Introduction

The Fe-based superconductors (SC) RFeAsO (R = La-Gd) and AFe2As2 (A = Ba, Sr, Ca, Eu) have been a topic of intense scientific investigation since their discovery1,2. In particular, the semi-metal member BaFe2As2 (Ba122) displays a spin-density wave (SDW) phase transition at 139 K which can be suppressed by hydrostatic pressure and/or chemical substitution (e.g. K, Co, Ni, Cu and Ru) inducing a SC phase3,40,61,62,60. Although the proximity to a SDW state suggests a magnetic-mediated pairing mechanism5,4, the precise nature and symmetry of the SC state, as well as the microscopic mechanism responsible for driving the SDW phase towards a SC state, remain open questions begging for further investigation. Importantly, suppressing the SDW phase – either via applied pressure or chemical substitution – is not sufficient for SC to emerge16,20. Furthermore, when SC is found, the achieved optimal Tc differs dramatically depending on the particular chemical substitution. This difference may be related to the pair-breaking effect associated with substitutions, which create local impurity scatterers, particularly when introduced in the FeAs planes21.

A complete understanding of the impurity pair-breaking (IPB) effect in the Fe-pnictides is hindered, however, by their multi-band character and by the absence of quantitative information about the impurity potential4. Indeed, the suppression of Tc by impurities has been used as an argument in favor of both a sign-preserving s++ state22,23 and a sign-changing s+− state in Ba122-derived materials25,26,24. In these analyses, the impurity potential is usually estimated by the changes in the residual resistivity. However, the latter is sensitive to the transport scattering rate, which may differ from the quasi-particle scattering rate related to the suppression of Tc. Furthermore, using optimally-doped (OPD) compositions to study the effects of impurities on Tc may introduce additional complications, since any kind of perturbation will likely drive the system away from the vicinity of the SDW phase and suppress SC by diminishing the strength of the pairing interaction instead of breaking the Cooper pairs23,27.

In this paper, we circumvent these issues by combining macro and microscopic experiments, namely pressure-dependent transport measurements and electron spin resonance (ESR) in order to investigate the magnetic IPB effects in BaFe1.9M0.1As2 (M = Mn, Co, Cu and Ni) single crystals slightly below the OPD concentration. A sizeable ESR signal for M = Mn, Cu samples provides not only direct evidence for their role as local magnetic impurities, but it also allows us to extract the averaged exchange coupling 〈J2(q)〉 between them and the Fe 3d conduction electrons. The estimated suppression of Tc derived from this quantity, which plays the role of the magnetic impurity potential in the Abrikosov-Gor'kov (AG) formalism30,29, is found to be significantly smaller than the observed one, in sharp contrast to the excellent agreement found previously in borocarbides31,38,37 – multi-band compounds that display conventional sign-preserving SC states. Furthermore, we find that pressure strongly enhances Tc of the M = Cu sample, presumably by promoting stronger Cu–Fe hybridization and consequently suppressing the IPB effect. Our findings impose strong constraints on the mechanism responsible for SC and provide a strong evidence for an unconventional gap symmetry in these materials.

Fig. 1 displays the in-plane electrical resistivity, ρab (T), at ambient pressure for the selected single crystals. A linear metallic behavior is observed at high-T and the SDW phase transition of the parent compound is suppressed for all substitutions. A slight upturn is still present (arrows in Fig. 1), as typically found for substituted samples of Ba122 slightly below the OPD concentration3. As T is further decreased, SC emerges with the onset of Tc, defined as the temperature at which dρab/dT = 0, at 26.1 K, 22.2 K and 3.8 K for Co, Ni and Cu substitutions, respectively. On the other hand, no Tc is observed for M = Mn.

Figure 1
figure 1

In-plane electrical resistivity, ρab (T), for BaFe1.9M0.1As2 (M = Mn, Cu, Ni, Co) single crystals.

The arrows show the minima of the first derivative in the vicinity of the SDW transition.

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Figs. 2a–b show ρab (T) as a function of pressure for Co and Ni-substituted compounds. A small increase of Tc is observed, as expected for nearly OPD samples3. For instance, Tc reaches 28.6 K at 18 kbar for M = Co, whereas the self-flux OPD compound reaches a maximum Tc of ~23 K in the same pressure range, suggesting that the In-flux samples are of high quality. On the other hand, for M = Ni, Tc only reaches 24.7 K. One can speculate that the reason the Ni-OPD sample does not achieve Tc ~ 29 K is that it introduces more disorder than cobalt9,10,8. Indeed, the residual resistivity is higher for M = Ni. Furthermore, the highest Tc found in FeAs-based SC is obtained through out-of-plane substitution42,41.

Figure 2
figure 2

ρab(T) vs. T for BaFe1.9M0.1As2 (M = Co, Cu, Ni and Mn) single crystals for P = 5–25 kbar.

The insets show the evolution of Tc with pressure.

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Now we turn our attention to the striking behavior of Mn- and Cu-substituted compounds, shown in Figs. 2c–d. First, we observe a substantial unexpected enhancement of Tc by a factor of ~2.5 (Tc = 10 K at 24 kbar) for the Cu-substituted compound. Although an increase of Tc is expected for underdoped samples18,19,17, the maximum Tc achieved is also expected to be roughly the same as in the OPD sample at ambient pressure. Surprisingly, this is not the case for the studied Cu-substituted compound, which presents Tc = 4.2 K for the OPD crystal. On the other hand, SC does not emerge for M = Mn up to P = 25 kbar, in agreement with previous reports16. In addition, there is a drastic decrease of ρab(T) with pressure by a factor of ~3 for M = Cu and of ~1.5 for M = Mn over all T range (see Fig. 1 for a comparison), suggesting a possible decrease of the impurity scattering potential. These results seem to be consistent with a magnetic IPB mechanism since – unlike their Co and Ni counterparts – Mn and Cu substitutions are expected to introduce local moments. In many compounds, pressure is well known to enhance the hybridization between the local moments and the conduction electrons44,45,46,47,43. Such enhancement would suppress the magnetic IPB effect and, consequently, increase Tc. As Mn2+ has a much higher spin (S = 5/2) than Cu2+ (S = 1/2), it is not surprising that the magnetic IPB is larger for M = Mn, which in turn does not display SC.

To investigate such magnetic IPB scenario, we performed ESR – a powerful spin probe technique sensitive to the presence of local moments and their coupling to the conduction electrons48. In agreement with the expectation that Cu and Mn ions have local moments, our ESR data reveal an intense resonance line for M = Cu and Mn, but not for M = Co and Ni. Fig. 3 shows the X-Band ESR lines normalized by the concentration of paramagnetic ions at T = 150 K for fine powders of gently crushed single crystals. The Lorentzian fitting of the spectra reveals a linewidth of ΔH = 600(60) G and a g-value of g = 2.08(3) for M = Cu. For M = Mn, g = 2.04(3) and the linewidth is slightly larger, ΔH = 750(80) G, indicating stronger Mn-Mn interactions. Finally, for M = Mn and Co, g = 2.05(3) and ΔH = 670(70) G. For all samples, the calibrated number of resonating spins at room-T is in good agreement with the concentrations obtained from Energy Dispersive Spectroscopy (EDS). As expected, the ESR intensity, which is proportional to S(S + 1), was found to be roughly twelve times larger for M = Mn samples, as compared to the M = Cu sample. These results also indicate that the oxidation states of Cu and Mn are indeed Cu2+ (S = 1/2) and Mn2+ (S = 5/2). In the former case, Cu+ (3d10 state) would not display an ESR resonance line since it is not a paramagnetic ion. In the case of copper, Cu+ (3d10 state) would not display an ESR resonance line since it is not a paramagnetic probe with unpaired electrons. In the case of manganese, for Mn3+ (S = 2) and Mn4+ (S = 3/2) ions, one would expect a distinct ESR response (i.e., different g-value and calibrated signal intensity). Consequently, one can infer that there is no effective charge doping into the system, as suggested previously both experimentally and theoretically6,8. Furthermore, our ESR results agree with other indirect probes that also suggest localized Cu2+ and Mn2+ moments in chemically-substituted Ba12250,51,52,53,49. We note that the detailed analysis of the ESR data confronted with Eu-substituted BaFe2−xMxAs2 (M = Co, Ni, Cu, Mn and Ru) requires further technical discussion. Therefore, it will be the focus of a separated report13,15.

Figure 3
figure 3

X-Band ESR lines at T = 150 K for powdered crystals of BaFe1.9M0.1As2 (M = Cu, Mn) and BaFe1.895Mn0.005Co0.1As2.

The spectra were normalized by the concentration of paramagnetic probes in order to clearly compare their intensities. The solid lines are Lorentzian fits to the spectra (sample grain size smaller than the skin depth48). It is worth mentioning that, in order to obtain the ESR signal, the sample surface must be completely clean and free of In-flux. The ESR signals for both samples were calibrated at 300 K using a strong pitch standard sample with 4.55 × 1015 spins/cm.

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Besides revealing the presence of localized moments, ESR also allows us to extract the averaged squared exchange coupling 〈J2(q)〉 between the localized moments and the conduction electrons from the linear increase of the linewidth with temperature (Korringa behavior) (see Table I)13,12,15,31,37,38. In a general approach for single-band metals, the thermal broadening b of the ESR linewidth is the linear well-known Korringa relaxation defined as 32. Here, 〈Jfs(q)2〉1/2 is the effective exchange interaction between the local moment and the conduction electrons (ce) in the presence of ce momentum transfer averaged over the whole Fermi surface (FS)34, η(EF) is the “bare” density of states (DOS) for one spin direction at the Fermi level, g is the local moment g-value and K(α) is the Korringa exchange enhancement factor due to electron-electron exchange interaction36,35. In the present analysis, we found empirically that “bottleneck” and “dynamic” effects are not present33. When “dynamic” effects are present the g-values are usually strongly T-dependent, which is not observed in our experimental data. Moreover, when “bottleneck” effects are relevant the Korringa rate b decreases with increasing concentration of the magnetic ions. However, in our data, we observe that spin-spin interaction dominates the entire temperature range for dilute concentrations of Mn and Cu ions. In addition, bottleneck effects are not observed in Eu-substituted BaFe2As212, indicating that FeAs-based compounds are intrinsically unbottlenecked systems likely due to fast relaxation rates between the 3d conduction electrons and the lattice. In fact, recent ultrafast spectroscopy measurements have found a very large spin-lattice coupling in BaFe2As228. Finally, even if bottleneck effects were present, they alone would hardly be able to account for the enormous difference between JESR and JAG observed here.

Table 1 Experimental and calculated parameters for BaFe1−xMyAs2 (this work) and conventional SC (refs. [31, 37])
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The key point here is that this parameter 〈J2(q)〉 is the same one determining the suppression of Tc by magnetic impurities within the AG formalism30,29. To estimate whether the extracted value of 〈J2(q)〉ESR for M = Cu and Mn compounds can account for the observed suppression of Tc in this formalism, we consider the “conventional case”, where the gap function has the same amplitude and sign across the entire Brillouin zone. This is the scenario in which magnetic impurities have the strongest effect on Tc – in fact, introducing anisotropies in the gap function would make the magnetic pair-breaking effect weaker55,54. In this situation, we have30:

where ψ(x) is the digamma function, Tc,0 is the transition temperature in the absence of magnetic impurities and is the magnetic scattering rate. Here, η(EF) is the density of states per spin at the Fermi level, Δc is the magnetic impurity concentration and S, the spin of the localized moment. Given that Δc < 0.1 in our samples, we can perform a series expansion of eq. 1 and obtain the simplified expression:

with ΔTc = Tc − Tc,0. The value for η(EF) is extracted from the linear coefficient of the low-temperature specific heat γ, yielding η(EF) = 3.34 states/eV.spin.FU for one mole, which is the same for all compounds2,13. Small variations of γ across different compositions would not alter our main conclusions, as we discuss below. Moreover, the nearly constant ESR g-shift value found for the various ESR probes as a function of different chemical substitutions in Ba122 compounds is a strong evidence that the density of states at the Fermi level is nearly the same for pure Ba122 and for all studied compounds13. The choice of Tc,0 = 26 K is a more subtle issue. Since the dependence of TSDW with x in the phase diagrams of the BaFe2−xMxAs2 compounds is nearly identical for M = Co, Ni, Cu27, if one assumes that superconductivity is governed by fluctuations associated with the normal state, then one would expect that the optimal Tc values of these three samples would be very similar. Indeed, this is the case for M = Co and Ni, which also display similar maximum values of Tc under pressure. However, for M = Cu the value of Tc is significantly smaller – but this sample displays an ESR signal, unlike M = Co and Ni. We therefore assume that Tc,0 of the M = Cu sample and also of the M = Mn sample, is approximately the same as the Tc value of the optimally doped M = Co and Ni samples, where magnetic pair-breaking is absent, according to our ESR analysis. Moreover, theoretical and experimental reports have shown that there is no effective doping in this class of materials6,8 and that the suppression of TSDW is given by structural parameters7,11. As such, in the absence of pair-breaking effects, a given structural change would lead to the same suppression of the SDW state (and the consequent emergence of SC), independent on the particular transition metal substitution. We will return to this assumption below.

With these assumptions, we can thus estimate the magnetic pair-breaking impurity potential 〈J2(q)〉AG that would be necessary to cause the observed suppression of Tc for three different samples, namely, BaFe1.9Cu0.1As2, BaFe1.88Mn0.12As2 and the mixed doping BaFe1.895Co0.100Mn0.005As2 compounds. The results are shown in Table I and reveal a remarkable disagreement (of two orders of magnitude) between 〈J2(q)〉AG and the experimentally measured 〈J2(q)〉ESR. This is in sharp contrast to the borocarbide multi-band compounds Lu1−xGdxNi2B2C and Y1−xGdxNi2B2C, as well as to La1−xGdxSn3, all of which display conventional pairing symmetry. For these materials, as discussed in Refs. [31, 37], the calculated 〈J2(q)〉AG and the 〈J2(q)〉ESR extracted from ESR experiments are in very good agreement, as expected for a conventional SC. We note that in these compounds, because of the presence of rare earth elements, one needs to properly rewrite the Abrikosov-Gor'kov Equation 1 by replacing S (S + 1) for (gJ − 1)2J (J + 1), where J = S + L is the total spin.

The huge difference between 〈J2(q)〉AG and 〈J2(q)〉ESR is clearly robust against small variations of Tc,0 and η(EF). As explained above, these conclusions rely on the assumptions that (i) the Abrikosov-Gor'kov formalism is valid and (ii) similar normal-state phase diagrams should give similar superconducting transition temperatures. To shed light on these possible issues, we also present in Table I the results for the mixed doping BaFe1.895Co0.100Mn0.005As2 compound15. The very small Mn concentration makes the AG formalism more reliable and the fact that the compound without Mn substitution displays a superconducting transition temperature of 26 K directly determines Tc,0 = 26 K. As shown in the Table, both 〈J2(q)〉AG and 〈J2(q)〉ESR values are very close to those of the BaFe1.9Cu0.1As2 and BaFe1.88Mn0.12As2 samples, displaying a deviation of two orders of magnitude.

Our findings have important consequences for the understanding of the superconductivity in the Fe-pnictides. The fact that implies that the Abrikosov-Gor'kov magnetic IPB alone cannot account for the suppression of Tc. The latter must therefore be related to an unconventional magnetic IPB which must be strongly associated with the local Cu2+ and Mn2+ spins. In addition, these substitutions could also present a stronger nonmagnetic IPB effect responsible for part of the observed suppression of Tc. This also favors a non-conventional sign-changing gap function over the more conventional sign-preserving one, since in the latter case the effects of nonmagnetic IPB are expected to be weak. We note that in a s+− superconductor, non-magnetic pair-breaking can be weak dependent on the ratio between intra and inter-band scattering25,56. Furthermore, it is also possible that the substitution of M = Cu, Mn affects directly the pairing interaction, besides promoting pair-breaking. Interestingly, for M = Mn substitution, along with the usual SDW-type fluctuations, Néel-type fluctuations are also observed by inelastic neutron scattering57. Even when these Néel fluctuations are weak and short-ranged, they have been shown theoretically to strongly suppress Tc58. We note that our results are in agreement with recent measurements on LiFeAs employing angle resolved photoemission spectroscopy (ARPES) combined with quasiparticle interference (QPI) by means of scanning tunneling microscopy/spectroscopy (STM/STS)59.

Finally, we comment on the effects of pressure on Tc, summarized in Fig. 4. For the Co and Ni substitutions, the rate dTc/dP is ~0.1 K/kbar and the application of pressure has little effect on Tc. Strikingly, this rate is three times larger for the M = Cu sample, while for M = Mn, no SC is observed. We argue that these results are linked to the magnetic pair-breaking discussed above. In particular, because pressure increases the hybridization between the Cu 3d bands and conduction electron bands, the copper bands become more itinerant, progressively losing their local moment character and consequently suppressing the magnetic IPB effect. Therefore, it is not surprising that the pure BaCu2As2 is a Pauli paramagnet with completely delocalized Cu 3d bands and no phase transition. Within this scenario, the fact that the Mn compounds do not display SC would follow from the fact that Mn2+ has a spin value five times larger than Cu2+. Interestingly, if the magnetic IPB mechanism is suppressed by pressure, Tc is, in principle, unconstrained to increase up to a maximum defined by the local distortions that the M-substitution creates. For Cu-substituted samples, it remains to be confirmed whether applying higher pressures with Diamond Anvil Pressure cells would further enhance or even suppress Tc in the impurity pair-breaking regime.

Figure 4
figure 4

Phase diagram for BaFe2−xMxAs2 (M = Co, Cu and Ni) single crystals as a function of pressure.

The dotted lines are guide to the eyes for the SC domes. The linear fit for the M = Cu compound (solid line) was obtained from the phenomenological expression ΔTc = S(S + 1)(a − bP). Using the same expression and S = 5/2, we obtain the dashed line for the M = Mn compound.

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To make this reasoning more quantitative, we assume that the enhancement of Tc caused by the magnetic IPB suppression with pressure follows a phenomenological expression of the form ΔTc = S(S + 1)(a − bP), where a and b are free parameters and P, applied pressure. The linear dependence with pressure is motivated by the same typical dependence of the Kondo temperature (TK) on pressure in several Ce-based heavy fermion compounds44,45,46,47,47. This linear regime can be applied to the M = Cu (S = 1/2) compound in the IPB region slightly below the optimally-doped concentration, where the spin fluctuactions are nearly constant as a function of pressure. This procedure allows one to obtain the linear fit to the experimental data (solid line) displayed in Fig. 4. On the other hand, for M = Cu compounds in the optimally-doped or overdoped regions, the spin fluctuation suppression starts to play an important role and would overcome the latter linear increase of Tc. A detailed study on the effects of Cu substitution in critical current measurements is presented in Ref. [14]. Now, by constraining the same linear dependence for M = Mn and changing only the spin value to S = 5/2, we obtain a lower limit for the critical pressure Pc ~ 66 kbar necessary for the emergence of SC (dashed line in Fig. 4). This Pc value is in good agreement with the experimental absence of SC in the M = Mn compounds up to 25 kbar (see Fig. 2d), also in agreement with previous reports16.

In conclusion, we have demonstrated the contrasting behavior of hydrostatic pressure effects on nearly OPD BaFe2−xMxAs2 (M = Co, Cu and Ni) high-quality single crystals grown from In-flux method. The striking enhancement of Tc with pressure for M = Cu and the existence of a Cu2+ ESR line provide strong evidence of a spin-dependent pair-breaking mechanism strongly suppressed by pressure, suggesting an increase of hybridization between the Cu 3d bands and the conduction electron bands. More interestingly, by using the magnetic impurity potential extracted from the ESR analysis in the absence of bottleneck effects, we find that the Abrikosov-Gor'kov pair-breaking mechanism, applied to a conventional sign-preserving pairing state, cannot account for the observed suppression of Tc in the Cu and Mn-substituted compounds. This result not only implies that the suppression of Tc in these samples is due to other mechanisms, but also that an unconventional pairing state is more likely to be realized.

Methods

Single crystals of BaFe1.9M0.1As2 (M = Mn, Co, Cu and Ni) were grown using In-flux as described elsewhere39. The crystals were checked by x-ray powder diffraction and submitted to elemental analysis using a commercial EDS microprobe. In-plane electrical resistivity measurements were performed using a standard four-probe method and a self-contained piston-cylinder type Be-Cu pressure cell, with a core of hardened NiCrAl alloy. ESR spectra were taken in a commercial ELEXSYS 500 X-band (ν = 9.5 GHz) spectrometer equipped with a continuous He gas-flow cryostat.