Unconventional superconductivity usually originates from several strongly coupled degrees of freedom, such as magnetic, charge and elastic. A highly anisotropic electronic phase, not driven by lattice degrees of freedom, has been proposed in some of these superconductors, from cuprates to iron-based compounds. In the iron pnictide BaFe2As2, this nematic phase arises in the paramagnetic phase and is present for wide doping and temperature ranges. Here we probe the in-plane electronic anisotropy of electron- and hole-doped BaFe2As2 compounds. Unlike other materials, the resistivity anisotropy behaves very differently for electron- and hole-type dopants and even changes sign on the hole-doped side. This behaviour is explained by Fermi surface reconstruction in the magnetic phase and spin-fluctuation scattering in the paramagnetic phase. This unique transport anisotropy unveils the primary role played by magnetic scattering, demonstrating the close connection between magnetism, nematicity and unconventional superconductivity.
Two decades of intense research have shown that unconventional superconductors, including those with particularly high critical temperatures, Tc, often neighbour antiferromagnetic phases. It is believed that while long-range magnetic order is detrimental to superconductivity, magnetic fluctuations can be instrumental in assisting to form the Cooper pairs. In iron-based superconductors, proximity to stripe-type magnetic order is particularly prominent, and these two phases even coexist in some compounds. Interestingly, the transition to the long-range magnetically ordered phase is preceded or accompanied by a structural transition (see Paglione and Greene1, and Johnston2 for review). In the family of AFe2As2 (A=Ca, Sr, Ba, Eu) compounds, the stripe magnetic order below TN breaks tetragonal symmetry3, with in-plane ordering vectors (π,0) or (0,π). The structural transition at TS≥TN preempts the magnetic one and reduces the tetragonal symmetry of the lattice to orthorhombic. It has been suggested by several experiments4,5,6,7 and theories8,9,10,11,12 that the tetragonal symmetry breaking is caused by magnetic, that is, electronic, rather than elastic degrees of freedom, giving rise to the so-called electronic nematic phase13. In a broader context, electronic nematicity has been experimentally observed in many systems such as semiconductor heterostructures14, ruthenates15, cuprate16 and iron pnictide4 superconductors. In BaFe2As2, doping with either electrons (by Co-substitution of Fe, Ba(Fe1−xCox)2As2) or holes (by K-substitution of Ba, (Ba1−xKx)Fe2As2) suppresses both magnetic and nematic orders, revealing superconductivity with a maximum Tc close to the edges of the magnetic/nematic dome (Fig. 1).
Below TS, the sample splits into structural twin domains with different directions of the orthorhombic a0 and b0 axes (a0>b0) (17). Applying a small uniaxial strain not only stabilizes one particular domain below TS, but also extends the nematic phase to temperatures well above TS, due to the coupling between the strain field and nematic fluctuations (red area in Fig. 1) (7,18,19). In these strained samples, the nematic state anisotropy reveals itself not only in the small orthorhombic distortion a0−b0<<a0+b0, but, more so, in a pronounced anisotropy of the in-plane electrical resistivity ρ≡ρb/ρa−1 (20,21,22). Regardless of the microscopic nature of the nematic order parameter, φ, symmetry imposes that close to the nematic transition temperature, ρ=κφ, where κ is a coupling parameter. Indeed, this relation was verified experimentally in the parent compound of BaFe2As2 (18). Not surprisingly, in the only system where the electronic anisotropy was systematically studied across the nematic dome, the ruthenate Sr3Ru2O7 (15), ρ was found to retain the same sign across the phase diagram. In the quantum Hall system of Cooper et al.14, on the other hand, the resistivity anisotropy was found to change sign for a particular direction of the external symmetry-breaking field, a behaviour that remains without clear microscopic interpretation.
In the BaFe2As2 family, most of the studies on its nematicity have focused on the electron-doped compounds, finding ρ>0 in both magnetic and nematic phases20,21,23. More recently, experiments in under-doped (Ba1−xKx)Fe2As2 found a rather small, but still positive, value of ρ22.
Here we report that for larger K-doping levels, not explored in the previous studies, the anisotropy ρ changes sign both near TS (nematic phase) and at very low temperatures (magnetically ordered phase). As the sign of φ is fixed by the small applied uniaxial strain, the coupling parameter κ must change sign across the magnetic/nematic dome. We interpret this sign-change as a result of asymmetric changes in the magnetic scattering and in the magnetically reconstructed band structure for electron- and hole-doping. This unique complexity of the nematic dome observed in the iron pnictides, suggests that spin-scattering dominates transport in the normal state, establishing a possible connection to a magnetically mediated mechanism of superconductivity.
Sign-change of resistivity anisotropy
Figure 2 presents our main experimental finding, the sign-reversal of the in-plane resistivity anisotropy. For (Ba1−xKx)Fe2As2 samples with x≤0.202, the resistivity is larger along the shorter orthorhombic axis, ρa<ρb, whereas for samples with x≥0.235, the longer axis has higher resistivity, ρa>ρb. This is clearly seen in the inset zooming in on the structural transition region. It is also apparent that, because of the applied uniaxial strain, the in-plane anisotropy starts to appear well above the structural transition TS of the unstrained sample.
In Fig. 2b, we plot the temperature-dependent anisotropy ratio, ρ, for several compositions. We use two characteristic features of the ρ(T) curves to further analyse the data. First, we plot in Fig. 1b the maximum in-plane anisotropy ρmax for different x. In Fig. 3a we plot ρ(T≈TN), that is, at temperatures immediately below the magnetic transition, which coincides with the structural transition temperature of the unstrainned (Ba1−xKx)Fe2As2 samples.
This sign-change happens at all temperatures, even near TN, as shown in Fig. 2b and in Fig. 3a. Furthermore, as it can be seen in Fig. 2b, the magnitude of the temperature-dependent anisotropy ratio, ρ(T), is maximal close to TN in the parent and slightly hole-doped compositions, but increases monotonically on cooling for higher hole doping levels. This signals that the low-temperature anisotropic reconstruction of the band structure due to long-range magnetic order has a progressively more important role near the hole-doped edge of the nematic/magnetic dome.
Electron versus hole doping
An interesting general picture emerges from the analysis of the experimental observations of this and previous studies20,21,22. On the one hand, for all electron-doped Ba(Fe1−xCox)2As2 and parent compositions, the resistivity anisotropy is positive, ρ(x)>0. The maximum anisotropy, ρmax(x), shown in Fig. 1b, is peaked at some intermediate electron doping, vanishing near the edge of the magnetic/nematic dome, due to the vanishing orthorhombic distortion. On the other hand, on the hole-doped side, ρmax(x) remains positive up to moderate hole doping, but decreases by more than one order of magnitude, from ρmax(x=0)≈+0.3 to ρmax(x=0.202)≈+0.02. Even more surprisingly, ρmax(x) changes sign and exhibits a minimum at a higher hole doping concentration, ρmax(x=0.235)≈−0.034, before it eventually approaches zero close to the edge of the magnetic/nematic dome, near x=0.3.
Naively, the fact that ρb>ρa across most of the phase diagram seems surprising, because the ferromagnetic direction appears to be less conducting than the antiferromagnetic one. From the orbital ordering point of view11,24,25 one expects the opposite effect. However, a closer look at the Fermi surface reconstruction21,23 and the magnetic scattering mechanisms26,27 suggests that the anisotropy sign is decided by quantitative factors that depend on the electronic structure, going beyond general order parameter arguments. Moreover, the different contributions to the transport anisotropy do not necessarily compete with each other. To sort them out, we focus first on the nematic paramagnetic phase, in which scattering by magnetic fluctuations dominates and the band structure is not yet reconstructed by the magnetic order.
The experimental doping evolution of ρ(T≈TN), shown in Fig. 3a displays a rather monotonic behaviour, changing sign for sufficient hole-doping levels and vanishing at the edges of the nematic dome. Such a sign-change was previously predicted by the theoretical model of Fernandes et al.26 for the anisotropic magnetic scattering in the nematic phase. The minimal model of Fernandes et al.26, shown in the Supplementary Note 1 to be consistent with first-principles calculations, consists of a circular hole pocket at the center of the square-lattice Brillouin zone and two elliptical electron pockets centred at momenta (π,0) and (0,π), which coincide with the magnetic-stripe ordering vectors (see Supplementary Figs S1 and S2). In the nematic phase, the amplitude of the fluctuations around these two ordering vectors becomes unequal12, breaking the tetragonal symmetry of the system and inducing anisotropic scattering. In the experiment, the applied strain selects the (π,0) fluctuations.
The work by Fernandes et al.26 showed that in the presence of impurities and in the low-temperature limit—but still in the paramagnetic phase—the scattering rates along a and b (and consequently the sign of the resistivity anisotropy) is controlled by the Fermi velocities of the hot-spots connecting the hole and electron pockets, see Fig. 3. Roughly in electron-doped compounds, the hot-spots Fermi velocity has a larger component along the b direction, giving rise to a larger scattering rate for electrons travelling along this direction, implying ρb>ρa. As the system is doped with holes, the hole pocket expands while the electron pocket shrinks, changing the position and the Fermi velocity of the hot-spots, which eventually acquires a larger component along the a direction, implying ρa>ρb. Although Fermi velocity measurements in detwinned hole-doped samples are not available, angle-resolved photoemission spectroscopy data in optimally Co-doped28 and K-doped29 twinned samples support such a change in the direction of the Fermi velocity at the hot-spots. The existence of hot-spots in optimally K-doped samples is also strongly supported by inelastic neutron scattering data, displaying overdamped-like behaviour in the normal state that disappears in the superconducting phase, where hot-spot electron states are gapped30. To go beyond the low-temperature paramagnetic limit and make closer connection to the experiment, we used the same model of Fernandes et al.26 and numerically obtained the maximum resistivity anisotropy in the paramagnetic phase as function of doping. The results, shown in Fig. 3b, agree qualitatively with the experimental data, capturing both the electron-hole asymmetry of ρ(T≈TN) and its sign-change in the hole-doped regime. This suggests that magnetic scattering has a central role in the paramagnetic phase.
Our data in Fig. 2 also show that the sign-change in the resistivity anisotropy persists down to T=0, deep inside the magnetic state, where magnetic fluctuations are weaker. In this regime, transport should be governed by anisotropic reconstruction of the band structure. By employing first-principles calculations, we obtained the Fermi surface in the magnetically ordered state and evaluated ρ in the relaxation-time approximation (see Supplementary Note 2).
Our calculations show that, in the parent compound, the reconstructed Fermi surface contains not only quasi-isotropic hole and electron pockets, but also Dirac cones whose crossing points are located slightly below the Fermi level (Supplementary Fig. S3). These features are in good agreement with quantum oscillation measurements23. Owing to the large value of their Fermi velocities, these Dirac cones dominate the transport in the magnetic state, giving rise to an anisotropy in the resistivity that is in agreement with the experimental observations for x=0. When holes are added to the system, the chemical potential shifts down, eventually crossing the Dirac points. Using the values extracted by angle-resolved photoemission spectroscopy31,32 and quantum oscillation measurements23, we estimate this Dirac-point crossing to happen between 0.03 and 0.1 holes/Fe. For this doping concentration, the contribution to ρ coming from the Dirac pockets is vanishingly small, making the contribution from the remaining pockets dominant (see Supplementary Figs S4 and S5). The latter depends on details that are beyond the accuracy of first-principles calculations, and can either yield a small positive or negative ρ. Yet, our first-principles approach correctly captures the tendency of a vanishing ρ inside the magnetically ordered phase in the hole-doped samples.
In conclusion, we observe the reversal of the in-plane resistivity anisotropy between electron- and hole-doped BaFe2As2 compounds. We attribute such behaviour to the spin-fluctuation scattering in the nematic phase and to the Dirac-cones contribution in the magnetically ordered phase. Both mechanisms complementarily predict a resistivity anisotropy that is larger in the electron-doped side and continuously smaller in the hole-doped side. We notice that other contributions not considered here, such as anisotropic impurity potential or anisotropic defects, can also affect the transport anisotropy in the iron pnictides. Our analysis offers an explanation for the change in the sign of the resistivity anisotropy in terms of the band structure of the pnictides, without invoking a change from itinerant to local moment physics, as suggested recently by Jiang et al.33 Interestingly, the changes in the band structure from electron to hole-doped compounds34,35 also cause a reversal of the anisotropy in the magnetic correlation length30, which, however, has little impact on the sign-changing of the resistivity anisotropy within our model26. Besides shedding light on the singular character of the nematic phase in the iron pnictides, our observation serves as a unique fingerprint for the predominance of electronic scattering due to spin fluctuations, rather than phonons, in the normal state of these superconductors. Therefore, our study provides strong support to the concept that anomalous magnetic scattering in the proximity of a putative quantum critical point is intimately connected to magnetically mediated unconventional superconductivity36,37.
Crystal growth and characterization
Single crystals of (Ba1−xKx)Fe2As2 with a size up to 7 × 7 × 1 mm3 were grown from FeAs flux as described in Luo et al.38 Potassium content in the samples was determined using electron probe microanalysis with wavelength dispersive spectroscopy, see Tanatar et al.39 for details. Samples, had typical dimensions of 0.5 mm wide, 2–3 mm long and 0.05 mm thick, and were cut from cleaved slabs along the tetragonal  direction (which becomes either the orthorhombic a0 or b0 axis below TSM). Optical imaging was performed on the samples while mounted on a cold finger in a continuous flow liquid helium cryostat (allowing for precise temperature control in 5 K to 300 K range) using a Leica DMLM microscope.
Polarized light microscopy was used for visualization of the structural domains17 and the sample selection was based on the clarity of domains in the image. In Fig. 4, we show polarized light images of the area between potential contacts in (Ba1−xKx)Fe2As2 crystals used in this study, with x=0.108 (non-superconducting), x=0.202 (Tc=10 K), x=0.235 (Tc=26 K) and x=0.259 (Tc=28 K). Images were taken on cooling at a temperature slightly above Ts and at base temperature. The highest contrast is observed when the sample is aligned with the  tetragonal direction at a 45° to the polarization direction of incident light (parallel and perpendicular to the orthorhombic a0 in different domains). The contrast of domain images depends on the quality of the surface and the homogeneity of the samples. Domains are observed for samples with x≈0.26, and are no longer observed for samples with a higher doping level, x=0.34, which also do not show any features associated with a structural transition in ρ(T).
Resistivity measurements and mechanical detwinning
Selected samples were mounted for four-probe electrical resistivity measurements, with contacts made by soldering 50 μm Ag wires using low-resistance Sn soldered contacts40. Initial resistivity measurements on each sample were carried out using a flexible wire arrangement with no strain applied to the sample (free standing state). The results are plotted in Fig. 5. As this measurement is performed in the twinned state of the sample and contains contributions from both components of the in-plane resistivity in the orthorhombic phase, we call it ρt. Samples were then mounted on a brass horseshoe straining device, and strain was applied through the voltage contact wires by deformation of the horseshoe, see Tanatar et al.21 and Blomberg et al.41 for the details of the procedure. Strain in this configuration is applied along the tetragonal  axis, which selects the orthorhombic a0-axis as a preferable direction upon cooling below TS. Very soft current leads apply no strain. The strain was incrementally increased, and for each increment, temperature-dependent resistivity measurements were made and the domain structure was imaged to determine the completeness of detwinning. Our previous studies18,21 using x-ray scattering have shown that when crystals are strained to the point at which no domains are visible in polarized microscopy, about 90% of the whole bulk of the sample represents the domain whose orthorhombic a0-axis is oriented along the direction of the strain and, therefore, parallel to the current. Therefore, in the detwinned state we are predominantly measuring the a0-axis resistivity, ρa, while in the unstrained state of the sample roughly equal contributions of both resistivity components are measured. Therefore, we may calculate the b0 axis resistivity, ρb(T)=2ρt(T)−ρa(T).
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We thank A.V. Chubukov for useful comments, suggestions and critical reading of the manuscript. R.M.F. and J.S. acknowledge useful discussions with E. Abrahams. Work at The Ames Laboratory was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under contract no. DE-AC02-07CH11358. The work in China was supported by the NSF of China, the Ministry of Science and Technology of China (973 projects: 2011CBA00102, 2012CB821403). R.M.F. acknowledges the support of the NSF Partnerships for International Research and Education (PIRE) programme OISE-0968226.
The authors declare no competing financial interests.
Supplementary Figures S1-S5, Supplementary Notes 1 and 2 and Supplementary References (PDF 3627 kb)
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