AFe2As2 (A = Ca, Sr, Ba, Eu) and SrFe_(2-x)TM_(x)As2 (TM = Mn, Co, Ni): crystal structure, charge doping, magnetism and superconductivity

The electronic structure and physical properties of the pnictide compound families $RE$OFeAs ($RE$ = La, Ce, Pr, Nd, Sm), $A$Fe$_{2}$As$_{2}$ ($A$ = Ca, Sr, Ba, Eu), LiFeAs and FeSe are quite similar. Here, we focus on the members of the $A$Fe$_{2}$As$_{2}$ family whose sample composition, quality and single crystal growth are better controllable compared to the other systems. Using first principles band structure calculations we focus on understanding the relationship between the crystal structure, charge doping and magnetism in $A$Fe$_{2}$As$_{2}$ systems. We will elaborate on the tetragonal to orthorhombic structural distortion along with the associated magnetic order and anisotropy, influence of doping on the $A$ site as well as on the Fe site, and the changes in the electronic structure as a function of pressure. Experimentally, we investigate the substitution of Fe in SrFe$_{2-x}TM_{x}$As$_{2}$ by other 3$d$ transition metals, $TM$ = Mn, Co, Ni. In contrast to a partial substitution of Fe by Co or Ni (electron doping) a corresponding Mn partial substitution does not lead to the supression of the antiferromagnetic order or the appearance of superconductivity. Most calculated properties agree well with the measured properties, but several of them are sensitive to the As $z$ position. For a microscopic understanding of the electronic structure of this new family of superconductors this structural feature related to the Fe-As interplay is crucial, but its correct ab initio treatment still remains an open question.


Introduction
Physics community around the world has been tirelessly working for the past months to find different ways of increasing the superconducting transition temperature T c following the discovery of superconductivity at 26 K in the rare-earth based (REOFeAs) system LaO 1−x F x FeAs (x = 0.05 -0.12) [1]. Spirited search by the experimentalists has led to eventually raising T c to 55 K for another member of this family of compounds, SmFeAsO 0.9 F 0.1 [2]. Shortly afterwards, another family of Fe-based compounds AFe 2 As 2 (A = Ca, Sr, Ba, Eu) was also found to be superconducting upon hole doping [3] on the A site with a maximum T c = 38 K [4,5,6]. These discoveries are followed by the announcements of other new parent compounds: LiFeAs, FeSe, SrFeAsF with a maximum T c of 18 K [7], 14 K [7] (27 K using pressure [8]) and 56 K [9], respectively. The basic features, that are common to many of these new parent compounds, are the anti-ferromagnetic ordering of the Fe-spins at T N ≈ 100-200 K, and the quasi-2D nature of the electronic structure. All the members belonging to the above mentioned families have been shown to superconduct upon either "hole" or "electron doping" only with the exception of LiFeAs, wherein it is considered that the Li layer acts as a charge reservoir for the system [7]. Superconductivity also emerges upon application of hydrostatic pressure for certain members of the REOFeAs, AFe 2 As 2 and FeSe families. Notwithstanding the abundant research that has already been performed, the microscopic nature of the mechanism of superconductivity has thus far remained elusive. A systematic study of the many members within one particular family, using both experimental and theoretical techniques, would pave way to a more concrete understanding of the electronic structure of the normal state. Although the REOFeAs systems have larger T c values, their sample preparation, characterization and quality, as is the case for many oxides, have to be considered with great care. Alternatively it has been demonstrated that the AFe 2 As 2 systems could be synthesized comparatively easier. Consequently, here we carry out a systematic investigation using both theoretical and experimental techniques for the AFe 2 As 2 systems.
All the AFe 2 As 2 compounds crystallize in the tetragonal ThCr 2 Si 2 -type structure at room temperature. They all exhibit a structural transition upon cooling to an orthorhombic lattice (T 0 for Ca ≈ 171 K [10], Sr ≈ 205 K [11], Ba ≈ 140 K [12], Eu ≈ 200 K [13]). The structural transition is coupled with an antiferromagnetic ordering of the Fe moments with a wave vector Q = [1,0,1] for the spin-density-wave (SDW) pattern. Suitable substitution on either the A site or the Fe site can suppress the magnetic ordering, and then the system becomes superconducting for certain ranges of doping (for example, maximum T c = 38 K (Ba,K)Fe 2 As 2 [6], 32 K (Eu,K)Fe 2 As 2 [14], 21 K Sr(Fe,Co) 2 As 2 [15], Ba(Fe,Co) 2 As 2 [16]). Superconductivity can also be induced in "undoped" and "under-doped" compounds by applying pressure [17].
In the following sections we describe the microscopic picture of the magnetostructural transition and the effects of external pressure, chemical pressure and charge doping on the AFe 2 As 2 systems. In order to make the manuscript more easily readable, we introduce the following abbreviations: REOFeAs: 1111, AFe 2 As 2 : 122, LiFeAs: 111, FeSe: 11, SrFeAsF: 1111 ′ ; ferromagnetic: FM, checkerboard (nearest neighbour) antiferromagnetic: NN-AFM, columnar/stripe-type antiferromagnetic order of the Fespins: SDW (spin-density-wave).

Theory
We have performed density functional band structure calculations using a full potential all-electron local orbital code FPLO [18,19,20] within the local (spin) density approximation (L(S)DA) including spin-orbit coupling when needed. The Perdew-Wang [21] parametrization of the exchange-correlation potential is employed. Density of states (DOS) and band structures were calculated after converging the total energy on a dense k-mesh with 24×24×24 points. The strong Coulomb repulsion in the Eu 4f orbitals are treated on a mean field level using the LSDA+U approximation in the atomic-limit double counting scheme [22]. Results we present below use the LSDA+U method [23] in the rotationally invariant form [24]. In accordance with the widespread belief that in the new Fe-based superconducting compounds the Fe 3d electrons have a more itinerant character than a localized one, and thereby are much less correlated in comparison to the Cu 3d electrons in the high-T c cuprates, we did not apply the LSDA+U approximation to the Fe 3d states. Effects of doping on either the cation site or the Fe site were studied using the virtual crystal approximation (VCA) treatment. The results obtained via VCA were cross checked using supercells for certain doping concentrations. The crystal structures are optimized at different levels to investigate or isolate effects that may depend sensitively to certain structural features. The full relaxation of the unit cell of the 122 systems at low temperatures involves optimizing a/b and c/a ratios in addition to relaxing the As-z position.

Experimental
Polycrystalline samples were prepared by sintering in glassy-carbon crucibles which were welded into tantalum containers and sealed into evacuated quartz tubes for heat treatment at 900 C for 16 hours with two regrinding and compaction steps. First precursors SrAs, Co 2 As, Fe 2 As, Mn 2 As and NiAs were synthesized from elemental powders sintered at 600 C for 48 h (Mn, Fe, Co, Ni 99.9 wt.%; As 99.999 wt.%; Sr 99.99 wt.%). These educts were powdered, blended in stoichiometric ratios, compacted to pellets, and heat treated. All sample handling was done inside argon-filled glove boxes. Crystals were grown in glassy-carbon crucibles by a modified self flux method [25,16] in melts with compositions SrFe 5−x Co x As 5 (0.5 ≤ x ≤ 0.85) by cooling from 1250 C to 1100 C within 48 hours. The melt was spun off at 1100 C using a centrifuge [26]. Metallographic investigations were performed on polished surfaces of selected secured crystal platelets. Electron-probe microanalysis (EPMA) with wavelength-dispersive analysis was accomplished in a Cameca SX100 machine. Crystal X1 was grown in a flux SrFe 4.25 Co 0.75 As 5 and crystal X2 in a flux SrFe 0.15 Co 0.85 As 5 . For crystal X1 from EPMA the composition (in at.%) Sr 19.9(2) Fe 36.2(1) Co 4.2(1) As 39.7 (1) was found which corresponds to SrFe 2−x Co x As 2 with x ≈ 0.21. For crystal X2 from EPMA the composition (in at.%) Sr 19.5(2) Fe 35.5(1) Co 5.0(2) As 39.9 (2) was found which corresponds to SrFe 2−x Co x As 2 with x ≈ 0.25. Crystals grown from a flux SrFe 4.5 Co 0.5 As 5 had a composition of Sr 19.9(3) Fe 36.9(1) Co 3.2(1) As 39.9 (2) corresponding to SrFe 2−x Co x As 2 with x ≈ 0.15 and showed no superconductivity. All crystals grown up to now exhibit some inclusions of flux-material which can be seen in Fig. 1 (for crystal X2 the second phase has the composition Sr 3(1) Fe 44(1) Co 8(1) As 45(1) (in at.%)).

Ambient-temperature phase : tetragonal
We begin with comparing the DOS computed for a representative member of each family of the iron pnictide compounds. In these calculations, experimental values of the ambient-temperature tetragonal lattice parameters and atomic positions were used for all the systems. Collected in Fig. 2 are the non-magnetic total and orbital-resolved DOS for five systems: 1111, 122, 111, 11, 1111 ′ . The states close to the Fermi energy (E F ) in all these systems are comprised mainly of Fe 3d contributions. The contribution of the pnictide atom (or Se in the case of FeSe) to the Fermi surface is small but non-zero. A pseudo-gap-like feature in the DOS slightly above the E F is common to all the systems. At the outset, all the five systems look quite similar to one another, but slight differences are already visible when analyzing the Fe 3d orbital resolved DOS, presented on right panels in Fig. 2. The contribution of the Fe 3d x 2 −y 2 orbital (the orbital pointing directly towards the nearest neighbour Fe ions) is the largest close to E F for all the systems. The corresponding bands (not shown here) are highly dispersive in the a − b plane and remain flat along the c-axis, indicative of the quasi-2D nature of this band. The distance of the 3d x 2 −y 2 edge from the E F varies for the different systems and is the largest for the 111 family and smallest for the 1111 family. The second largest contribution to the Fermi surface comes from the doubly degenerate 3d xz and 3d yz orbitals and this feature is again consistent for all the iron pnictide compounds.   Figure 3. Total energy as a function of b/a for the AFe 2 As 2 (A = Ca, Sr, Eu, Ba) systems with two possible spin arrangements between the Fe spins. In NN-AFM the spins of all the nearest neighbours are antiparallel to each other. In the SDW pattern, the spins along the longer aaxis are anti-parallel while the spins along the shorter b-axis are parallel. The solid vertical lines denote the minimum value of the energy. The minimum energy for each system has been set to zero. For clarity, Sr122, Eu122 and Ba122 curves are offset by 5, 10 and 15 meV. We calculated total energies for different b/a ratios for different magnetic models. For the nonmagnetic (NM), ferromagnetic (FM) (not shown) as well as the nearestneighbour antiferromagnetic (NN-AFM) (Fig. 3, upper panel) patterns, lowest total energy occurred at a = b, indicating that for these patterns the tetragonal structure is more stable than the orthorhombic structure. Inclusion of spin-orbit effects did not change this result. The tetragonal to orthorhombic distortion is obtained only for the SDW pattern as displayed in the lower panel of Fig. 3. Hence, LSDA calculations clearly show that the SDW state is necessary for the tetragonal-to-orthorhombic transition to take place. The size of this effect, namely the deviation of the calculated b/a ratio from unity, depends on the size of the cation, the ratio being smallest in BaFe 2 As 2 , and largest in CaFe 2 As 2 . The values obtained via LSDA are collected in Table 1 and compared to the experimental reports. The trend obtained in LSDA fits well with the experimental b/a ratios with the exception of CaFe 2 As 2 . Experimentally, CaFe 2 As 2 crystals are shown to have complex microstucture properties. Recent studies using transmission electron microscopy (TEM) [30] have shown a pseudo-periodic modulation and structural twinning arising from tetragonal to orthorhombic transition only in CaFe 2 As 2 but not in Sr or Ba 122 systems. A structural twinning hinders the correct estimation of the lattice parameters and thereby may explain the experimental deviation in the trend of b/a ratio for CaFe 2 As 2 with respect to LSDA.
In all four compounds the coupling along the shorter in-plane axis is FM in agreement with experimental findings. Although these results are robust with respect to details of structure and calculations, the preferred direction of the spins are found to be quite sensitive. We performed fully-relativistic calculations for A = Ca, Sr and Ba cases using (i) SDW with Q = [1 0 0], (ii) SDW with Q = [1 0 1]. The latter SDW pattern requires the doubling of the c lattice parameter and the corresponding calculations are highly time consuming. Therefore, only the cartesian axes are considered for possible spin orientations, and the structural data corresponding to the minima in Fig. 3 are used. In the Sr122 case for both SDW patterns we find the direction of the AFM coupling (along the longer a-axis) as the easy axis in agreement with the neutron scattering study result [28]. However, in Ca and Ba 122 cases different axes in the (a, b) plane are found as easy axes for different SDW patterns. The longer a-axis, is the easy axis for Ba (Ca) 122 for Q = [1 0 0] (Q = [1 0 1]); the shorter axis, b, the direction of FM coupling, for Ba (Ca) 122 for Q = [1 0 1] (Q = [1 0 0]). Since the involved energy differences are tiny (of the order of 15-30 µeV per atom), a satisfactory resolution of this issue requires further study. Experimental study on Ba122 [31] has been able to determine that spins lie along the longer a-axis.

3.2.2.
Plasma frequency and effective dimensionality Band structure calculations can provide information on the "effective dimensionality" in a compound through various means, such as dispersionless (flat) energy bands along certain symmetry lines, van Hove singularities in DOS, etc. A simple quantitative measure, however, can be obtained by computing plasma frequencies along the main unit cell axes. For all of the 122 compounds as well as the representative compounds for the other families, plasma frequencies are calculated by nonmagnetic calculations using the experimental structural data of the tetragonal phase. In Table 2 we present the ratio Table 2. Ratio of the in-plane plasma frequency ω a P to the out-of-plane plasma frequency ω c P for various members of the Fe-based superconducting systems. The observed trend in the plasma frequency ratios follows the trend in the ratios of the (inter-layer to intra-layer) Fe-Fe distances, d Fe−Fe c /d Fe−Fe a . As we go down the column, the systems go from being more 2D towards being more 3D. The maximum superconducting transition temperature T max c obtained either via doping or pressure is also collected in the last column. The trend in T max c also follows the trend in ω a P /ω c P , with decreasing temperatures when the systems become more 3D. 2.1416 20 [32] of the in-plane plasma frequency (ω a P = ω b P ) to the plasma frequency along the c-axis (ω c P ). One notices that for the 122 family the results are in line with expectations: the compound is least anisotropic (more 3D-like) for the smallest cation (Ca), and strongly anisotropic (less 3D-like) for the largest cation (Ba). Additionally, the 1111 and 1111 ′ families are seen to be much more anisotropic (more 2D-like) than all of the others.
In the case of iron arsenides, in a rather simplified picture, one expects the plasma frequency ratio to be proportional to the ratio of the shortest interlayer d  Table 2 shows that these two ratios are largely correlated with apparently the exception of FeSe [33].

3.2.3.
Effect of the As z position and magnetic moments from LDA: In any first-principles study of a magnetic system, an essential aspect is the comparison of the computed magnetic moments with the experimentally deduced ones. This standard procedure proves to be quite tricky in these FeAs-based compounds due to the unexpected sensitivity of the magnetism to the As z position [34]. We performed a series of calculations [35] for Ca, Sr and Ba 122 systems for FM, NN-AFM and SDW spin patterns using the experimental volume (ambient pressure, below T N ) both with a = b and a = b and optimizing the Fe-As distance (via As z position) for each case. Table 3 compares the Fe moments computed for the SDW pattern (the lowest-total-energy spin pattern among those considered) with the experimental values obtained using neutron diffraction and muon spin rotation (µSR). In comparison to the situation in the 1111 systems, here for the 122 systems, the agreement between theory and experiment is seen to be better. However, the computed Fe magnetic moment is found to increase from Ca to Ba 122, whereas the trend is just the opposite according to the estimation of moments from µSR results. The moments obtained from neutron diffraction experiments are more reliable and remain rather constant for the three 122 systems considered here. The influence of the orthorhombic distortion on the calculated moments is quite negligible.
The better agreement between theory and experiment regarding the Fe magnetic moment in the case of 122 systems can be understood as follows. The computed vs measured magnetic moment discrepancy in the 1111 systems is usually explained to be a result of large spin fluctuations [36]. It is also known that spin fluctuation effects are reduced when going from 2D systems to 3D systems. Hence, the results presented in Table 3 provide additional support for the effective dimensionality considerations described above: the 122 systems have a more pronounced 3D nature than the 1111 systems. Since the description of spin fluctuation effects is insufficient in LSDA, the computed values are immune to such effects, while, of course, the values deduced from experiments do reflect these effects. Furthermore, since the Ba 122 system is more 2Dlike than the Ca 122 system (cf. Table 2), it is expected to exhibit a smaller Fe moment (stronger spin fluctuation effects), and this is in agreement with the µSR results. Table 3. Comparison of the magnetic moments in µ B per atom calculated using LSDA with the experimental values obtained via µSR (a local probe) and neutron diffraction measurements. In LSDA, the moments were calculated for the SDW pattern for the Fe spins using a tetragonal lattice ( a = b ) and orthorhombic lattice ( a = b ). The Fe-As distance has been optimized for all the calculations reported in this table.

LDA -SDW
µSR  [40] The interplay between the Fe-As distance and different magnetic long-range orders is illustrated in Fig. 4 for SrFe 2 As 2 . Similar results are found for the other 122 systems. The experimental value of the Fe-As distance in SrFe 2 As 2 in the orthorhombic phase is reported to be 2.391Å at 90 K [29]. Using the FM or the NN-AFM spin pattern produces a minimum in energy at around 2.31Å along with a complete loss of the Fe magnetic moment. In the SDW pattern, the optimum value of the Fe-As distance is 2.327Å, only slightly larger than that obtained using the FM or NN-AFM pattern, but the Fe magnetic moment is still 1.13 µ B .
The As-z position is most likely one of the key issues for understanding of the iron pnictides. Present day density functional theory based calculations using LDA (described above) and also GGA [34,41] are not able to reproduce all the experimental findings consistently. Since the magnetism and therefore the superconductivity crucially depends on this structural feature and the related accurate description of the Fe-As interaction, the improvement of the calculations in this respect may offer the key to the understanding of superconductivity in the whole family.   . Energy and Fe magnetic moment as a function of the Fe-As distance using different spin patterns for SrFe 2 As 2 at the experimental volume around 90 K [29]. Optimization using FM and NN-AFM pattern leads to a nonmagnetic solution, while the SDW pattern stabilizes with a Fe moment of 1.13 µ B . The energy curves have been shifted by setting the minimum energy value to zero. The dashed vertical line refers to the experimental Fe-As distance obtained from Ref. [29]. The arrows indicate the position of the energy minima.  Figure 5. Left: Energy as a function of volume for AFe 2 As 2 systems, with c/a ratio optimized. The two curves correspond to the antiferromagnetically ordered Fe spins in the SDW pattern with a non-zero moment (red circles) and zero moment (blue triangles). The kink at the intersection of these two curves is caused by a collapse of the c/a ratio upon pressure, which happens at the juncture when the systems lose their Fe moments and become non-magnetic. The c/a ratio collapse is most pronounced in CaFe 2 As 2 due to the small size of the Ca ion and as the size of the A ions increases, this feature becomes more and more subtle. Right: The evolution of the c/a ratio collapse for CaFe 2 As 2 . Notice the emergence of the double minima. CaFe 2 As 2 SrFe 2 As 2 EuFe 2 As 2 BaFe 2 As 2 SDW Figure 6. Volume dependence of the Fe moments corresponding to the energy-volume curves in Fig. 5. The quenching of the spin magnetic moment is highly abrupt for the compounds with pronounced c/a ratio collapse. The Fe moment in BaFe 2 As 2 goes to zero smoothly reflecting the much smoother c/a variation obtained for this compound.

Effects of pressure
As mentioned above, superconductivity in the FeAs based systems can be achieved via doping of charge carriers. This kind of chemical substitution is quite convenient, but changes the electronic structure of the doped systems in a non-trivial way as compared to the undoped systems. Using external pressure as a probe on these systems creates a similar effect as doping, without the added complexity. Application of hydrostatic pressure suppresses both the tetragonal to orthorhombic distortion and the formation of the SDW, and leads to the onset of superconductivity in a similar fashion as charge doping. All the parent members of the 122 family have been reported to superconduct or show signs of its onset under pressure [42,27,17,43,44]. Ca122 was originally reported to superconduct (T c ≈ 10 K) at 0.4 GPa pressure [42,27] but recent work by Yu and collaborators [45] do not observe any signature of bulk superconductivity and . Total DOS per cell as a function of reduced volume for SrFe 2 As 2 corresponding to the energy-volume curves in Fig. 5. In the SDW pattern, the total DOS for both the spin-up and spin-down channels are the same. Therefore, we show here the DOS from only one of the spin channels. The DOS at the Fermi level E F at first decreases with decreasing volume, but later starts to increase after the Fe spin magnetic moment is quenched.
suggest a possible phase separation due to non-hydrostatic conditions. Similarly, Sr122 was first reported to superconduct at 2.8 GPa pressure with a T c of 27 K [44], while on the contrary Kumar et al. [17] did not observe a zero-resistance state up to 3 GPa pressure. A sharp drop in resistivity above 2 GPa pressure was reported for Eu122, suggesting the onset of superconductivity and, more interestingly, signatures of possible re-entrant superconductivity. Though there exist conflicting reports of the transition pressure and possible phase separation in the sample under pressure, it is worthwhile to explore the evolution of the electronic structure and magnetism as a function of pressure.
Pressure studies [27] on the CaFe 2 As 2 system report a significant c/a collapse along with a structural transition (orthorhombic to tetragonal) under modest pressures of less than 0.4 GPa, while no such collapse has been reported for the other compounds. X-ray diffraction refinements carried out at 180 K for SrFe 2 As 2 [17] observe an orthorhombic to tetragonal transition above 3.8 GPa, but no collapse of the c/a ratio is observed. Band structure calculations allow for the study of such features up to very large pressures, that might not be easily attainable through experiments. We have calculated energy as a function of volume for all the four systems in the 122 family. Firstly, we wanted to investigate the possibility of a c/a collapse for each member of the 122 family. Therefore, we calculated energy as a function of volume using the SDW pattern and optimizing only the c/a ratio at each volume. The internal As-z parameter was kept fixed at the experimental (room temperature) value. The results from these calculations are collected in Fig. 5. Surprisingly, all the four 122 systems have a kink in the energyvolume curve caused by a non-continous change in the c/a ratio, which happens at the juncture when the systems lose their Fe moments and become non-magnetic (see Fig. 6). The sharpness of the kink is largest for Ca122 and decreases with the increasing size of the A ion. Such an A-ion size effect was also observed and discussed in section 3.2.1 when investigating the size of the orthorhombic b/a ratio. Our result obtained from LSDA (via a common tangent construction) for CaFe 2 As 2 is in excellent agreement with the previously reported [27] experimental data, volume collapse: δV LDA ≈ 4.7%, δV exp ≈ 5%; ratio collapse: δ(c/a) LDA ≈ 9.8%, δ(c/a) exp ≈ 9.5%. Experimentally [27] a pressure of ∼ 0.3 GPa induces a transition from the orthorhombic phase to a collapsed non-magnetic tetragonal phase for CaFe 2 As 2 . Scaling the volumes of the different 122 systems with respect to the experimental values (V /V exp ), one observes that the kink in the energy-volume curve for the other three 122 systems happens at lower volume ratios (or larger pressures) as compared to the Ca122. It should be worthwhile to investigate this structural feature experimentally by applying higher pressures to the Sr, Ba and Eu 122 systems.
Changes in the electronic structure as a function of reduced volumes were carefully monitored. Shown in Fig. 7 are the total DOS for SrFe 2 As 2 at selected volumes. Similar results are obtained for other 122 systems. The DOS at E F decreases gradually at first for up to 10% volume reduction with respect to the experimental volume. The Fe ions continue to carry a magnetic moment though the actual values are quite reduced. Upon further reduction of the volume, the spin moments get quenched and the DOS at E F  Table. 3, because no c/a optimization was carried out for the latter.
begin to increase and the system becomes non-magnetic. At the experimental volume, the net moments on the various Fe orbitals are quite similar; with the Fe-3d x 2 −y 2 having a slightly larger value than the other orbitals. With the application of pressure, the net moments of all the five d orbitals decrease in a similar fashion and tend to zero. Another important feature that needs to be addressed in regard to the energyvolume curves is the serious underestimation of the equilibrium volume within LDA. Generally, equilibrium volumes obtained from LDA are smaller within up to 8% of the experimentally reported values. In the case of 122 systems using SDW pattern, we obtain values that are 13%, 15%, 10%, and 13% smaller than the experimental reports for Ca, Sr, Ba and Eu 122 systems respectively. Moreover, at the LSDA equilibrium volume, contrary to the experimental reports, all the parent compounds are computed to be nonmagnetic. The reason for this discrepancy is unclear. In the previous sections we discussed the pronounced sensitivity of the Fe moments to the various structural parameters in these FeAs systems. Although with partial optimization (fixed As-z parameter) we have satisfactorily accounted for the experimentally observed c/a collapse in CaFe 2 As 2 , it is necessary to find out what the ultimate LSDA solution is regarding the geometrical structure and magnetism in the 122 systems. Consequently, for Ca and Sr 122 systems and using the SDW pattern, at each volume we have optimized all three free structural parameters in the following order: 1) As-z position, 2) c/a ratio, 3) b/a ratio. This sequence of steps has been repeated until the energies obtained are converged to an accuracy of 10 −6 eV. Collected in Fig. 8 are the energy-volume curves for the Ca and Sr 122 systems. The equilibrium volume obtained after a full optimization is only slightly larger than the values obtained after just a c/a optimization (see Fig. 5). Contrary to the results depicted in Fig. 5, we now no longer observe any kink at the juncture when the Fe ions lose their magnetic moments. The loss of moment for Sr122 is more gradual than for Ca122. As volume is decreased (higher pressures are applied) the Fe spin magnetic moments tend to zero while the orthorhombic distortion ratio b/a tends to unity so that at increased pressures the tetragonal lattice is favored. This observation of the lattice structure preferring the tetragonal symmetry when the Fe ions become nonmagnetic is consistent with our previous results in Sec. 3.2.1, and reaffirms the intimate connection between structure and magnetism for the 122 systems. Optimizing the As z parameter again tends to confirm certain experimental findings (the connection between SDW magnetic pattern and orthorhombic distortion) but not all (for example, lack of c/a collapse under pressure for CaFe 2 As 2 ). This again re-affirms the need for a correct description of the Fe-As interplay to obtain consistent results. We have used the experimental lattice parameters (at ≈ 300 K) and As-z value for all the calculations.

Effects of charge doping
In order to understand the influence of charge doping (both electrons and holes) on the electronic structure and henceforth the magnetism, we performed total energy calculations using the VCA for three different spin patterns: FM, NN-AFM and SDW. Non-magnetic total and Fe orbital resolved DOS for a 30% electron doping on the Sr site in Sr122. Addition of electrons changes the shape of the DOS close to E F drastically. A pronounced peak starts to appear close to E F which tends to destabilize the system. The changes in the total DOS for various doping concentrations are shown in the right panel. Right: Non magnetic total DOS as a function of additional electrons on the Sr site in Sr122.
We considered both electron and hole doping on the A site as well as the Fe site. Our results for the changes in the Fe moment in SrFe 2 As 2 are collected in Fig. 9. Similar results were obtained for other members of the 122 family. We observe very different effects depending on the sign (electrons or holes) and site (Sr or Fe) of the doping. Regardless of the choice of magnetic ordering, electron doping on the Fe (Sr) site weakens (enhances) the magnetism. This behaviour can be explained by analyzing how the nonmagnetic electronic structure changes with electron doping (see Fig. 10). Electron doping on the Fe site (left upper panel of Fig. 10) results in DOS very similar to that of the undoped case, main effect being the E F moved toward higher energies to accommodate the added electrons. On the other hand, electron doping on the Sr site changes the resultant DOS drastically (see left lower and right panel of Fig. 10). Most of the major changes to DOS occur in the close vicinity of E F giving rise to pronounced peaks at the E F . A large value of DOS at the Fermi level, N(E F ), is usually a sign of instability for an electronic system. The system can lower N(E F ) by, for example, developing a long-range magnetic order provided the Stoner criterion is satisfied. The larger values of the computed Fe magnetic moments may reflect such an increased instability to magnetic order. Additionally, with reservations for possible thermodynamical considerations, appearance of this feature may explain why La doped 122 samples could not be synthesized until now.
Substitution of holes on the Sr site does not introduce significant changes to the Fe magnetic moment. Substitution of holes on the Fe site tends to enhance magnetism for both AFM patterns whereas for the FM pattern the magnetism vanishes beyond a critical level of doping. However, this feature for the FM spin pattern is of no significance, because energetically it lies above both of the AFM patterns at all levels of doping.

Electric field gradient
Nuclear magnetic resonancce (NMR) is a local probe that is extremely sensitive to certain details of the structure. Since the As z position is a key determinant of many of the electronic properties of the FeAs systems, the quadrupole frequency ν Q from NMR measurements can provide a direct measure to the Fe-As interaction. Theoretically, ν Q can be obtained by calculating the electric field gradient (EFG). The EFG is defined as the second partial derivative of the electronic potential v( r) at the position of the nucleus This traceless and symmetric tensor of rank 2 is described in the principal axis system by the main component V zz and the asymmetry parameter η = (V xx − V yy )/V zz . V zz is per definition the component with the largest magnitude |V zz | ≥ |V yy | ≥ |V xx | and is not necessarily parallel to the z-axis of the crystal. From these two parameters (V zz and η) and the quadrupole moment for 75 As Q = (0.314 ± 0.006) b [46] the quadrupole frequency ν Q for 75 As (with a nuclear spin of I = 3/2) can be calculated [47] ν Q = eQV zz 2h 1 + η 2 3 . (2) The experimental lattice parameters, including the As z position for the calculation of the EFG for As in CaFe 2 As 2 , SrFe 2 As 2 and BaFe 2 As 2 were obtained from Ref. [27], [48], [12] respectively. For the parent compounds we investigated the influence of the As z position, the structural phase transition, the magnetism and the pressure on the EFG. We also investigated the effects of doping on the EFG. First we focus on the As z dependence of the EFG. Just as the computed Fe magnetic moment, whose value show a strong dependence on the As z position (see Sec. 3.2.3), the EFG is also found to display a strong As z dependence. The EFG increases strongly for all three compounds, as the Fe-As distance decreases, see Fig. 11. In case of CaFe 2 As 2 , there is a minimum in the EFG for a displacement of roughly ∆z = −0.1Å from the experimental position, while for larger Fe-As distances the EFG increases again. The same trend is observed for the other two compounds, middle and lower panels in Fig. 11. They exhibit the minimum in the EFG at about ∆z = +0.05Å. For all the three parent compounds, the Fe-As distance at which the minimum in total energy occurs is smaller than that corresponds to the EFG minimum (see arrows in Fig. 11). For CaFe 2 As 2 we observe a good agreement between the calculated EFG at the experimental As z position (for 250 K) and the measured EFG at 250 K [49] (the light green symbol in the upper panel of Fig. 11). In case of BaFe 2 As 2 the magnitude of  Figure 11. Dependence of the EFG for As on the As z position. ∆z = z − z exp . Different symbols show different calculations: cross = nonmagnetic with tetragonal symmetry, full circle = nonmagnetic with orthorhombic symmetry (almost identical to tetragonal symmetry for SrFe 2 As 2 and therefore not shown) and empty circle = magnetic (SDW pattern) with orthorhombic symmetry. The total energy minimum is marked by an arrow for each nonmagnetic curve. The error bars show the experimental results for the tetragonal phase (at 250 K for CaFe 2 As 2 and at 200 K for BaFe 2 As 2 (the two error bars indicate the experimentally unknown sign of the EFG)).
the measured EFG at 200 K is roughly 0.7 × 10 21 V/m 2 [50], while the sign is unknown since it cannot be extracted from NQR measurements (In Fig. 11 the experimental EFG values with both signs are shown). The calculated V zz for the experimental As z position is −1.1×10 21 V/m 2 . If the experimental EFG is negative, reasonable agreement between experiment and calculation is obtained. In a preliminary measurement for SrFe 2 As 2 the quadrupole frequency ν Q was determined to be positive and less than 2 MHz [51] and this is also consistent with the calculated EFG of 0.8 MHz at the experimental As z position. For members of the 1111 family; LaFeAsO and NdFeAsO: the calculated EFG for the optimized As z position agreed better with the experimental EFG [52,53].
Our results for three representative members of the 122 family as shown above follow a different trend: the calculated EFG using the experimental As z position agree better with the measured EFG values.
To study the influence of the orthorhombic distortion, but without the influence of magnetism we perform non-magnetic calculations both in tetragonal and orthorhombic symmetry. The orthorhombic splitting of the axes in the (a, b) plane has a rather small influence on the EFG. The EFG is larger for the orthorhombic symmetry for small Fe-As distances, i.e. ∆z < −0.1Å. In case of SrFe 2 As 2 , the effect of the orthorhombic splitting is so small, that the orthorhombic EFG curve in Fig. 11 is not shown (see middle panel of Fig. 11). In case of BaFe 2 As 2 , we observe similar behaviour as for CaFe 2 As 2 . The tetragonal and orthorhombic EFG curves cross close to the EFG minimum and the EFG is larger for the orthorhombic symmetry for smaller Fe-As distances, i.e. ∆z < +0.1Å. For all three compounds we find that V zz is parallel to the crystallographic z-axis for the non-magnetic calculations in both the tetragonal and orthorhombic symmetry. Investigation of the influence of the magnetism on the EFG in the orthorhombic symmetry show that, FM or NN-AFM ordering of the Fe atoms does not change the EFG much, however, the SDW order has a huge influence on the EFG, cf. Table 4. For all the three systems, as the Fe-As distance is decreased, the magnetic moment is reduced and finally tends to zero. At this displacement value, the SDW EFG curves smoothly join the non-magnetic orthorhombic EFG curves as one would expect. In Fig. 11 the component of the EFG, that is parallel to the z-axis of the crystal is shown. As mentioned before, V zz is found to be parallel to the crystallographic z-axis in all nonmagnetic calculations. For the magnetic SDW phase the same behaviour is observed for CaFe 2 As 2 , but not for SrFe 2 As 2 and BaFe 2 As 2 . For the latter two compounds, V zz changes the axis, i.e., the axis along which EFG is the largest changes as Fe-As distance is varied. For BaFe 2 As 2 , such a behaviour was also observed experimentally [50] when The three components of the EFG tensor for SrFe 2 As 2 in the orthorhombic SDW phase as a function of the As z position. ∆z = z − z exp . The component of the EFG, parallel to the crystallographic x-axis is shown by triangles up, the component parallel to the crystallographic y-axis by squares and the one parallel to the crystallographic z-axis by solid circles. V zz , the largest one of these three, is marked by a large shaded circle for each As z position. Right: The three components of the EFG tensor for BaFe 2 As 2 in the orthorhombic SDW phase as a function of the As z position. The rest of the notation is the same as the left panel.
going from the high-temperature nonmagnetic tetragonal phase to the low temperature SDW phase. Unfortunately for CaFe 2 As 2 , only the quadrupole frequency parallel, and not perpendicular to the crystallographic z-axis is provided in Ref. [49]. The three diagonal components of the EFG tensor V ii , which are parallel to the x, y and z-axis of the crystal, vary continuously as a function of the As z position, as can be seen in Fig. 12. In case of SrFe 2 As 2 , V zz is parallel to the x-axis for a displacement of As between +0.05Å and −0.075Å (which includes the experimental As z position) and parallel to the z-axis for a displacement between −0.1Å and −0.15Å. For BaFe 2 As 2 according to its definition as the largest component V zz fluctuates between all the three different axes (Fig. 12) In particular, at the experimental As z position V zz is parallel to the y-axis. We also observe that the component parallel to the x-axis is very similar for both Sr and Ba 122 compounds. The components parallel to the yand z-axis show the same variation with As z position, only the values for the two compounds are shifted by an almost constant amount. Fig. 3 in Ref. [49] shows the temperature dependence of the quadrupole frequency ν Q for CaFe 2 As 2 : ν Q increases drastically from 300 K to 170 K. At 170 K there is a large jump in the frequency due to the orthorhombic SDW phase transition. Between 170 K and 20 K ν Q is rather constant. The calculated EFGs correspond to lattice parameters at 250 K and 50 K. For these two temperatures the quadrupole frequency (parallel to the crystallographic z-axis) is almost identical. This is in agreement with our result for the experimental As z position as seen in the upper panel of Fig. 11. We also investigated the influence of pressure on the EFG. V zz for different pressures was calculated for CaFe 2 As 2 [50] and SrFe 2 As 2 [17] using the experimental structural parameters reported as a function of pressure. Our result is shown in the inset of Fig. 13. In case of CaFe 2 As 2 , the EFG increases when the applied pressure is increased from 0 GPa to 0.24 GPa. For these pressures the structure is in the (orthorhombic) SDW phase. The next experimental pressure point is larger than the critical pressure of 0.3 GPa (Sec. 3.3), where the c/a collapse takes place. The structure changes into the nonmagnetic tetragonal phase and the calculated EFG increases drastically from roughly 3 to 10×10 21 V/m 2 . Experimentally, the applied pressure for SrFe 2 As 2 was much higher (up to 4 GPa) than for CaFe 2 As 2 , but no indications of a collapsed phase was found till now. Contrary to the jump in the calculated EFG at 0.3 GPa for CaFe 2 As 2 , EFG for SrFe 2 As 2 increases monotonously without any kinks upto 4 GPa. It is worthwhile to measure the EFG for these systems to get a more clear picture.
Finally, the EFGs of the A site doped compounds were calculated with VCA. The validity of the VCA was checked by super cell calculations for SrFe 2 As 2 and BaFe 2 As 2 . Due to the super cell construction, there are three different Wyckoff positions for As and hence three different EFGs, which lie reasonably close to the VCA EFG curve. In the VCA calculation we keep the structural parameters fixed for the different levels of doping. In Fig. 13 EFGs calculated in this manner are shown for CaFe 2 As 2 , SrFe 2 As 2 and BaFe 2 As 2 . In case of CaFe 2 As 2 , the EFG increases when electrons are taken out and decreases when electrons are added to the system. This implies that the As electron  Figure 13. EFGs calculated for doped CaFe 2 As 2 (green circles), SrFe 2 As 2 (red squares) and BaFe 2 As 2 (blue diamonds) using VCA. Results obtained from a fourfold super cell for x = -0.25 for SrFe 2 As 2 (shaded orange squares) and BaFe 2 As 2 (shaded blue diamonds) in the nonmagnetic tetragonal phase are also shown. Inset: Dependence of the EFG on pressure for CaFe 2 As 2 (left) and SrFe 2 As 2 (right). The latter is in the (nonmagnetic) tetragonal phase. density gets more isotropic, when the system is electron doped. For BaFe 2 As 2 , the trend is the same as in CaFe 2 As 2 whereas for SrFe 2 As 2 the situation is slightly different: hole doping does not change the EFG much, while electron doping increases the EFG. Note however, that the calculated EFG for SrFe 2 As 2 are quite small.
We conclude that the EFG in the 122 and in the 1111 systems behave similar [52,53]: the effect of electron doping on the EFG is much smaller than the influence of the As z position and pressure (compare Fig. 11 and Fig. 13). This finding emphasizes again the crucial importance of a correct description of the Fe-As interaction (that is mostly responsible for the density around As) for the physical properties of the iron pnictides.

Substitutions of Fe by other 3d-metals
As already mentioned, at ambient pressure, no bulk superconductivity has been observed in stoichiometric REOFeAs and AFe 2 As 2 (A = Ca, Sr, Ba, Eu) compositions (except for one report on SrFe 2 As 2 crystals [54]). Instead, these parent compounds display the SDW transition at typically 100-200 K. A modification of the intralayer d Fe−Fe a and interlayer d Fe−Fe c distances and thus of the electronic states at E F can be achieved by different means: (i) application of hydrostatic (or uniaxial) pressure, (ii) isovalent substitution of a constituent atom by a smaller/larger ion in order to apply chemical pressure, (iii) hole doping or (iv) electron doping by non-isovalent substitution of any of the constituent atoms. The latter two methods usually also excert chemical pressure. Most excitingly, all these methods have been proven to be successful in generating bulk superconductivity in iron arsenide systems.
Application of pressure has widely been used to explore the phase diagrams of the superconducting chemical systems [42,55,44]. The method usually introduces no crystallographic disorder in the structural building units. In contrast when substituting a chemical constituent (methods ii-iv) always a certain degree of structural disorder is introduced. First, only substitutions on sites in-between the Fe-As layers were attempted. Based on the experience gained from extensive work on cuprates, such an indirect doping of the Fe-As layers is expected to introduce only minor structural disorder. In a localized (cuprate-like) as well as in an itinerant model of the arsenides, this type of doping amounts to a simple charge doping. Such experiments are therefore not suitable for discriminating between both models.
In contrast, a substitution of an atom species within the Fe-As layer can yield more information on the underlying physics. In an itinerant model the substitution of a small amount of Fe by another d element (T M) is expected to be similar to indirect doping since only the total count of electrons is relevant, i.e. a rigid-band picture should work in first approximation. In a picture with localized d electrons, on the other hand, doping on the Fe site should directly affect the correlations in the Fe-As layers. A behaviour drastically different from indirect doping should evolve. In cuprates the substitution of a few percent Ni or Zn on the Cu site leads to a strong reduction of T c . Therefore, several groups recently investigated the properties of solid solutions of the type REO(Fe 1−x Co x )As or AFe 2−x Co x As 2 . Sefat et al. [56] and Wang et al. [57] first reported superconductivity in cobalt doped LaOFeAs with a maximum T c ≈ 10 K. Our group concentrated on the system SrFe 2−x T M x As 2 : while the pure Fe compound undergoes a lattice distortion and SDW ordering at T 0 = 205 K [11], Co substitution leads to a rapid decrease of T 0 , followed by the onset of bulk superconductivity in the concentration range 0.2 ≤ x ≤ 0.4 [15]. The maximum T c of ≈ 20 K is achieved for x ≈ 0.20. This was in fact also the first observation of electron-doping induced superconductivity in AFe 2 As 2 compounds. Co substitution also generated bulk superconductivity with maximum T c ≈ 22 K in BaFe 2−x Co x As 2 [16], however, the optimal doping seems to be lower than in the Sr system [58]. Substitution of the following T M, nickel, introducing twice as many electrons per atom into the Fe-As layer, also generates bulk superconductivity, albeit with lower T c than Co substitution in the Sr compound [15]. However, for the corresponding Ba compound T c up to 21 K is reported for BaFe 1.90 Ni 0.10 As 2 [59]. Only very recently another internal substitution, namely of As by P, was reported for EuFe 2 As 2 [60] and LaOFeAs [61]. Also by this means the SDW transition can be influenced and superconductivity can be induced.
In Table 5 we present the lattice parameters and the SDW and superconducting transition temperatures (T 0 , T c ) of several SrFe 2−x T M x As 2 solid solutions. Values for T 0 can be most easily obtained from the corresponding anomaly in resistivity data (see Fig. 14). Besides Co and Ni substitutions in the Sr122 and Ba122 systems, no further d element substitutions have been reported yet. As demonstrated recently [15], substitution of Fe by Co suppresses rapidly T 0 (see Fig. 14). Bulk superconductivity, as proven by specific heat, magnetic shielding, and resistivity data, appears when T 0 = 0 or T 0 < T c , which is reached for x > 0.20 [15]. Only about half of the substituting element (x ≈ 0.10) is necessary to induce bulk superconductivity when using nickel [59]. Both elements then introduce 0.2 excess electrons into the FeAs layers. While the a lattice parameter does not change significantly with Co substitution the c lattice parameter decreases continuously in SrFe 2−x Co x As 2 [15] and with Ni content in BaFe 2−x Ni x As 2 [59]. Chemical homogeneity of the Co or Ni distribution is still an issue in current samples. One of the most important questions, the co-existence or mutual exclusion of SDW state and bulk superconductivity, bas been discussed heavily for AFe 2 As 2 -based alloy series [62,63,64]. The answer is currently open and can be only given for really homogeneous samples.
Direct, in-plane hole doping might also induce superconductivity. Our new investigations show, that a substitution of Fe by Mn is possible and that it leads to a continuous increase of both the a and c lattice parameters with Mn content. Under these conditions a hole doping does not generate superconductivity. In contrast, in the indirectly-doped Sr 1−x K x Fe 2 As 2 [4,65] and Ba 1−x K x Fe 2 As 2 [6] compounds the a lattice parameter decreases with x while c increases, keeping the unit cell volume almost constant. Also, the SDW transition temperature T 0 is suppressed with increasing Mn content in a different way (see Fig. 14) than for the Co and Ni substitutions where T 0 is suppressed for x ≈ 0.20 and x ≈ 0.10, respectively. Indeed, after an initial decrease of T 0 to ≈140 K for x = 0.20 the transition temperature seems not to decrease further with x. Thus, the doping with holes or electrons is not the only important factor for the appearance of superconductivity but a corresponding tuning of the distances d Fe−Fe a and d Fe−Fe c has to be accomplished also. At present, the microscopic origin of the differences upon Mn doping compared to Co or Ni doping is unclear. Therefore, further investigations for different substitutions are currently underway.
Magnetic susceptibility and specific heat data for polycrystalline samples SrFe 2−x Co x As 2 have already been presented [15]. Here, instead we report newer data obtained on two crystals with Co contents x > 0.2 grown by a flux method (see section 2.2).
Both crystals show strong diamagnetic signals in measurements after zero field cooling (ZFC). The onset temperatures T mag c are 17.8 K and 15.3 K, respectively. While the transition for crystal X1 is much wider than that of crystal X2 the T c of the latter is somewhat lower, indicating a slightly larger Co-content in accordance with the EPMA investigations. The shielding signals (ZFC) corresponds to the whole sample volume, however the Meissner effect (FC) is very small. This is typical for Cosubstituted AFe 2 As 2 materials and probably due to strong flux line pinning. The random (and somewhat inhomogeneous) substitution of Fe by Co within the superconducting   (7) -130 this work layers seems to introduce effective pinning centers. This is a remarkable difference to superconducting compositions with substitutions outside the Fe-As layers.
As already demonstrated [15], the SDW ordering and the connected lattice distortion at T 0 = 205 K in SrFe 2 As 2 [11,29] is strongly suppressed by Co substitution, similar as for K substitution (indirect hole doping) [65]. For the two crystals no corresponding anomaly in ρ(T ) is observed. The specific heat c p (T ) for the two crystals are shown in Fig. 15 in a c p (T )/T 2 versus T representation. It can be clearly seen that crystal X1 has a very broad transition (with a "foot" at the high-temperature side) while crystal X2 displays a rounded but singlestep anomaly. The specific heat jumps ∆c p /T c and the transition temperatures T cal c can be evaluated by a fit including a phonon background (harmonic lattice approximation) and an electronic term c es (T ) according to the BCS theory (∆c p /T c = 1.43γ) or the phenomenological two-liquid model (∆c p /T c = 2γ, a model for stronger e-ph coupling). The inclusion of a residual linear term γ ′ T was found to be absolutely necessary for a good fit.
c p (T ) = γ ′ T + βT 3 + δT 5 + c es (T ) The jump at T c is "broadened" in order to simulate the rounding of the transition steps due to chemical inhomogeneities. For the more homogeneous sample X2 no difference in the least-squares deviation is observed between the BCS and two-fluid model. We find for crystal X2 ∆c p /T cal c ≈12.0 mJ mol −1 K −2 at T cal c = 12.34 K and also for crystal X1 similar values (≈12.5 mJ mol −1 K −2 ; T c = 13.22 K). Similar values of ∆c p /T cal c were observed in our previous study [15] of polycrystalline samples with Co-contents x = 0.20 and x = 0.30.
The existence of a linear specific heat term well below T c is found for several AFe 2 As 2 -based alloys [15,66]. For H = 0 we observe for both crystals values of γ ′ around 20 mJ mol −1 K −2 . γ ′ generally increases with field. Whether the residual γ ′ is due to defects as in the case of early cuprate superconductor samples (see e.g. Ref. [67]) or whether it is an intrinsic contribution has to be clarified by further experiments. An intrinsic reason could be some ungapped parts of the Fermi surface [68]. For the specific heat jump ∆c p /T c in BaFe 2−x Co x As 2 also relatively small values are reported (≈ 25 mJ mol −1 K −2 [58]) while for Ba 0.6 K 0.4 Fe 2 As 2 (∆c p /T c ≈ 100 mJ mol −1 K −2 [66,62]) much larger jumps are observed. This may indicate that the superconducting Fermi surface portions in the Co-substituted compounds (in-plane doping) are strongly different from those in indirectly doped superconductors. Recent photoemission (ARPES) investigations indeed point out severe differences between (non-superconducting) BaFe 1.7 Co 0.3 As 2 and (superconducting) Ba 0.6 K 0.4 Fe 2 As 2 [69]. In conclusion, our doping experiments on the Fe site strongly favor an intinerant picture over a localized scenario. Further thermodynamic and Fermi surface studies are required to resolve this issue.

Summary
In this paper, we presented a joint theoretical and experimental study of the systems AFe 2 As 2 (A = Ca, Sr, Ba, Eu) and SrFe 2−x T M x As 2 (T M = Mn, Co, Ni) to investigate the relation of crystal structure and charge doping to magnetism and superconductivity in these compounds. Based on ab-initio electronic structure calculations we focused on the relationship between the crystal and electronic structure, charge doping and magnetism for the 122 family since their electronic structure and physical properties are quite similar to the other superconducting iron pnictide families (1111, 1111', 111, 11).
Although problems with an accurate description of the Fe-As interaction persist in present-day density functional calculations, this approach provides deep inside into many questions. We demonstrated that tetragonal to orthorhombic transition in the 122 compounds is intrinsically linked to the SDW formation in agreement with experimental observations. We find an anisotropic, pressure-induced volume collapse for AFe 2 As 2 (A = Ca, Sr, Ba, Eu) that goes along with the suppression of the SDW magnetic order. For A = Ca our calculations are in excellent agreement with the experimental observations [27]. An experimental verification for the other compounds (A = Ca, Sr, Ba, Eu) would be desirable. With respect to the doping dependence in SrFe 2−x T M x As 2 , we find the correct trends compared to the experimental results. A more quantitative comparison will require the explicit treatment of the influence of the substitutional disorder on electronic structure and magnetism. This task is left for an extended future study.
As demonstrated also for the EFG, many properties of these compounds are sensitive to the As z position. Since the magnetism and therefore the superconductivity crucially depend on this structural feature and the related accurate description of the Fe-As interaction, the improvement of the calculations in this respect may offer the key to the understanding of superconductivity in the whole family. In order to improve the present-day density functional calculation for this class of materials, the first step requires a deeper understanding of where, how and why these DFT calculation fail. Besides further calculational effort, a broader experimental basis, especially high pressure studies will be necessary to approach this complex issue.
Experimentally, we investigate the substitution of Fe in SrFe 2−x T M x As 2 by other 3d transition metals, T M = Mn, Co, Ni. In contrast to a partial substitution of Fe by Co or Ni (electron doping) a corresponding Mn partial substitution does not lead to the suppression of the antiferromagnetic order or the appearance of superconductivity.
The observed existence of a linear specific heat term in SrFe 2−x Co x As 2 well below T c is extremely important for the understanding of the superconductivity in this compound and all related 122 superconductors with doping on the Fe site. Therefore, a careful investigation whether this feature is intrinsic or not is a crucial question. In order to answer it, further studies on carefully prepared and characterized high-quality samples are required. Since in many experiments a considerable sample dependence is observed, this issue is of large general importance for a future understanding of the superconducting iron pnictide materials.