Phase diagrams of electron- and hole-doped BaFe₂As₂

In BaFe₂As₂, superconductivity can be tuned by 3d (Co, Ni, Cu, Co/Cu mixture),Reference Canfield and Bud’ko³ 4d (Rh, Pd),Reference Ni, Thaler, Kracher, Yan, Bud’ko and Canfield⁹ and 5d (Ir, Pt)Reference Wang, Shi, Yan, Yuan, Lu, Wang and Zhao^10–Reference Saha, Drye, Kirshenbaum, Butch, Zavalij and Paglione¹² electron doping. The phase diagrams of these doped series show universal behavior and can be compared quantitatively due to the successful growth of homogeneous single crystals of the doped materials.Reference Canfield and Bud’ko³Figure 1c and 1d summarize two pairs of phase diagrams of Ba(Fe_1–xTM_x)₂As₂ single crystals: the TM = Co, Rh pair and the TM = Ni, Pd pair.Reference Canfield and Bud’ko^3, Reference Ni, Thaler, Kracher, Yan, Bud’ko and Canfield^9, Reference Nandi, Kim, Kreyssig, Fernandes, Pratt, Thaler, Ni, Bud’ko, Canfield, Schmalian, McQueeney and Goldman^13, Reference Kreyssig, Kim, Nandi, Pratt, Tian, Zarestky, Ni, Thaler, Bud’ko, Canfield, McQueeney and Goldman¹⁴ In these doping series, the structural and magnetic phase transitions at T _s= T _m= 134 K in BaFe₂As₂ are monotonically suppressed and separated with doping. Superconductivity up to ∼24 K for Co- or Rh-doping and ∼19 K for Ni- or Pd-doping is found in both tetragonal/paramagnetic and orthorhombic/antiferromagnetic phasesReference Canfield and Bud’ko³ and stabilized in a dome-like region of the phase diagram. Figure 1c and 1d clearly show that (1) the phase diagram of Co-doped BaFe₂As₂ is almost identical to that of Rh-doped BaFe₂As₂, and the phase diagram of Ni-doped BaFe₂As₂ is almost identical to that of Pd-doped BaFe₂As₂, despite the differences in the lattice parameters and related structural quantities between 3d and 4d dopants in each pair;Reference Canfield and Bud’ko³ (2) there is a clear difference between these two pairs of phase diagrams in the sense that the extent of the superconductivity dome, in terms of x, for the Co/Rh pair is twice that for the Ni/Pd pair; the lines of structural and magnetic transitions behave somewhat similarly.

Superconductivity has not been observed so far in the transition metal, hole-doped series: Ba(Fe_1–xTM_x)₂As₂ (TM = Mn and Cr.Reference Sefat, Singh, VanBebber, Mozharivskyj, McGuire, Jin, Sales, Keppens and Mandrus^15–Reference Kim, Kreyssig, Thaler, Pratt, Tian, Zarestky, Green, Bud’ko, Canfield, McQueeney and Goldman¹⁸ Instead, the competing orders in these doping series are different types of magnetism.Reference Marty, Christianson, Wang, Matsuda, Cao, VanBebber, Zarestky, Singh, Sefat and Lumsden^17, Reference Kim, Kreyssig, Thaler, Pratt, Tian, Zarestky, Green, Bud’ko, Canfield, McQueeney and Goldman¹⁸Figure 2 shows the phase diagrams of Ba(Fe_1–xTM_x)₂As₂ (TM = Mn and Cr) inferred from neutron diffraction and bulk measurements.Reference Sefat, Singh, VanBebber, Mozharivskyj, McGuire, Jin, Sales, Keppens and Mandrus^15, Reference Marty, Christianson, Wang, Matsuda, Cao, VanBebber, Zarestky, Singh, Sefat and Lumsden^17, Reference Kim, Kreyssig, Thaler, Pratt, Tian, Zarestky, Green, Bud’ko, Canfield, McQueeney and Goldman¹⁸ For both Mn- and Cr-doping, (1) the structural and magnetic phase transitions in BaFe₂As₂ are initially monotonically suppressed with doping, and no separation of these two transitions like that seen for electron doping is detected; (2) when T _s and T _m are suppressed down to ∼50–70 K, instead of superconductivity, G-type AFM ordering with a propagation vector of (1, 0, 1) (in the tetragonal basis) for Cr-doping and “stripe-like” or “two-Q” AFM ordering with a propagation vector of (1/2, 1/2, 1) for Mn-doping are found. The magnetic ordering temperatures of these new magnetic phases increase upon further doping. These trends differ from the Ba(Fe_1–xCo_x)₂As₂ case, in which superconductivity occurs when the magnetic order is suppressed. Such contrasting behavior between transition-metal electron- and hole-doping suggests that in the case of Mn- and Cr-doping, superconductivity might be precluded by the stabilization of new magnetic phases. It is noteworthy that the initial suppression rate of T _m with doping (dT _m/dx) is very similar for TM = Cr and Mn and is approximately a factor of two lower than that in the case of TM = Co, Rh, Ni, and Pd. Qualitatively, such difference in dT _m/dx can be expected since the magnetic moment is approximately constant for the former doped series,Reference Marty, Christianson, Wang, Matsuda, Cao, VanBebber, Zarestky, Singh, Sefat and Lumsden^17, Reference Kim, Kreyssig, Thaler, Pratt, Tian, Zarestky, Green, Bud’ko, Canfield, McQueeney and Goldman¹⁸ whereas it decreases monotonically to zero for the latter series.Reference Kreyssig, Kim, Nandi, Pratt, Tian, Zarestky, Ni, Thaler, Bud’ko, Canfield, McQueeney and Goldman^14, Reference Fernandes, Pratt, Tian, Zarestky, Kreyssig, Nandi, Kim, Thaler, Ni, Canfield, McQueeney, Schmalian and Goldman^19–Reference Dioguardi, Roberts-Warren, Shockley, Bud’ko, Ni, Canfield and Curro²¹

Figure 2.

T–x phase diagrams as well as the ordered moment obtained from neutron scattering measurements of (a) Ba(Fe_1–xCr_x)₂As₂ seriesReference Marty, Christianson, Wang, Matsuda, Cao, VanBebber, Zarestky, Singh, Sefat and Lumsden¹⁷ and (b) Ba(Fe_1–xMn_x)₂As₂ series.Reference Kim, Kreyssig, Thaler, Pratt, Tian, Zarestky, Green, Bud’ko, Canfield, McQueeney and Goldman¹⁸ PM, paramagnet; SDW, spin density wave; AFM, antiferromagnet; O, orthorhombic; T, tetragonal.

Isoelectronic doping and pressure

As discussed previously, hole doping (on the alkaline-earth site) and, particularly, electron doping (on the Fe site) present relatively simple ways to suppress magnetism and induce superconductivity. However, two alternative approaches, which do not imply distinct shifts of the Fermi level, have also been successfully implemented.

Superconductivity has been induced by Ru substitution on the Fe siteReference Sharma, Bharathi, Chandra, Reddy, Paulraj, Satya, Sastry, Gupta and Sundar^22–Reference Kim, Pratt, Rustan, Tian, Zarestky, Thaler, Bud’ko, Canfield, McQueeney, Kreyssig and Goldman²⁵ and by P substitution on the As site.Reference Jiang, Xing, Xuan, Wang, Ren, Feng, Dai, Xu and Cao^26, Reference Kasahara, Shibauchi, Hashimoto, Ikada, Tonegawa, Okazaki, Shishido, Ikeda, Takeya, Hirata, Terashima and Matsuda²⁷ Angle-resolved photoemission spectroscopy (ARPES) measurementsReference Brouet, Rullier-Albenque, Marsi, Mansart, Aichhorn, Biermann, Faure, Perfetti, Taleb-Ibrahimi, Le Fevre, Bertran, Forget and Colson²⁸ suggest that Ru doping is indeed isoelectronic, with no holes or electrons added. Figure 3 presents the phase diagrams of Ba(Fe_1–xRu_x)₂As₂Reference Kim, Pratt, Rustan, Tian, Zarestky, Thaler, Bud’ko, Canfield, McQueeney, Kreyssig and Goldman²⁵ and BaFe₂(As_1–xP_x)₂Reference Kasahara, Shibauchi, Hashimoto, Ikada, Tonegawa, Okazaki, Shishido, Ikeda, Takeya, Hirata, Terashima and Matsuda²⁷ single crystals. For both doping schemes, the appearance of the phase diagrams is similar to those of electron doping, although for Ru doping, no splitting between the structural and magnetic phase transitions—as was found for electron doping—is detected. (In the case of P doping,Reference Kasahara, Shibauchi, Hashimoto, Ikada, Tonegawa, Okazaki, Shishido, Ikeda, Takeya, Hirata, Terashima and Matsuda²⁷ it is not clear if the splitting between structural and magnetic transitions develops, since the transition temperatures were determined from bulk measurements using a criterionReference Kasahara, Shibauchi, Hashimoto, Ikada, Tonegawa, Okazaki, Shishido, Ikeda, Takeya, Hirata, Terashima and Matsuda²⁷ different from the one used for Co doping, which was confirmed by neutron/x-ray scattering.Reference Kreyssig, Kim, Nandi, Pratt, Tian, Zarestky, Ni, Thaler, Bud’ko, Canfield, McQueeney and Goldman¹⁴) In Ba(Fe_1–xRu_x)₂As₂, the maximum T _c is around 18 K, with the superconducting dome spanning from x ∼0.18 to ∼0.36. In BaFe₂(As_1–xP_x)₂, superconductivity is stabilized over an extended dome regime from x ∼0.14 to ∼0.7, with the highest T _c around 31 K.

Figure 3.

(a) T–x phase diagrams of Ba(Fe_1–xRu_x)₂As₂ single crystals determined by bulk and neutron scattering measurements.Reference Kim, Pratt, Rustan, Tian, Zarestky, Thaler, Bud’ko, Canfield, McQueeney, Kreyssig and Goldman²⁵ Inset: The T–P phase diagram of BaFe₂As₂ obtained using a modified Bridgman anvil cell.Reference Colombier, Bud’ko, Ni and Canfield³⁰ (b) BaFe₂(As_1–xP_x)₂ single crystals determined by transport and thermodynamic measurements.Reference Kasahara, Shibauchi, Hashimoto, Ikada, Tonegawa, Okazaki, Shishido, Ikeda, Takeya, Hirata, Terashima and Matsuda²⁷ SDW, spin density wave; TET, tetragonal; PM, paramagnetic; AFM, antiferromagnetic; Ort, orthorhombic.

Superconductivity can also be induced in BaFe₂As₂ by external pressure P.Reference Alireza, Ko, Gillett, Petrone, Cole, Lonzarich and Sebastian^29–Reference Yamazaki, Takeshita, Kobayashi, Fukazawa, Kohori, Kihou, Lee, Kito, Iyo and Eisaki³¹ It is known that the degree to which the pressure is hydrostatic can strongly affect the T–P phase diagramReference Paglione and Greene^4, Reference Yamazaki, Takeshita, Kobayashi, Fukazawa, Kohori, Kihou, Lee, Kito, Iyo and Eisaki^31, Reference Canfield, Bud’ko, Ni, Kreyssig, Goldman, McQueeney, Torikachvili, Argyriou, Luke and Yu³² due to the highly anisotropic compressibility and high responsivity to (local and global) stresses and strains of the materials in the 122 family. This leads to different T _s and T _m suppression rates and to different extents of the superconducting dome under pressure. However, despite these differences, the key features of the T–P phase diagram are similar. The inset in Figure 3a shows the T–P phase diagram obtained using a modified Bridgman anvil cell.Reference Colombier, Bud’ko, Ni and Canfield³⁰ With applied pressure, the structural and magnetic phase transitions at 134 K are monotonically suppressed, and no separation of these two is observed. Superconductivity occurs when T _s and T _m are suppressed sufficiently, and T _c(P) has a dome-like shape, with its maximum occurring at a pressure close to that needed to suppress T _s and T _m to zero.

The induced superconductivity in these two isoelectronic doping cases is often viewed as a chemical analogue to applied pressure. This view appears to be oversimplified because (1) Ru doping and P doping do not change the lattice in a similar manner; and (2) the substitution of Ba by isoelectronic Sr, which has a smaller ionic radius and thus introduces chemical pressure into the system, results in neither superconductivity nor the suppression of T _s and T _m.Reference Wang, Yang, Ma, Tian, Shi, Lu, Zeng and Li³³ Recent high-resolution x-ray diffraction measurementsReference Rotter, Hieke and Johrendt³⁴ suggest that although Sr doping results in similar unit-cell parameters to that of the superconducting BaFe₂(As_1–xP_x)₂ samples, the Fe–As bond length decreases by less than 0.5% with x = 1 Sr doping, whereas it monotonically decreases by 1.5% with x ∼0.5 P doping. This suggests a possible relation between the Fe–As bond length and the suppression of T _s and T _m.Reference Rotter, Hieke and Johrendt³⁴

Transition metal electron-doped BaFe₂As₂—Empirical trends

The effects of 3d and 4d transition metal electron dopants on BaFe₂As₂ single crystals have been discussed in detail in References Reference Canfield and Bud’ko3 and Reference Ni, Thaler, Yan, Kracher, Colombier, Bud’ko, Canfield and Hannahs35. Here we present a brief summary. Considering that the T–x phase diagrams of Co/Rh- and Ni/Pd-doping pairs are basically identical (Figure 1), for simplicity, we plot the structural, magnetic, and superconducting critical temperatures of BaFe₂As₂ doped with Co-, Ni-, Cu- and two different sets of (Co+Cu)-dopings as a function of the number of extra electrons. We define e, the extra electron count per TM site as x for Co or Rh doping, 2x for Ni or Pd doping, and 3x for Cu doping. Except for Cu doping, the superconducting dome, in particular in the overdoped part, scales well with e (Figure 4a), whereas the structural/magnetic transitions scale reasonably well with doping concentration.Reference Canfield and Bud’ko³ For the underdoped part of the dome, there appears to be a clear correlation between T _c and T _s (or between T _c and T _m) (Figure 4a, inset). These observations lead to the understanding that T _c in the underdoped regime is determined by T _s(T _m), while T _c in the overdoped regime is controlled by the extra electrons added.

Figure 4.

(a) T–e phase diagrams of Ba(Fe_1–xTM_x)₂As₂ (TM = Co, Ni, Cu, and Co/Cu).Reference Ni, Thaler, Yan, Kracher, Colombier, Bud’ko, Canfield and Hannahs³⁵ Inset: superconducting transition temperature T _c as a function of structural phase transition temperature, T _s, in Ba(Fe_1–xTM _x)₂As₂ (TM = Co, Rh, Ni, and Pd). Note that T _c versus T _m results in similar scaling. (b) Comparison of the effects of chemical doping and application of pressure for the Ba(Fe_1–xCo_x)₂As₂ series.Reference Ni, Thaler, Yan, Kracher, Colombier, Bud’ko, Canfield and Hannahs^35, Reference Colombier, Torikachvili, Ni, Thaler, Bud’ko and Canfield³⁶ ORTH, orthorhombic; TET, tetragonal; AFM, antiferromagnetic; PM, paramagnetic; SC, superconducting; WDS, wavelength dispersive spectroscopy.

Taken together, these observations suggest that there are two necessary, but individually not sufficient, conditions for superconductivity: (1) the structural/magnetic phase transitions should be suppressed to a sufficiently low temperature; and (2) there exists a range of extra electron values e, inside which superconductivity can be stabilized if T _s(T _m) are sufficiently suppressed. For the case of Cu doping, the extra electron window is missed, thus only limited superconductivity with T _c ∼2 K is observed.

This argument appears to be consistent with the examples of isoelectronic doping discussed previously and is reinforced by the pressure measurements for pure and Co-doped BaFe₂As₂,Reference Colombier, Bud’ko, Ni and Canfield^30, Reference Colombier, Torikachvili, Ni, Thaler, Bud’ko and Canfield³⁶ which are summarized and compared with the T–x phase diagram in Figure 4b.Reference Canfield and Bud’ko³ For the overdoped side of the superconductivity dome, T _c^max(x), the maximum T _c value measured under pressure for a given x differs only slightly from the T _c values at ambient pressure; however, for the underdoped side, it increases and shows how large T _c can potentially be if T _s(T _m) are fully suppressed. This observation clearly indicates that the two necessary, but not individually sufficient, conditions for superconductivity in this series seem to apply to different halves of the superconducting dome.

Phase diagrams and Lifshitz transitions

The picture of simple filling of rigid bands that was assumed in the extra-electron, e, scaling discussed previously has been challenged in some band structure calculations.Reference Wadati, Elfimov and Sawatzky³⁷ Experimentally, though, it appears to be supported by a recent Hall and Seebeck coefficientReference Deok Mun, Bud’ko, Ni, Thaler and Canfield³⁸ and ARPES measurements.Reference Liu, Kondo, Fernandes, Palczewski, Mun, Ni, Thaler, Bostwick, Rotenberg, Schmalian, Bud’ko, Canfield and Kaminski³⁹ Both Hall and Seebeck coefficients measured at constant temperature (below T _s and T _m for Hall) for Ba(Fe_1–xCo_x)₂As₂ and Ba(Fe_1–xCu_x)₂As₂ approximately scale with e, suggesting the applicability of the rigid-band approximation (at least for small x values). However, the results of these studiesReference Deok Mun, Bud’ko, Ni, Thaler and Canfield^38, Reference Liu, Kondo, Fernandes, Palczewski, Mun, Ni, Thaler, Bostwick, Rotenberg, Schmalian, Bud’ko, Canfield and Kaminski³⁹ and their recent extensionsReference Liu, Palczewski, Kondo, Fernandes, Mun, Hodovanets, Thaler, Schmalian, Bud’ko, Canfield and Kaminski^41, Reference Lifshitz⁴² go beyond mere recognition of applicability of the rigid-band approximation in these materials. Drastic changes of the Fermi-surface topology (Lifshitz transitionsReference Lifshitz⁴²) have been suggested by anomalies in the transport measurementsReference Deok Mun, Bud’ko, Ni, Thaler and Canfield^38, Reference Hodovanets, Mun, Thaler, Bud’ko and Canfield^40, Reference Fang, Luo, Cheng, Wang, Jia, Mu, Shen, Mazin, Shan, Ren and Wen^43, Reference Rullier-Albenque, Colson, Forget and Alloul⁴⁴ and observed by ARPESReference Liu, Kondo, Fernandes, Palczewski, Mun, Ni, Thaler, Bostwick, Rotenberg, Schmalian, Bud’ko, Canfield and Kaminski^39, Reference Liu, Palczewski, Kondo, Fernandes, Mun, Hodovanets, Thaler, Schmalian, Bud’ko, Canfield and Kaminski⁴¹ for several ranges of Co concentrations in Ba(Fe_1–xCo_x)₂As₂ (Figure 5).Reference Liu, Palczewski, Kondo, Fernandes, Mun, Hodovanets, Thaler, Schmalian, Bud’ko, Canfield and Kaminski⁴¹

Figure 5.

(a) Location in the Ba(Fe_1–xCo_x)₂As₂ phase diagram of the known Lifshitz transitions, at which the Fermi surface topology changes, and the associated features in the superconducting and antiferromagnetic transition temperatures T _c and T _N. Top insets show the schematic Fermi surface topology in the a–b and a–c planes for each region in the phase diagram. (b) Thermoelectric power (TEP) versus doping for two different temperatures.Reference Liu, Palczewski, Kondo, Fernandes, Mun, Hodovanets, Thaler, Schmalian, Bud’ko, Canfield and Kaminski⁴¹

These topological changes appear to be relevant for superconductivity. On the underdoped side, the superconductivity emerges at the doping level, where a Lifshitz transition reduces the magnetically reconstructed Fermi surface to its paramagnetic appearance.Reference Liu, Kondo, Fernandes, Palczewski, Mun, Ni, Thaler, Bostwick, Rotenberg, Schmalian, Bud’ko, Canfield and Kaminski³⁹ Upon further doping, T _c starts to decrease when the cylindrical, central hole pocket changes to ellipsoids centering at the Z point, and goes to zero before these ellipsoids disappear around x = 0.2. Beyond this doping level, the central pocket changes from hole- to electron-like, and superconductivity does not exist.Reference Liu, Palczewski, Kondo, Fernandes, Mun, Hodovanets, Thaler, Schmalian, Bud’ko, Canfield and Kaminski⁴¹ A necessary condition for superconductivity in Ba(Fe_1–xCo_x)₂As₂ appears to be the presence of the central hole pockets rather than perfect nesting between central and corner pockets.

Summary

Either doping or applying pressure to BaFe₂As₂ results in qualitatively similar phase diagrams. The closely linked structural and magnetic transitions are suppressed, and if they are suppressed to a sufficiently low temperature (or/and low enough magnetic moment), and the material is within a certain range of carrier concentration (certain Fermi-surface topology), superconductivity emerges. With increasing doping or pressure, superconductivity and magnetism initially coexist, but after complete suppression of structural and magnetic transitions, T _c starts to decrease and ultimately disappears. However, in non-superconducting Ba(Fe_1–xMn_x)₂As₂, Ba(Fe_1–xCr_x)₂As₂, new magnetic phases emerge, while in (Ba_1–xSr_x)Fe₂As₂, no suppression of magnetism is observed, so the empirical trends just outlined are not satisfied.

Very similar behavior was reported on doping or under pressure for SrFe₂As₂ and CaFe₂As₂, although these two materials are more sensitive to the local or global stress that may lead to the observation of filamentary superconductivity. The pressure behavior of CaFe₂As₂, however, is much more complex due to the appearance of the collapsed tetragonal phase (Reference Reference Canfield, Bud’ko, Ni, Kreyssig, Goldman, McQueeney, Torikachvili, Argyriou, Luke and Yu32 and references therein). For these and historical and practical reasons, T–x and T–P phase diagrams have been explored to a lesser extent.

We would like to conclude with a word of caution. It is tempting to look for universalities in the physical properties and mechanism of superconductivity for all iron-pnictide superconductors. On a gross level, the issues discussed previously appear to extend beyond the cases of doped BaFe₂As₂, at least to the 1111 family. However, ∼30 K superconductivity was recently discovered in A_xFe_2–ySe₂ (A = K, Rb, Cs),Reference Guo, Jin, Wang, Zhu, He and Chen⁴⁵ which has a crystal structure very similar to the 122 family. In the case of A_xFe_2–ySe₂, the superconducting state (1) occurs very deep in the magnetically ordered state with a large magnetic moment,Reference Shermadini, Krzton-Maziopa, Bendele, Khasanov, Luetkens, Conder, Pomjakushina, Weyeneth, Pomjakushin, Bossen and Amato^46–Reference Ryan, Rowan-Weetaluktuk, Cadogan, Hu, Straszheim, Bud’ko and Canfield⁴⁸ and (2) possibly has an insulating/semiconducting parent compoundReference Bao, Li, Huang, Chen, He, Green, Qiu, Wang and Luo⁴⁹ that might violate the premises of some models of superconductivity that have been suggested for iron-pnictides. At this stage, it might be wiser to patiently continue collecting reliable experimental data on different families with an optimistic hope that “everything in this world can volunteer some reply, what takes up time is posing the questions,”Reference Saramago and Pontiero⁵⁰ and the physical picture will emerge later.