Arsenic chemistry of iron-based superconductors and strategy for novel superconducting materials

Abstract The progress of materials discovery of iron-based superconductors is reviewed with the emphasis on the valence states and chemical bonds of arsenic. We demonstrate that monovalent As– produces the 112-type CaFeAs2 with arsenic zigzag chains. When co-doping of La and Sb is performed, the superconducting transition temperature rises to 47 K. In the 10-4-8-type Ca10(Pt4As8)(Fe2−xPtxAs2)5, the divalent As2– produces As2 molecules, and creates an interlayer substance with PtAs4 planar squares. The maximum superconducting transition temperature is 38 K. In the 122-type CaFe2As2, Rh doping induces a lattice collapse transition accompanying the formation of As2 molecules between the adjacent FeAs layers. This transition can be viewed as a valence transition between As3– and As2–. These properties of arsenic that produces various chemical bonds can be used to create new superconducting materials.

For this reason, arsenic makes various chemical bonds and as a result, produces various crystal structures. In neutral arsenic As 0 (4p 3 ), three electrons occupy each p x , p y , and p z atomic orbitals. The three unpaired electrons each form covalent bonds. An example of this is α-As (space group R3m, D 5 3d , #166). As shown in Figure 1(a), an arsenic atom makes chemical bonds with the adjacent three arsenic atoms. As a result, the crystal structure is distorted to become trigonal. In monovalent arsenic As -(4p 4 ), two unpaired electrons exist and two chemical bonds per As are made. Examples of this are the As zigzag chain and the As 4 tetramer. Zigzag chains appear in the 112-type iron-based superconductor Ca 1-x La x FeAs 2 (space group P2 1 , C 2 2 , #4), as shown in Figure 1(b) [1][2][3][4][5]. Tetramers appear in CoAs 3 and other Skutterudites [6]. Since As 2-(4p 5 ) has a single unpaired electron, arsenic makes a single chemical bond. In other words, As forms an As 2 molecule. This can be seen in the BaCu 2 As 2 shown in Figure 1(c), or in the collapsed tetragonal structure of the 122-type iron-based superconductor CaFe 2 As 2 [7][8][9][10][11][12][13][14]. Furthermore, in As 3-(4p 6 ) with an additional electron, the 4p orbital becomes a closed shell, and arsenic does not form a covalent bond. As a result, arsenic becomes the isolated anion As 3-. This structure can be seen in the BaFe 2 As 2 , shown in Figure 1(d) [15], or in the uncollapsed tetragonal structure of CaFe 2 As 2 [7][8][9][10][11][12][13][14].

Arsenic dimers in the 122-type structure
Figure 1(c) and (d) show the crystal structures of BaCu 2 As 2 and BaFe 2 As 2 . Both compounds crystallize in the tetragonal ThCr 2 Si 2 -type structure (space group I4/mmm, D 17 4h , #139). However, the c-axis length is different sharply. This is because, while in BaCu 2 As 2 , As-As bonds, or in other words, As 2 molecules, are formed between the adjacent CuAs layers, in BaFe 2 As 2 , there is no covalent bond between As and As in the adjacent FeAs layers. The As-As distances in these two structures are, respectively, 2.558 and 3.390 Å. The respective chemical formulae are Ba 2+ Cu + 2 As 2− 2 and Ba 2+ Fe 2+ 2 As 3− 2 . In BaFe 2 As 2 , since arsenic is trivalent and has a closed shell (4p 6 ), it does not make a covalent bond. On the other hand, in BaCu 2 As 2 , since arsenic is divalent, it makes a single covalent bond, or an As 2 Figure 2. Relationship of the d band filling of BaTM 2 As 2 (TM = Mn, Fe, co, ni, cu), and molecular orbital energy of the As 2 molecule [22,23]. notes: The π and π * molecular orbitals are omitted. At TM = Fe, the σ * molecular orbital energy is lower than Fermi energy E F , and since the σ * molecular orbital is occupied, the As 2 molecule is not formed. On the other hand, at TM = cu, since the σ * molecular orbital is not occupied, the As 2 molecule is formed.
molecule. The As 2 molecular orbitals are, in order from the lowest energy, σ, π, π * , and σ * . In the neutral As 2 molecule, six electrons occupy the σ and the twofold degenerate π orbitals. When four more electrons are added, the π * orbital is completely occupied. As a result, the arsenic molecule is stable in a tetravalent state . When we focus on the As 2 molecule, the above chemical formula becomes Ba 2+ Cu + 2 As 2 4− . The valence state of Cu + has been confirmed by photoemission measurements [20,21]. When two more electrons are supplied to the As 2 4− molecule, the antibonding orbital σ * is occupied, and the molecule dissociates to become As 3− [22,23].  According to Hoffmann [22,23], differences between the crystal structures of BaCu 2 As 2 and BaFe 2 As 2 can be understood by the relative relationship between the Fermi energy in the transition metal d band and the energy of the As 2 antibonding orbital σ * . In BaCu 2 As 2 , the Fermi energy of the Cu 3d band is lower than the energy of σ * orbital. As a result, the σ * orbital is unoccupied, and As 2 molecules are formed. In BaFe 2 As 2 , the Fermi energy of the Fe 3d band is higher than the energy of As 2 σ * orbital. As a result, since the antibonding σ * orbital is occupied, the As-As covalent bond is broken to become As 3− . This situation is schematically shown in Figure 2. The 3d orbital energy decreases as the atomic number, or equivalently positive nuclear charge, increases. On the other hand, the band filling increases with the increase in the atomic number. As a result, the Fermi energy E F decreases in the order of Fe, Co, Ni, and Cu. Figure 3 shows the c-axis lengths of the BaTM 2 As 2 , SrTM 2 As 2 , and CaTM 2 As 2 for the transition metal element TM. If the As-As bond is formed, the c-axis length becomes approximately 11 Å or less. For BaTM 2 As 2 , the As-As bond is formed between Ni and Cu. For Sr or Ca, which have smaller ionic radii than Ba, formation of the As-As bond occurs more easily: for SrTM 2 As 2 , the As-As bond is formed between Co and Ni, and for CaTM 2 As 2 , between Fe and Co. CaFe 2 As 2 is a parent compound of iron-based superconductors. Therefore, in CaFe 2 As 2 , the interplay between superconductivity and the As 2 molecule formation can be investigated.
We used Rh in place of Co because tiny Rh doping can cause As 2 molecule formation to occur [9]. Figure 4 shows the c-axis parameter as a function of doping x for Ca(Fe 1−x Rh x ) 2 As 2 at 300 K. First, the c-parameter decreases gradually upon doping. At x = 0.2, the c-parameter length shrinks discontinuously by approximately 5%. This is due to As 2 molecule formation, and is a first-order structural phase transition. The crystal structure symmetry remains unchanged across the transition as the tetragonal ThCr 2 Si 2 -type (space group I4/mmm). Since the volume decreases discontinuously, this transition is called as lattice collapse transition. The phase where the As 2 molecule is broken is called the uncollapsed phase, and the phase where the As 2 molecule is formed is called the collapsed phase. Interestingly, even if it is an uncollapsed phase at room temperature, thermal contraction promotes the formation of As 2 molecule and the phase transition to a collapsed phase occurs at low temperatures. Figure 5 shows a temperaturecomposition phase diagram for Ca(Fe 1−x Rh x ) 2 As 2 . For example, the lattice collapse transition temperature is approximately 50 K at x = 0.024. At such a low temperature, and moreover in a solid state, it is surprising that As 2 molecule formation, or 'chemical reaction, ' takes place.
It should be noted here that the electron count of Ba 2+ Cu + 2 As 2 4− is reasonable because the Cu 3d orbitals are well below the Fermi level and fully occupied (3d 10 ) [20]. In contrast, a simple electron count, such as Ca 2+ Fe + 2 As 2

4−
, cannot be applied because of the significant hybridization between Fe 3d and As 4p orbitals exists in the collapsed phase of CaFe 2 As 2 [24]. However, a fractional electron count Ca 2+ Fe +2− 2 As 2 −6+2 is likely, where 0 < δ < 1 denotes the number of electrons transferred from As 4p to Fe 3d orbitals. The reduction of negative valence of As is consistent with the observed shift of the As core level in the collapsed phase of Ca(Fe 1−x Rh x ) 2 As 2 [25]. Superconductivity appears in the uncollapsed tetragonal phase following the suppression of the antiferromagnetic ordering upon Rh doping [9]. The superconducting phase is limited to a narrow composition in the x = 0.02 region. In the uncollapsed phase, antiferromagnetic fluctuations are present, as observed by inelastic neutron and NMR/NQR measurements [11][12][13][14], and the electrical resistivity exhibits T 1.5 behavior [9,10], which is likely due to magnetic fluctuations. In the collapsed phase, antiferromagnetic fluctuations disappear [11][12][13][14], and the electrical resistivity shows a temperature dependence of T 2 [9,10], a hallmark of Fermi liquid. In this way, As 2 molecule formation causes the iron magnetic moment to disappear, and the superconducting phase disappears [7][8][9][10][11][12][13][14]. The As 2 molecule formation also causes increased interlayer interactions, which result in the loss of the Fermi surface nesting [25,26]. Both should be relevant to the disappearance of superconducting phase.
The lattice collapse transition of CaFe 2 As 2 can be viewed as an arsenic valence transition. This is because the As valence in the uncollapsed phase is As 3− , and in the collapsed phase, is As 2− . As mentioned above, this phase transition is a first-order, accompanying a discontinuous decrease in the lattice volume, and the crystal structure symmetry remains unchanged. At the same time, the iron magnetic moment disappears. This is similar to the cerium α-γ phase transition [27]. Cerium valence in the high-temperature phase γ-Ce is trivalent (Ce 3+ , 4f 1 ), and in the low-temperature phase α-Ce, is tetravalent (Ce 4+ , 4f 0 ). The α-γ transition is a first-order, and the crystal structure symmetry remains unchanged as face-centered cubic (space group Fm3m, O 5 h , #225). With this transition, the volume decreases by approximately 15%, and the Ce magnetic moment disappears in the low-temperature phase. This first-order phase transition line terminates at a critical point of approximately 600 K and 2 GPa [27]. In the heavy-fermion superconductor CeCu 2 Si 2 , the temperature of the critical point of the Ce valence transition is reduced to near absolute zero, at which 'high-temperature' superconductivity emerges [28][29][30]. When hydrostatic pressure and Ge doping are applied to CeCu 2 Si 2 , the antiferromagnetic phase is suppressed and a superconducting phase with a maximum T c = 0.4 K appears. By further applying pressure, the second superconducting phase with a maximum T c = 1 K appears at the vicinity of the quantum critical point of Ce valence transition. The latter is considered to be superconductivity mediated by valence fluctuations, while the former by spin fluctuations, suggesting valence fluctuations are favorable for enhancing superconductivity. The lattice collapse transition of CaFe 2 As 2 , like the α-γ transition of Ce, is also expected to have a critical point at high temperatures. If this critical point could be lowered all the way to absolute zero, there is a possibility that superconductivity mediated by the As valence quantum fluctuations would emerge. In CaFe 2 As 2 doped with La and P, a superconducting phase with T c = 45 K has been discovered in a region distant from the antiferromagnetic phase [31]. This observation raises interest in the As valence transition of iron-based superconductors.

Arsenic dimers in the 10-4-8-type structure
When we performed doping various transition metal elements into CaFe 2 As 2 , we noticed that weak superconductivity appeared at high temperatures exceeding 30 K, limited to the case of Pt doping. As a result of trial-and-error, we confirmed that this superconductor was Ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5 currently called the 10-4-8-type [16]. The maximum observed value of the superconducting transition temperature was 38 K. In addition, the 10-3-8-type Ca 10 (Pt 3 As 8 )(Fe 2−x Pt x As 2 ) 5 Figure 6. (a) crystal structure of ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5, and (b) its Pt 4 As 8 layer [16].
with lower T c values was confirmed [16]. Ni et al. [17] and Löhnert et al. [18] also discovered same compounds in the same time period. Figure 6 shows the crystal structure of Ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5 . Between the superconducting FeAs layers, a Pt 4 As 8 layer exists. This layer is formed from corner sharing PtAs 4 planar squares. These PtAs 4 planar squares are alternately rotated, and As 2 molecules are formed between the adjacent squares. The 10-3-8-type Ca 10 (Pt 3 As 8 )(Fe 2−x Pt x As 2 ) 5 in which Pt is periodically vacant also exists [16][17][18][19]. This is the parent compound for this group, since it can be expressed as Ca 2+ 10 Pt 2+ 3 As 2 4− 4 Fe 2+ 2 As 3− 2 5 for x = 0. This compound is also important from the perspective of coordination chemistry. Fe 2+ favors tetrahedral or octahedral coordination. In fact, in iron-based superconductors, edge-sharing FeAs 4 tetrahedra form superconducting FeAs layers. On the other hand, Pt 2+ favors planar square coordination [32]. Planar square coordination also appears in complexes that include Ni 2+ or Pd 2+ , and is the characteristic of the d 8 configuration [32]. In fact, reflecting the favoring by Fe 2+ and Pt 2+ of differing coordination, the platinum solubility limit in Ca(Fe 1−x Pt x ) 2 As 2 was low, at x = 0.08 [33]. This shows that the substitution of Pt for Fe at the tetrahedral site is difficult. Cobalt and other transition metal elements that favor tetrahedral coordination exhibit continuous solid solution with Fe. Therefore, when the Fe favoring tetrahedral coordination is mixed with Pt favoring planar square coordination, it appears that, because they do not favor formation of a solid solution in nature, a new compound, 10-4-8-type, is produced. In the same way, compounds including the PdAs 4 planar squares [34][35][36] and IrAs 4 planar squares [37][38][39][40] were discovered. Since Ir 2+ favors tetrahedral coordination rather than planar square coordination, the crystal structure is unstable, and shows a structural phase transition at low temperatures [38,39].

Arsenic chains in the 112-type structure
Finally, we introduce an iron-based superconductor that is created using monovalent As − . LaFeAsO is a compound that serves as a prototype for iron-based superconductors [41]. The crystal structure is a laminated structure, alternating between fluorite and anifluorite-type layers of LaO and FeAs, respectively. In the fluorite-type structure, anions are found at the tetrahedral coordination center, while in the antifluorite-type structure, cations are found at the center. The replacement of LaO layers to CaF layers results in CaFeAsF [42,43]. With awareness of valence, this becomes Ca 2+ Fe 2+ As 3− F − . If the hydride H − is substituted for the fluoride ion F − , then Ca 2+ Fe 2+ As 3− H − results [44]. Both CaFeAsF and CaFeAsH exhibit superconductivity when doped [42][43][44]. For a monovalent anion, there is also the halogen Cl − , Br − , or I − . However, an 1111-type structure containing these elements does not exist. Since the ion radius is large, it appears that the fluorite structure is not formed. So then, is this the end for compounds that are derived from the 1111-type structure? Here, let us introduce the newly discovered 112-type CaFeAs 2 [1][2][3][4][5]. As was mentioned at the outset, arsenic can take the monovalent state As − . This As − can be substituted for F − or H − . In this manner, Ca 2+ Fe 2+ As 3− As − = CaFeAs 2 is obtained [41]. Synthesizing this compound requires approximately 10% La doping [1]. Without La, the 122-type CaFe 2 As 2 is yielded. Figure 7 shows the crystal structure of Ca 1−x La x FeAs 2 , in which arsenic zigzag chain structure that is characteristic of As − can be seen. Because of the weak ionic character of As − , the distance between Ca and As widens. In contrast, the distance between Ca and F(H) is considerably short due to the strong ionic character of F − and H − . This compound exhibits superconductivity at 35 K [1,4,5]. Furthermore, in the Ca 1−x La x Fe(As 1−y Sb y ) 2 simultaneously doped with La and Sb, the superconducting transition temperature rises up to 47 K [5]. According to single crystal X-ray structure analysis, Sb substitutes preferably to As in zigzag chains, rather than As in the FeAs layer [45], as predicted by first-principles calculations [46]. In contrast, excess doping of La causes antiferromagnetic and structural phase transitions [47][48][49], which results in loss of superconductivity. The observation of optical second-harmonic generation confirmed the lack of spatial inversion symmetry for Ca 1−x La x FeAs 2 [49], which makes the 112-type a unique among iron-based superconductors.

Conclusion
In this review paper, we introduced the progress of novel iron-based superconducting materials utilizing the 'pluripotency' of arsenic, such as the arsenic electron count of various valence states to create various chemical bonds and various crystal structures. We have demonstrated that monovalent Asplays an important role to produce the 112-type CaFeAs 2 with arsenic zigzag chains. When co-doping of La and Sb was performed, the superconducting transition temperature rose to 47 K. In the 10-4-8-type Ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5 , the divalent As 2produced an As 2 molecule, and created an interlayer substance from PtAs 4 planar squares. The maximum superconducting transition temperature was 38 K. In the 122type CaFe 2 As 2 , Rh doping caused a lattice collapse transition accompanying the formation of an As 2 molecule between the FeAs layers.
The results shown in this review paper provide two hints regarding the strategy for new superconductors. The first is that, when two energies compete, interesting phenomena will occur. In the iron-based superconductors, the Fe 3d orbital and the As 4p orbital energies competed. Owing to this competition, a 'chemical reaction' in formation of the As 2 molecules occurred at the low temperature of 50 K. This transition could be viewed as a valence transition between the trivalent As 3and divalent As 2-. By analogy with heavy fermion superconductors, arsenic valence transition may be used for further enhancing superconductivity if a quantum critical point was realized. The other was that when setting a problematic situation, nature presents interesting answers. In this research, as a result of mixing elements such as Fe and Pt that favor differing coordination environments (tetrahedral and planar square coordination), a new interlayer substance called Pt 4 As 8 was precipitated, and a new iron-based superconductor called 10-4-8-type was created.