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In-Plane Resistivity Anisotropy in an Underdoped Iron Arsenide Superconductor

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Science  13 Aug 2010:
Vol. 329, Issue 5993, pp. 824-826
DOI: 10.1126/science.1190482

De-Twinning a Superconductor

Insight into the mechanism of electrical transport in a solid can often be gained by measuring its resistivity along different spatial directions. However, iron-based superconductors form numerous twin boundaries where two different orientations of a crystal meet, and so the measured resistivity along any in-plane direction will be averaged over these orientations. Chu et al. (p. 824) were able to “de-twin” the compound Ba(Fe1−xCox)2As2, enabling unambiguous measurements of its normal-state resistivity along the in-plane lattice axes. Differences were observed in the resistivity values along the two axes, which suggests that the breaking of the symmetry of the lattice and electron subsystems occur simultaneously.

Abstract

High-temperature superconductivity often emerges in the proximity of a symmetry-breaking ground state. For superconducting iron arsenides, in addition to the antiferromagnetic ground state, a small structural distortion breaks the crystal’s C4 rotational symmetry in the underdoped part of the phase diagram. We reveal that the representative iron arsenide Ba(Fe1−xCox)2As2 develops a large electronic anisotropy at this transition via measurements of the in-plane resistivity of detwinned single crystals, with the resistivity along the shorter b axis ρb being greater than ρa. The anisotropy reaches a maximum value of ~2 for compositions in the neighborhood of the beginning of the superconducting dome. For temperatures well above the structural transition, uniaxial stress induces a resistivity anisotropy, indicating a substantial nematic susceptibility.

The iron-arsenide family of compounds appears to present a new paradigm for high-temperature superconductivity. The parent compounds are multiband itinerant antiferromagnets (1, 2) with a Fermi surface consisting of several small pockets resulting from reconstruction due to the broken translational symmetry (3, 4). Suppression of the antiferromagnetic ground state by various means eventually leads to superconductivity, with critical temperatures of up to 55 K (5). Notably, the antiferromagnetic transition is always preceded by or coincident with a tetragonal to orthorhombic structural distortion (68). It has been proposed that this structural distortion is driven by an electronic phase transition (912), perhaps due to orbital ordering (1316) or fluctuating antiferromagnetism (9, 10). In both proposals, a large in-plane electronic anisotropy is anticipated in the “nematic” state (17).

Although electron nematic phases have been intensively studied in quantum Hall systems (18) and in Sr3Ru2O7 (19), there is growing evidence for substantial electronic anisotropy in underdoped cuprates (20, 21) that cannot be explained by the structural orthorhombicity alone. In particular, the recent observation of a large in-plane anisotropy in the Nernst effect in YBa2Cu3O7–δ suggests that the much-debated pseudogap phase is a rotational symmetry-breaking phase (22). The crucial experiments in all of these cases probe the in-plane transport anisotropy that arises due to the nematic order (17). Here, we report measurements of in-plane resistivity anisotropy of Ba(Fe1−xCox)2As2 over a wide range of doping and temperature, to elucidate the nature of the structural phase transition in the iron pnictides.

One difficulty with probing the in-plane electronic anisotropy of the iron arsenides is that the material naturally forms dense structural twins below the orthorhombic transition at TS (Fig. 1, A and B) (23). Measurements of twinned samples present only an average of the intrinsic anisotropy, from which little detailed information can be extracted. For the present study, we have developed a mechanical cantilever device (shown in Fig. 1 C) that is able to detwin crystals in situ. Crystals were cut such that the orthorhombic a and b axes were aligned parallel to the direction of applied stress. With only modest pressures (~5 MPa, estimated from the deflection of the cantilever), small enough that the critical temperature associated with the Neel order (TN) is unaffected, the device is able to almost fully detwin underdoped crystals, revealing the previously hidden in-plane electronic anisotropy.

Fig. 1

(A) Diagram of the crystal structure of BaFe2As2 in the antiferromagnetic state. The magnetic moments on the iron sites point in the a direction and align antiparallel along the longer a axis and parallel along the shorter b axis. (B) Diagram illustrating a twin boundary between two domains that form on cooling through the structural transition at TS. Dense twinning in macroscopic crystals obscures any in-plane electronic anisotropy in bulk measurements. (C) Diagram of the device used to detwin single crystals in situ. The sample is held sandwiched between a cantilever and a substrate, with a screw in the center of the cantilever to adjust the uniaxial pressure. The (0 0 1) surface of the crystal is exposed, enabling transport measurements.

Evidence of the efficacy of this method for detwinning can be obtained from high-resolution x-ray diffraction measurements performed on the 4-ID-D beamline at the Advanced Photon Source (APS). Data shown in Fig. 2A reveal the splitting of the (–2 –2 20) Bragg peak (with respect to the tetragonal lattice) in the orthorhombic state of a crystal with composition x = 0.025 held under uniaxial pressure with the cantilever. Comparison of the integrated intensity of the two peaks yields a relative volume fraction of 86% of the twin orientation with the shorter b axis along the applied stress. Direct optical images were also taken to confirm this result. Samples were illuminated by polarized light, and the reflected light was collected through an almost crossed polarizer so as to maximize the contrast caused by the different birefringence of the two twin orientations. Representative images of a BaFe2As2 sample surface at 5 K are shown for the relaxed cantilever (Fig. 2B) and strained cantilever (Fig. 2C). Stripes associated with the twin domains are clearly visible for the unstrained crystal, but these have completely disappeared for the strained sample.

Fig. 2

(A) Splitting of the (–2 –2 20) Bragg peak (referenced to the tetragonal lattice) at 40 K for a sample with x = 0.025 under uniaxial pressure, as revealed by high-resolution x-ray diffraction. The two-dimensional surface is formed by interpolating between Gaussian fits to a dense mesh of points from h-k scans in reciprocal space. Each peak corresponds to one of the two twin domains. The relative volume fraction of the larger domain, corresponding to the shorter b axis aligned parallel to the applied stress, is approximately 86%. (B) Polarized-light image of the surface of an unstressed BaFe2As2 crystal at 5 K without applying uniaxial pressure. Vertical light and dark stripes reveal the existence of twin domains with a and b axes reversed. (C) Polarized-light image on the surface of the same crystal under uniaxial pressure at 5 K. The absence of stripes indicates the applied pressure has detwinned the crystal.

Resistivity data were collected for detwinned samples as a function of temperature. Eight representative cobalt concentrations were measured, from the undoped parent compound x = 0 through to fully overdoped composition (x = 0.085). Representative data for each of these compositions are shown in Fig. 3. Measurements were made for currents applied parallel and perpendicular to the applied stress, yielding ρb (in red) and ρa (in green), respectively.

Fig. 3

Temperature dependence of the in-plane resistivity ρa (green) and ρb (red) of Ba(Fe1−xCox)2As2 for Co concentrations from x = 0 to 0.085. Solid and dashed vertical lines mark critical temperatures for the structural and magnetic phase transitions TS and TN, respectively, obtained from a combination of scattering, thermodynamic, and transport measurements (7). Values of TN for stressed samples, obtained from the peak in the derivative of the resistivity, are identical to those found for unstressed samples, indicating that the uniaxial pressure serves as a weak symmetry-breaking field to orient twin domains without affecting the bulk magnetic properties. The uniaxial stress does, however, affect the superconducting transitions in some underdoped samples, inducing a partial superconducting transition for x = 0.016 and 0.025, which are not observed for unstressed crystals. Diagrams on the right illustrate how measurements of ρaand ρb were made. Dark arrows indicate the direction in which uniaxial pressure was applied, and smaller arrows indicate the orientation of the a and b crystal axes. In all cases, the same samples and the same contacts (shown in gold for a standard four-point configuration) were used for both orientations.

Inspection of Fig. 3 reveals that ρb > ρa for all underdoped compositions. This result, anticipated from earlier magnetoresistance measurements (24), is somewhat counterintuitive. Given that the a-axis lattice constant is larger than that of the b axis, the smaller orbital overlap along the a axis would ordinarily give rise to a higher resistivity, all else being equal. Equally, the collinear spin arrangement below TN comprises rows of spins that are arranged ferromagnetically along the b axis and antiferromagnetically along the a axis (Fig. 1A). Scattering from spin fluctuations would ordinarily result in a higher resistivity along the antiferromagnetic a direction. Our observation therefore indicates a more complex situation and provides a strong constraint for theoretical models of the electronic structure in the orthorhombic state. The degree of in-plane anisotropy can be characterized by the ratio ρba, which is shown as a color scale in Fig. 4A. The anisotropy varies with temperature and composition but reaches a maximum value close to two for 0.02 ≤ x ≤ 0.04 at low temperatures, in the neighborhood of the beginning of the superconducting dome. In contrast, the overdoped composition x = 0.085, which remains tetragonal for all temperatures, reveals no in-plane anisotropy.

Fig. 4

(A) Evolution of the in-plane resistivity anisotropy as a function of temperature and doping, expressed in terms of the resistivity ratio ρba. Structural, magnetic and superconducting critical temperatures, determined following (27), are shown as circles, squares, and triangles, respectively. Notably, the resistivity ratio deviates from unity at a considerably higher temperature than TS, indicating that nematic fluctuations extend far above the phase boundary. (B) The difference in the temperature derivative of ρa and ρb: Embedded Image, where Embedded Image and Embedded Image, as a function of temperature and doping. The resistivity has been normalized by its room temperature value to avoid uncertainty due to geometric factors. Regions of highest intensity are those regions where ρb appears to be insulator-like (dρb /dT < 0) while ρa remains metallic (dρa /dT > 0). This behavior is clearly correlated with the nematic phase between the structural and magnetic transitions.

The temperature dependence of the resistivity (Fig. 3) is especially striking. At high temperatures, the resistivity is isotropic and starts off as almost linear. For currents running in the b direction, the resistivity deviates from this behavior at a temperature well above TS and increases steeply with decreasing temperature. This insulator-like behavior is cut off near TN for the lowest doping levels but extends to much lower temperatures for larger cobalt concentrations. In contrast, for currents flowing in the a direction, the resistivity behaves similarly to a normal metal, continuing to decrease with decreasing temperature over the entire temperature range, except for a small jump near TN. The superconducting transition at the lowest temperatures causes both ρa and ρb to drop to zero. The difference of the temperature derivatives of ρb and ρa (normalized by the room temperature value), shown in Fig. 4B, reveals a strong correlation with the orthorhombic distortion.

The composition dependence of the anisotropy in the in-plane resistivity (Fig. 4, A and B) is in stark contrast to that of the structural anisotropy that develops below TS. The orthorhombic distortion, characterized by the ratio of in-plane lattice constants, has a maximum value for x = 0 at low temperature of (a − b)/(a + b) = 0.36% and decreases monotonically with increasing cobalt concentration (25), whereas the resistivity anisotropy is a nonmonotonic function of doping, exhibiting a maximum near the beginning of the superconducting dome. These contrasting behaviors suggest that the itinerant electrons do not passively follow the lattice distortion. Rather, it appears that the material suffers an underlying electronic phase transition that profoundly affects the low energy excitations near the Fermi level and in a manner that is much less apparent in the response of the crystal lattice.

Notably, the resistivity anisotropy is evident for temperatures well above TS. Even though the crystal symmetry is tetragonal in this temperature range, the uniaxial stress applied by the cantilever breaks the fourfold symmetry in the basal plane. The external symmetry-breaking field induces a nonzero order parameter above the critical temperature, smoothing the divergent behavior associated with the critical point observed under ambient conditions (26). As the temperature is reduced toward TS from above, the resistivity anisotropy for the strained samples increases rapidly, indicating that the nematic susceptibility diverges at the critical temperature and providing compelling evidence that the resistivity anisotropy observed above TS reflects fluctuations associated with the phase transition that occurs at TS in the zero stress limit (more discussion can be found in the supporting online material). There is no evidence in either thermodynamic or transport properties for a third phase transition above TS (27).

Co-doped BaFe2As2 was chosen for this initial study because the structural and magnetic transition are clearly separated in temperature and the material can be readily tuned in a controlled and reproducible fashion. However, given the rather generic phase diagram found in this family of compounds (28), it is possible that the observed anisotropy is quite general to underdoped iron pnictides. For example, recent scanning tunneling microscopy measurements also reveal a large electronic anisotropy of Co-doped CaFe2As2 at low temperatures (29).

In comparison to other electron nematic systems, such as Sr3Ru2O7 (19) and the quantum Hall system (18), the phase transition of iron pnictides occurs at zero field and at a temperature range between 50 and 150 K, providing an accessible platform for spectroscopy and thermodynamic measurements. Although the pseudo-gap phase in underdoped cuprates exists for similar conditions to these, the iron arsenides have a well-defined phase boundary associated with the nematic phase transition. In this sense, the iron arsenides present a cleaner system in which to investigate the physical origin of nematic order and the consequences for superconductivity.

Supporting Online Material

www.sciencemag.org/cgi/content/full/329/5993/824/DC1

Materials and Methods

Figs. S1 to S4

References

References and Notes

  1. Nematic order refers to a spontaneously broken rotational symmetry without the breaking of translational symmetry. Systems for which the crystal lattice appears to preserve the original rotational symmetry (as found in the quantum Hall effect and Sr3Ru2O7) might be dubbed “electron nematic,” whereas systems for which the crystal lattice also breaks rotational symmetry [for example, YBa2Cu3O7δ and Ba(Fe1−xCo x)2As2] might be more appropriately named “system nematic.” In both cases, a strong electronic anisotropy is observed that is much more pronounced than consideration of the crystal lattice alone would otherwise suggest. We refer to this general phenomenon as “nematic order” in the rest of the text. For a recent review, see (30).
  2. For the Fe arsenides and oxy arsenides typified by BaFe2As2 and LaFeAsO, the structural transition is from tetragonal to orthorhombic symmetry. The closely related Fe chalcogenides, typified by FeTe, also suffer a structural distortion, but in this case from tetragonal to monoclinic (31).
  3. The authors thank C. D. Batista, C.-C. Chen, T. P. Devereaux, S. A. Kivelson, A. P. Mackenzie, R. D. McDonald, S. C. Riggs, D. J. Scalapino, and Z.-X. Shen for helpful discussions. This work is supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, under contract DE-AC02-76SF00515. Use of the APS is supported by the DOE, Office of Science, under contract DE-AC02-06CH11357.
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