within a deep pseudogap is a requirement for chemical stability in the endohedral gallide phases, superconductivity and structural stability can be seen to compete in this family. Nonetheless, a compromise is clearly met between the two competing factors in the real materials, resulting in a large family of superconducting endohedral gallium cluster compounds. Electron Counting Rules for Ga-Rich Compounds and a Molecular Perspective on Ga-Clusters in Solids Mo8Ga41 and Mo6Ga31. In the crystal structure of Mo8Ga41, the most striking features are Mo atoms inside 10-atom Ga clusters, i.e., Mo@Ga10 endohedral clusters (23, 24). These endohedral clusters are arranged such that an almost regular cube of Mo atoms is found. The Mo@Ga10 clusters share all their vertex Ga, an architecture that creates a Ga cuboctahedron in the interstitial space between clusters that is itself centered by a Ga atom in Mo8Ga41; this compound can thus be written as Ga(MoGa5)8. The whole architecture is strongly reminiscent of an A-site deficient perovskite oxide, i.e., Ga1/8Mo@Ga10/2 ∼ AxTO6/2, although with 10-vertex-connected dodecahedral Mo@Ga10 clusters rather than 6-vertex-connected M@O6 octahedral clusters. The perovskite structure is known to host many important superconductors, ranging from the high Tc copper oxides to low Tc Na0.23WO3, and in analogy Mo8Ga41 is also superconducting (25). The overall symmetry of the thus-arranged endohedral clusters in Mo8Ga41 is rhombohedral, which is one of the variants of the many possible distortions of the simple cubic lattice found in oxide perovskites (8). E7050 | www.pnas.org/cgi/doi/10.1073/pnas.1522191112

In the crystal structure of the related superconducting cluster phase Mo6Ga31, two of the Mo@Ga10 endohedral clusters are fused together, such that 4 of the 10 Ga are shared between two Mo, in an edge sharing motif (23). The four peripheral Ga’s shared between endohedral clusters are on the vertices of a square, creating an overall face sharing motif of double clusters. These double clusters share vertices with other double clusters to create a mixed corner sharing plus edge sharing architecture. This kind of double cluster architecture in Mo6Ga31 is again reminiscent of the motif found in other superconducting phases: in this case, the family of Chevrel structure-derived phases made from corner and face-sharing Mo6S8 clusters (26). To investigate the electronic factors behind the vertex-sharing Mo@Ga10 cluster architecture in Mo8Ga41, we begin with the electronic structure of the hypothetical model compound Mo8Ga40, which is based on removing the Ga that is in the interstitial region between the Mo@Ga10 clusters in Mo8Ga41. Hypothetical Mo8Ga40 (i.e., MoGa5) made only of the endohedral clusters sharing corner Ga, was then subject to complete structural optimization using Vienne Ab Initio Simulation Package (VASP) (27). The electronic structure of this compound is shown in Fig. 2A. We find that the Fermi level of MoGa5, which has 21e(6 from Mo and 3 × 5 from Ga) is located in a pseudogap in the electronic DOS. An important question to next consider is how the endohedral Mo atom affects the stability of the Ga10-cluster. To get further insight, then, extended Hückel theory was used to analyze isolated molecular “Ga10” and “MoGa10” clusters (28).

Fig. 4. The crystal structure of ReGa5. ReGa5 crystalizes in an orthorhombic structure with space group Cmce (S.G. 64). (green, Ga; pink, Re.) (A) This view emphasizes the shapes of the clusters. (B) This view emphases the vertexsharing of the clusters and the square faces with four-corner Ga atoms that are shared to create the double cluster architecture.

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Fig. 2 (Top Left) illustrates the crystal orbital energy diagrams for the two cases evaluated (the primitive unit cell used contains one 10-atom Ga-cluster or one 11-atom Mo-centered Ga-cluster at the corners of the cell) at the Γ-point in the Brillouin zone, with the orbital energies given relative to the corresponding Fermi levels. We find that after inserting the Mo atom into the Ga10 cluster to create an endohedral cluster, the degenerate orbitals at EF in the Ga10 cluster are split significantly in energy, resulting in EF (the Fermi energy) for Mo@Ga10 being in an energy gap rather than in a partially occupied state with a significant DOS, and stabilizing the cluster. These crystal orbital energy diagrams provide a rationale for how Ga10-clusters are stabilized through the presence of endohedral transition metal elements. Rh2Ga9 (Ir2Ga9) and PdGa5. Superconducting Rh2Ga9 and Ir2Ga9

both crystalize in the Co2Al9-type structure (22). The Ga clusters in these compounds are single-capped square antiprismatic Ga9

Fig. 6. Characterization of the superconducting transition of ReGa5. (A) χv (T) measured in a 10 Oe applied magnetic field from 1.8 to 6 K with zero-field cooling. (Inset) Resistivity vs. temperature over the range of 2–50 K measured in different applied magnetic fields. (B) Temperature dependence of the electronic specific heat Cel of ReGa5. The sample was measured with (μ0H = 5T) and without magnetic field, presented in the form of Cp/T (T), and the electronic part was obtained from heat capacity at μ0H = 5T. (Inset) Temperature dependence of specific heat Cp of ReGa5 sample measured with (5T) and without magnetic field, presented in the form of Cp/T (T2).

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PNAS | Published online December 7, 2015 | E7051

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Fig. 5. The calculated electronic structure for ReGa5: the physics-based picture. (Left) The total DOS as a function of energy near the Fermi energy (E = 0) obtained from LDA calculations in WEIN-2k with spin-orbit coupling (SOC) included. (Right) The corresponding energy dispersion of the bands in selected directions in the orthorhombic Brillouin zone.

(or Al9) clusters with endohedral transition metal atoms, creating T@Tr9 (T = Co, Rh, or Ir and Tr = Al or Ga) endohedral clusters. These endohedral clusters are assembled in edge-sharing zig-zag strands along one crystallographic axis (the c axis in the monoclinic unit cell) and share corners between strands. Thus, in this Co2Al9 structure type, the T@Tr9 clusters share both corners and edges. As was the case for Mo8Ga41, we calculated the electronic structure of Rh2Ga9 and find that the Fermi level is again located in a pseudogap in the density of states at an electron count of 22.5 e- per RhGa4.5 (Rh2Ga9/2) unit (Fig. 2, Middle Right). A sharp, deep pseudogap is seen about 0.25 eV below the Fermi level, associated with 22 e- per RhGa4.5. Similarly to what we observed for Mo@Ga10 clusters from molecular orbitals calculations, we find that the Rh-centered Ga9 cluster is more stable than the empty Ga9 cluster due to the splitting in energy of degenerate orbitals at the Fermi level (Fig. 2, Middle Left). PdGa5 crystalizes in a tetragonal crystal structure (29). In binary PdGa5, each palladium atom is coordinated by 10 gallium atoms in the form of a bicapped tetragonal antiprism, forming Pd@Ga10 clusters. The Pd@Ga10 clusters share edges (8 Ga) and vertices (2 Ga). The Fermi level in the electronic structure of PdGa5 is located in a pseudogap with 25 e-/PdGa5, again in analogy to what is seen in the other gallate cluster compounds. A sharp narrow gap about 1.5 eV above the Fermi level is associated with 26 e- per Pd. Thus, just as we find in the other endohedral cluster compounds, the Pd atoms play an important role in splitting the orbitals of Ga10 to place the Fermi level in the gap and thus yield chemical stability. From these and similar analyses, considering Ga-rich binary phases, we find that electron-deficient compounds such as Mo8Ga41 prefer vertex-sharing of the Ga clusters, whereas electron-rich (26e-) compounds like PdGa5 favor edge-sharing of the clusters. A single formula for the formation of stable T-Ga compounds can therefore be found. The formula is TGa(n-1/2*m+l) (n = number vertices of the T-centered cluster; m = shared vertices; l = isolated Ga atoms in interstitial positions). Moreover, the superconducting transition temperature changes for the endohedral cluster compounds as one progresses in the transition metal series from Mo, to Rh/Ir, to Pd. Noting the missing members of the series in both electron count and structure, we thus postulated the

observed. Four neighboring Ga atoms on one of the square faces of a Re@Ga9 cluster are shared with a neighboring Re@Ga9 cluster, creating an overall double cluster architecture. Each Re@Ga9 double cluster then also shares 4 vertex Ga with neighboring clusters in a corner sharing geometry, and, finally, a “capping” Ga is left coordinated to only a single Re.

Fig. 7. The structural and electronic characteristics of the binary endohedral gallide cluster superconductor family. The horizontal axis is the number of electrons (e-) per transition metal and the vertical axis is the superconducting transition temperature (Tc). The formulas of the compounds are shown. The endohedral clusters shown in the insets illustrate the crossover from corner sharing to edge sharing cluster architectures as a function of electron count.

existence of several possible new compounds and set out to synthesize them and test their properties. Structural and Physical Properties of the Previously Unreported Superconductor ReGa5 The Synthesis of ReGa5 and Phase Information. Based on the understanding above, we realized that that there were no compounds known with 22 electrons per T atom and we thus attempted their synthesis. Loading compositions of Re1.5Ga98.5 and Re3Ga97 (Re: powder, 99.999%, Alfa Aesar; Ga: sponge, 99.995%, Alfa Aesar) about 1 g total mass, were sealed into evacuated SiO2 jackets ( 3σ(I).With the SHELXTL package, the crystal structure was solved using direct methods and refined by full-matrix least squares on F2. All crystal structure drawings were produced using the program VESTA. Physical property measurements. The magnetization measurements were performed in a 10 Oe applied field using a Quantum Design Superconducting Quantum Interference Device (SQUID) magnetometer, over a temperature range of 1.8–6 K. The magnetic susceptibility is defined as χ = M/H where M is the measured magnetization in emu and H is the applied field in Oe. The resistivity and specific heat measurements were measured using a Quantum Design Physical Property Measurement System (PPMS) from 1.85 to 300 K with and without an applied field. Resistivity measurements were made in the standard four-probe configuration, and the specific heat measurements were performed on a polycrystalline sample of approximate weight 10 mg.

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Fig. S1.

Fig. S2.

Powder X-ray diffraction pattern for polycrystalline ReGa5 sample.

Calculated DOS of RuGa3, showing the Fermi level located at the edge of a band gap.

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Table S1. Single crystal crystallographic data for ReGa5 at 293(2) K Refined formula

ReGa5

F.W. (g/mol); Space group; Z a (Å) b (Å) c (Å) V (Å3) Absorption correction Extinction coefficient μ (mm−1) θ range (°) hkl ranges

534.8 Cmce (No.64); 8 9.2127(5) 10.1043(5) 9.2321(5) 859.40(8) Multiscan 0.0005(1) 58.739 2.992–29.576 −12≤ h ≤ 12 −14≤ k ≤ 14 −12≤ l ≤ 12 6,243; 0.0309 639 36 0.0540; 0.1154 1.142 5.161; –5.945

No. reflections; Rint No. independent reflections No. parameters R1; wR2 (all I) Goodness of fit Diffraction peak and hole (e−/Å3)

Table S2. Atomic coordinates and equivalent isotropic displacement parameters of ReGa5 Atom Wyckoff Occupancy Re1 Ga2 Ga3 Ga4 Ga5

8f 8c 16g 8f 8f

1 1 1 1 1

x

y

z

Ueq

0 1/4 0.3412(2) 0 0

0.3435(1) 1/4 0.4877(2) 0.2842(1) 0.0922(2)

0.0119(1) 0 0.6595(2) 0.2787(1) 0.0749(2)

0.007(1) 0.028(1) 0.047(2) 0.014(1) 0.061(2)

Ueq, one-third of the trace of the orthogonalized Uij tensor (Å2).

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