Work supported in part by US Department of Energy contract DE-AC02-76SF00515.

Bulk superconductivity and disorder in single crystals of LaFePO

James G. Analytis1, Jiun-Haw Chu1, Ann S. Erickson1, Chris Kucharczyk1, Alessandro Serafin2,

Antony Carrington2, Catherine Cox3, Susan M. Kauzlarich3, Hakon Hope3, I. R. Fisher11Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, CA 94305, USA.

2H. H. Wills Physics Laboratory, University of Bristol, 1 Tyndall Ave., Bristol BS8 1TL, UK and3Department of Chemistry, University of California, Davis, California 95616, USA

(Dated: November 8, 2009)

We have studied the intrinsic normal and superconducting properties of the oxypnictide LaFePO.These samples exhibit bulk superconductivity and the evidence suggests that stoichiometric LaFePOis indeed superconducting, in contrast to other reports. We find that superconductivity is indepen-dent of the interplane residual resistivity ρ0 and discuss the implications of this on the nature of thesuperconducting order parameter. Finally we find that, unlike Tc, other properties in single-crystalLaFePO including the resistivity and magnetoresistance, can be very sensitive to disorder.

PACS numbers: 74.25.Fy, 74.25.Ha, 74.70.-b, 72.80.Ng

I. INTRODUCTION

High-temperature superconductivity in the iron-pnictides has recently attracted considerable attentionbecause it is the first family of materials since the discov-ery of the cuprates to exhibit critical temperatures above40K. However, in the initial flurry of activity, single-crystal measurements of the lower Tc analogue LaFePOhave been somewhat overlooked. Early measurements ofpolycrystalline samples indicated Tc values in the rangefrom 4 to 7 K,1,2,3,4,5 with F-substitution (i.e. electrondoping)2 or Ca-substitution (hole doping)3 modestly in-creasing Tc values. However, more recent measurementshave queried whether the stoichiometric compound is ac-tually superconducting, suggesting rather that oxygendeficiency plays a significant role.6 Initial single-crystalwork revealed superconducting transitions in the resis-tivity and susceptibility, but not in the heat capacity,leading the authors to speculate that the superconduc-tivity might be associated with an oxygen deficient sur-face layer, while the bulk remains metallic to the lowesttemperatures.7 Given the close structural and electronicsimilarity to the parent compounds of the higher Tc oxy-arsenides, it is particularly important that a clear pictureof superconductivity in this lower-Tc analog is elucidated.

LaFePO is interesting for reasons other than this con-troversy. Because of its lower Tc and Hc2, quantum oscil-lations can be measured in relatively moderate fields.8 Inaddition, despite the appearance of a nearly-nested Fermisurface, LaFePO does not appear to exhibit any mag-netism and so the properties of the metallic ground stateof the pnictides can be examined in detail. In contrastLaFeAsO has a spin-density-wave ground state at lowtemperature and only exhibits superconductivity whendoped, which naturally introduces disorder, inhibitingsuch detailed probes of the Fermiology.

In this paper we present results of heat capacity, mag-netization, resistivity and magnetoresistance measure-ments of single-crystal samples of LaFePO. The evidencesuggests that these samples are stoichiometric, and we re-port three major results. Firstly, we find that supercon-

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FIG. 1: (Color online)(a) Specific heat (left axis) of a mosaicof single-crystals and resistivity (right axis) of a single-crystal.The heat capacity anomaly corresponds to the disappearanceof resistance. (b) The susceptibility of powdered LaFePOcrystals measured in an applied field of 50 Oe following zerofield cooling (ZFC) and field cooling (FC) cycles. (c) Pow-der x-ray diffraction pattern (black) of crystals taken fromthe same batch as in (b). All peaks can be indexed to thecalculated pattern (red).

ductivity is present in the bulk of the material, contraryto the findings of some other authors.6,7 Second, we findthe superconducting gap is uncorrelated with the inter-plane residual resistivity ρ0. If this quantity is represen-tative of disorder, the lack of Tc suppression is consistentwith s-wave superconductivity.11 Finally, in contrast tothe superconductivity itself, properties near Tc can varygreatly with disorder. We illustrate this with measure-ments of the magnetoresistance.

SLAC-PUB-13900

SIMES, SLAC National Accelerator Center, 2575 Sand Hill Road, Menlo Park, CA 94309

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II. EXPERIMENT

Single-crystals of LaFePO were grown from a moltenSn flux, using conditions modified from the original workby Zimmer and coworkers.12 Elemental and oxide pre-cursors were placed in alumina crucibles and sealed inquartz tubes under a small partial pressure of argon. Thegrowths were ramped up in temperature to 1190C fol-lowed by a slow cool. We used either La2O3 or Fe2O3

to introduce oxygen into the melt. When La2O3 wasused, the highest yield was obtained for a melt contain-ing La:La2O3:Fe:P:Sn in the molar ratio 1:1:3:3:57, whilewith Fe2O3 the best yield was obtained from a combi-nation La:Fe2O3:P:Sn in the molar ratio 3:1:2:24. Theformer method yielded our largest crystals (up to 0.7mmon a side) and with the highest RRR (residual resistivityratio, ρ(300K)/ρ(0)), but the yield was very sensitive tothe packing in the crucible, the temperature profile of theinitial warm up, and the proportion of the other elements.The temperature was raised from room temperature to1190C in 6 hours, held for a further 6 hours and thenlowered to 900C at a rate of 4.8 C/hour. Using Fe2O3

yielded crystals of the right phase more consistently, al-though smaller (typically 0.1-0.4mm) and with a lowerRRR. In this case, optimal results were obtained by heat-ing over the same amount of time, but the mixture washeld at 1190C for 18hrs, before cooling at 10 C/hour to650C. The remaining liquid was decanted at the basetemperature using a centrifuge, and the crystals removedfrom the crucible. Excess Sn on the surface of the crys-tals was removed by etching in dilute HCl followed byan immediate rinse in methanol. Both methods resultedin multiphase growths, the principle second phase beingLaFe2P2, which has the ThCr2Si2 structure. Care mustbe taken to distinguish these two phases.

Crystals grown using La2O3 precursor as describedabove had RRR values up to 85, Tc ∼ 5.9K and an in-terplane residual resistivity of ρ0 = 0.04mΩcm. Crys-tals grown by this technique have been used for re-cent ARPES13 measurements while crystals grown us-ing Fe2O3 were used to measure de Haas-van Alphen(dHvA) magnetization oscillations.8 The second method,using Fe2O3, with a melt composition much closer to thatused in Reference 7, yielded crystals with a RRR∼ 25,Tc = 6.7K and an interplane residual resistivity ofρ0 =0.18mΩcm.

While optimizing the synthesis conditions, batches ofcrystals extracted from individual growths were checkedby powder x-ray diffraction using an SSI XPERT diffrac-tometer. Individual crystals were screened by measure-ment of the c-axis lattice parameter. A well-formed singlecrystal grown with La2O3 precursor and the melt compo-sition and temperature profile that produced the highestquality crystals (as measured by the residual resistivity)was selected for X-ray study. A tin deposit on the crys-tal was removed by rinsing in a drop of 12 N HCl. Amultiply-redundant MoKα data set of 1643 reflections(2θmax = 63.9) was measured on a Bruker Apex II

diffractometer. The crystal temperature was 90±1 K.Data were corrected for absorption vith the face-indexedprocedure of SADABS9 . The structure refined withSHELX10 to a standard R index of 0.0084, and a weightedR index of 0.02 for all 156 unique reflections. The oxygenoccupancy is 100% within the statistical uncertainty of1.8%. The crystals are tetragonal, space group Pnmm,with cell dimensions a = 3.941±0.002, c = 8.507±0.005.

FIG. 2: (Color online) The specific heat Cp/T as a function ofT2 for a mosaic of LaFePO crystals taken in zero field (solidcircles) and in an applied field of 1 T (open circles) with fieldoriented parallel to the c-axis. The dotted line indicates thelinear fit as described in main text which extrapolates to avalue of γ ∼ 7.0 ± 0.2 mJ/molK2.

Inter-plane (c-axis, ρc) and in-plane (ab-plane, ρab) re-sistivity measurements were made with a standard four-probe configuration and metallic contact was made usingEpotek H20E paste. The paste was annealed in air at200C for 20 minutes. Inter-plane measurements weremade on crystals as small as 0.15x0.1x0.02mm3 and in-plane measurements were made on larger crystals. How-ever, the larger crystals tended to suffer from inhomo-geneity (evidenced by a broad superconducting transi-tion), and/or flux inclusions, and the c-axis data weregenerally better. Resistivity and heat capacity mea-surements were performed on a Quantum Design PPMS(14T). Due to the small size of the crystals, the heat ca-pacity was measured for a mosaic of around 100 crystalsgrown from a melt containing La2O3, with a total massof 800±50µg, each oriented such that the ab-plane wasparallel to the platform. Crystals from a separate batchwere powdered, half of which was checked for phase pu-rity by powder x-ray diffraction ( Figure 1 (c)). Suscepti-bility measurements were made for the other half of thispowder sample using a Quantum Design MPMS 5 Super-conducting Quantum Interference Device magnetometer

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FIG. 3: Heat capacity data on a single-crystal (∼5µg) mea-sured using the AC technique giving the relative change of thethe heat capacity C from the normal state CN (in arbitraryunits), where ∆C = C −CN . In (a) we show the field depen-dence of the heat capacity anomaly, approximately agreeingwith the suppression of Tc extracted from resistivity (see Fig-ure 10). In (b) we show data fitted with weak-coupling BCStheory assuming an isotropic s-wave order parameter. Thedata agrees very well to the theory.

in a range of applied fields.

Measurements of heat capacity were also made on asingle crystal using an AC method.14 The sample withdimensions 140×220×30µm3 (with mass ∼ 5µg) we at-tached with GE varnish to a 12µm diameter Chromel-Constantan thermocouple, and heated with light at afrequency of 16Hz. The size of the temperature oscilla-tions is inversely proportional to the heat capacity of thesample plus the addenda (varnish plus thermocouple).Although with this method it is possible to measure avery small single-crystal it is not possible to determinethe absolute value of the specific heat. The heat capacitywas measured as a function of field from -0.4T to 1T with

FIG. 4: (Color online) (a) Interlayer (c-axis) resistivity forLaFePO crystals grown using Fe2O3 (blue and green curves)and La2O3 (all other curves). The room temperature val-ues are in approximate agreement for either method but theresidual resistance ρ0 shows significant variability (inset). (b)In-plane (ab-plane) resistivity. The room temperature valueshows more variability than the interplane resistivity, primar-ily due to difficulties in finding homogeneous samples largeenough to mount for in-plane measurements. This was oftenmanifested in a broader superconducting transition (inset).

B ‖ c, in a 14T superconducting magnet. To account forthe residual field in our magnet the actual field was de-termined from the field which produced the maximumfield in a Tc versus H plot (the offset was 0.065 T).

III. RESULTS

Heat capacity data for the mosaic of single-crystal sam-ples described above are shown in Figure 1(a) togetherwith representative resistivity data for a single-crystalfrom a separate batch. The total heat capacity of this

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mosaic is extremely small due to the small mass, makingmeasurements of the relaxation time particularly chal-lenging. Despite these difficulties, a clear superconduct-ing anomaly is evident at 5.9 K, corresponding to thetemperature at which the resistivity disappears. Thesuperconducting state can be suppressed by an appliedfield greater than µ0Hc2, leaving only the normal statecontribution to the heat capacity (Figure 2). Data be-tween approximately 5 and 10 K can be fitted usingCv/T = βT 2 + γ where β and γ are the lattice and elec-tronic heat capacity coefficients respectively. This yieldsan estimate of γ = 7.0 ± 0.2 mJ/molK2 where one molerefers to the formula unit LaFePO. This value is similarto that obtained from values extracted by other authorsfor polycrystalline3,6 and single-crystal7 samples, thoughcare should be taken on the definition of a mole (the valueis doubled if one mole refers to the unit cell). Data on thelow-temperature side of the superconducting transitionare less reliable due to the small value of the heat capac-ity and the experimental difficulties measuring the relax-ation time as described above. Due to these difficulties,the data does not appear to conserve entropy. Combinedwith the rounding of the superconducting anomaly seenin the data, it is difficult to obtain an accurate estimateof the heat capacity jump, but we can obtain a conserva-tive lower bound by comparing the peak of the transitionwith the normal state extrapolation (vertical arrow inFigure 1). This results in an estimate of the normalizedheat capacity jump ∆C/γTc ≈ 0.6±0.2, which is greaterthan Kamihara et al.’s estimate based on measurementsof polycrystalline samples,2 and is less than (about 40%)the BCS result (∆C/γTc)BCS = 1.43. The actual valueis likely somewhat larger than this lower bound. Suscep-tibility measurements for a sample consisting of severalpowdered single-crystals are shown in Figure 1 (b) for anapplied field of 50 Oe following both zero field cooling(ZFC) and field cooling (FC) cycles. Perfect diamag-netism (4πM/H = −1, shown on the right axis in Figure1b) corresponds to a value of -1.32×10−2emu/g. Assum-ing that the particle size is larger than the penetrationdepth (∼ 0.2µm17), the FC value (∼ −0.32emu/g) pro-vides the better estimate of the superconducting volumefraction, giving a lower bound of approximately 24%.This likely substantially underestimates the actual valuedue to flux pinning effects.

Heat capacity data for a single crystal, obtained usingthe AC technique, are shown in Figure 3. For a field of> 0.47T the superconducting anomaly was suppressed tobelow T=2.3 K so we used this data as an estimate of thenormal state heat capacity CN (including addenda), andsubtracted this from the data in zero field. The supercon-ducting anomaly is now clearly visible, with Tc (mid pointof the increase in C of T=5.6 K and width (10-90%)of 0.4K. In Figure 3 (a), we show the field dependenceof the anomaly in C. The decrease in Tc correspondsto dTc/dH = 7.2 ± 0.1K/T. Also shown Figure 3 (b) isthe temperature dependence calculated from the weak-coupling BCS theory assuming an isotropic s-wave order

FIG. 5: Plot showing the dependence of the critical temper-ature Tc on the residual resistivity ρ0 extracted from the lowtemperature normal state of LaFePO. The higher residual re-sistivities correspond to a ratio of the coherence length tomean free path ξab/l ∼ 0.17 − 0.25, and so a partial, sys-tematic suppression in Tc is expected for an anisotropic orderparameter.

FIG. 6: (Color online) (a) c-axis resistivity data from Figure3(a) replotted on a logarithmic scale. Plotted this way, alldata fall on the same curve. The black line shows the valueA ∼ 3.2 × 10−5mΩcm/K2, while the grey lines illustrate ourerror bars in A. (b) The coefficient A extracted from fits ofthe resistivity data to ρ = ρ0 + AT 2, which is independent ofdisorder.

parameter. Apart from the data very close to Tc or forT<2.8K the theory fits the data very well. The departurebelow ∼2.8K probably arises from the field dependenceof the thermocouple thermopower and field dependenceof the addenda which we have not attempted to correctfor.

In the strong coupling Eliashberg theory the slope nearTc normalised to the jump at Tc R = Tc

∆C

∂C

∂T|Tc

is indica-

tive of the coupling strength.15 The fact that our data fitwell the weak coupling BCS form shows that LaFePO isin the weak coupling limit (note however this does notprove the order parameter is necessarily isotropic).

In Figure 4(a) we show the inter-plane (c-axis) resistiv-ity ρc for five crystals grown from slightly different meltconditions. Absolute values of the room temperature re-sistivity are in excellent agreement, and the principal dif-ference between the samples is the residual resistivity ρ0.A small upturn is seen in the resistivity of some but notall samples, just above Tc. Tc values are also in excel-

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FIG. 7: (a) The magnitude of the interplane resistivity up-turn ∆ρc = ρp − ρ0 normalized to the residual resistivity ρ0,where ρp is the peak resistivity of the upturn. There does notappear to be a correlation with Tc. (b) The magnitude of theinterplane resistivity upturn ∆ρc as a function of the inter-plane residual resistivity ρ0, which also shows no correlation.

lent agreement, and show no correlation with the resid-ual resistivity (see Figure 5). Similar data for in-planeresistivity measurements ρab are shown in Figure 4(b).In contrast to the c-axis data, in-plane measurementstend to exhibit both broader transitions and also a widervariation in the absolute value of the resistivity. As de-scribed above, this difference can be ascribed to the use oflarger crystals for the in-plane measurements, which areconsequently more susceptible to defects, flux inclusionsand, due to the malleability of the crystals, macroscopicdistortion. The anisotropy of the interplane to in-planeresistivity ρc/ρab is in the range from 13 to 17, in approx-imate agreement with band structure calculations.18,19,20

Neglecting the low-temperature upturn seen in somesamples, resistivity data below 25K can be well-fit bythe standard Fermi liquid behavior, ρ = ρ0 +AT 2, whereρ0 is the residual resistivity.21 To confirm the reliabilityof this fitting, log(ρ − ρ0) vs log(T ) is shown in Figure6(a) for the c-axis data, which reveals that each data setnot only has a gradient of 2 ± 0.3, but also falls on thesame value of A ∼ 3.2 ± 0.5 × 10−5mΩcm/K2 (Figure6(b)). We note in passing, that when A is combinedwith our value of γ we find a Kadowaki-Woods ratio ofA/γ2 = 65 ± 15 × 10−5µΩcm(mol K/mJ)2.22

As mentioned above, a small resistivity upturn is ob-served in some, but not all, samples just above Tc. Thiseffect is seen for both current orientations (i.e. for ρab

and ρc). Significantly, the size of the upturn is not cor-related with either Tc (Figure 7(a)), or with the abso-lute value of the residual resistivity ρ0 extrapolated fromhigher temperatures (Figure 7(b)). We return to the fielddependence and origin of this feature below.

Representative data showing the variation in the c-axis resistivity as a function of applied field at varioustemperatures are shown in Figure 8 for fields applied(a) parallel and (b) perpendicular to the c-axis. From

data like these we are able to extract µ0Hc2, choosingfor simplicity to define µ0Hc2 in terms of the midpointof the resistive transition, and using 10 and 90% of thetransition to determine the error bars. Plotting µ0Hc2

extracted in this manner, as shown in Figure 9 and ex-trapolating to T = 0K, we determine µ0H

⊥c2(0) ∼ 0.6T

and µ0H‖c2(0) ∼ 3.5T , giving an anisotropy of ∼ 6. There

is some variation in this value, perhaps due to the sen-

sitivity of H‖c2 to orientation, but most samples yield an

anisotropy between 6 and 15, similar to that observed byother authors.7

The resistivity upturn which is observed in severalsamples is suppressed by an applied field, resulting ina pronounced “hump” feature in the magnetoresistanceρ(H) for fields just above Hc2 (see Figure 8 ). Themagnitude of the resistivity upturn in zero field, andhence the associated negative magnetoresistance, variesbetween samples grown under different conditions, andto a lesser extent even between samples from the samebatch. This variation is illustrated in Figure 10 whichshow representative c-axis and in-plane magnetoresistiv-ity data for samples with small (panel (a)) and large(panel (b)) upturns respectively. The field is orientedparallel to the c-axis in both cases to allow direct com-parison. For the sample shown in panel (a), the anomalyis suppressed by fields as small as 0.3T , whereas for thesample shown in panel (b) it survives to fields of morethan twice this value. In all cases, once the anomalyis completely suppressed, a positive magnetoresistanceappears which is approximately linear with field in thehigh-field limit.

Significantly, the suppression of the resistivity upturnis strongly dependent on the orientation of the appliedfield with respect to the c-axis. For example, for thesample shown in Figure 11 (a-c), the resistivity upturnis suppressed for fields exceeding a modest 1 T when ap-plied parallel to the c-axis, but is only suppressed forfields exceeding 12 T when directed perpendicular to thec-axis. Although the absolute values of the fields at whichthe resistivity upturn are suppressed vary between crys-tals depending on the magnitude of the zero-field upturn,this anisotropy is always observed. This anisotropy ap-pears to mirror the anisotropy in µ0Hc2, such that ifmagnetoresistance data for the two orientations are plot-ted as a function of field scaled by the appropriate valuefor µ0Hc2 for that orientation, the data lie almost on topof each other (Figure 11 (d)). It is not clear whetherthis is coincidental, or reflects a deeper inter-relation be-tween superconductivity and the origin of the resistivityupturn.

IV. DISCUSSION

The results summarized in Figure 1-3 provide the firstevidence of superconductivity in single-crystals of sto-ichiometric LaFePO, manifested in a bulk thermody-namic transition in both the magnetization and the heat

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FIG. 8: (Color online) Interlayer (c-axis) resistivity as a func-tion of magnetic field for (a) field parallel and (b) orthogonalto the c-axis for temperatures from 1.8 to 6.0 K (see legendin upper panel). The anisotropy in Hc2 is approximately 6 inthis case, though other samples show an anisotropy of up to15.

capacity. In contrast, despite the observation of bulksuperconductivity in polycrystalline samples by severalother groups,3,4,5 McQueen et al. have recently sug-gested that the stoichiometric compound is actually non-superconducting, and that the onset of superconductivityis perhaps associated with the presence of oxygen de-ficiencies, among other possibilities.6 However, the ab-sence of superconductivity in LaFePO would be surpris-ing given that there is nothing anomalous in the densityof states19 of the stoichiometric compound, no evidenceof a competing phase transition, and doping with eitherholes or electrons results in superconductivity.1 Usingcrystals grown by a similar technique to our own, Hamlinet al. observed a substantial diamagnetic susceptibility,but no anomaly in the heat capacity, causing them to sug-gest the possibility that their crystals have a thin surface

FIG. 9: The critical field µ0Hc2 for fields oriented parallel(solid symbols) and perpendicular (open symbols) to the c-axis. Data points were determined from resistivity data asdescribed in the main text. Error bars indicate 10 and 90 %of the superconducting transition.

layer of oxygen-deficient superconducting material sur-rounding a stoichiometric non-superconducting center.7

Refinements of single-crystal x-ray diffraction data forour crystals indicate full site occupancy, with a standarduncertainty in the oxygen content of only 1.8%. Thisis not the best probe of the oxygen content, but severalother pieces of evidence suggest that oxygen deficiency,or at least variation in oxygen deficiency, does not playa significant role in these crystals. Specifically, neitherthe T 2 coefficient of the resistivity nor Tc itself (Figures6 and 5 respectively), show any significant variation withthe residual resistivity, in contrast to what would be ex-pected if variation in the oxygen content were responsiblefor the different residual resistivity values if this were theprinciple source of disorder in these samples. Further-more, these values do not depend on details of the syn-thesis conditions, including whether oxygen is introducedto the melt using Fe2O3 or La2O3, and even the rela-tive concentration of these precursors in the melt. Theseobservations demonstrate that there is remarkably littlevariation in oxygen deficiency between crystals grown bythis technique. In addition, the extremely high resid-ual resistivity ratios, up to 85, indicate that the materialis in fact exceptionally well-ordered. Finally, analysisof recent dHvA data taken for samples grown by thistechnique indicate that the electron and hole pockets arealmost balanced, in agreement with the anticipated re-sult for stoichiometric material,23 with a mismatch thatwould correspond to a doping smaller than the error ofour x-ray diffraction refinements.

Experiments involving annealing in an oxygen atmo-

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sphere may be revealing, and though these are in progressone will always have the problem of establishing by howmuch the material has departed from perfect stoichiome-try, which is a difficult measurement for such small crys-tals. Thus we cannot definitively prove the absence ofoxygen deficiency from the present measurements, andin fact the breadth of the specific heat anomaly in Fig-ure 1 may be indicative of slight variation in stoichiom-etry even within a single sample. However, given thesmall departure from stoichiometry that our errors al-low, together with the above observations, it seems ex-tremely unlikely that the stoichiometric compound isnon-superconducting. Furthermore, the absence of othercompeting phases suggests that superconductivity is thenatural low temperature ground state. In this case, theabsence of a superconducting anomaly in the heat capac-ity data of Hamlin et al. likely reflects similar difficultiesthat we experienced in the measurement of such smallsample masses. It is difficult to speculate on the rea-son for the absence of superconductivity in the polycrys-talline samples of McQueen et al.6 but we note that theresistivity of those samples exhibits a substantial low-temperature upturn. We return to the possible signifi-cance of this below.

From the range and variety of samples measured inthis work, we are also able to consider the role of dis-order on the superconductivity of LaFePO. Even thoughthese materials are anisotropic, the interplane transfer in-tegral for the electron pockets is relatively large8 and sothe interplane residual resistivity should be a good mea-sure of the number of defects in a given crystal, thoughthis argument is weaker for the hole pockets which havelittle warping in the kz direction.24 Assuming that this isthe case, the plot of Tc vs ρ0, as shown in Figure 5 illus-trates that Tc is, within our uncertainties, uncorrelatedwith disorder. For other high-temperature superconduc-tors the absence of Tc suppression has been attributedto the smallness of the coherence length26 ξab. From thepresent measurements ξab can be estimated from the rela-tion µ0H

⊥c2 = Φ0/2πξ2

ab, giving ξab ∼ 0.03µm. The mean

free path can be estimated from a quasi-two-dimensionalDrude model σ‖ = (e2/h) × kF l/c, which yields a dif-ferent conductivity for electron and hole pockets. Us-ing the results of Reference 8, we estimate the electronand hole pockets to have a mean free path l ∼ 1700Aand l ∼ 1200A respectively for the dirtiest samples, ap-proximately in agreement with estimates from de Haasvan Alphen oscillations.8 For the electron (hole) pocketsthis suggests the ratio ξab/l has shifted from a value of∼ 0.04 (0.06) for the cleanest samples to ∼ 0.17 (0.25)for the dirtiest samples. If the disorder were magnetic,a partial, systematic suppression of Tc should manifestfor any pairing symmetry according to the relationshipfirst calculated by Abrikosov and Gor’kov.25,26 Similarly,Tc for anisotropic d-wave or p-wave superconductors inthe weak coupling limit should be suppressed due to theinevitable phase mixing of the order parameter, whichshould be noticeable by this value of ξ/l.24,26,27 Con-

versely, according to Anderson’s theorem,11 an s-wavesuperconductor should be robust against non-magneticdisorder due to the ability of the quasiparticle states toform time reversed pairs. The data in Figure 5 suggeststhat the predominant form of disorder is therefore non-magnetic. More importantly, if the dominant scatteringis strong enough to scatter across the Brillouin zone, thenthis plot also illustrates that the order parameter mediat-ing superconductivity is likely to be s-wave, an observa-tion consistent with recent measurements of penetrationdepth17 on SmFeAsO1−xFx. However, if the scatteringis small angle, or only occurs intra-Fermi surface, thenan s-wave order parameter which reverses sign betweenFermi surfaces centered at the Γ and M points may alsobe possible, as proposed by Mazin et al.28 On the otherhand, if the disorder is inhomogeneous on scales of orderξ, then it is possible than an anomalously clean path willyield a resistive transition Tc which is essentially disor-der independent, though the superfluid density would berapidly suppressed. This behavior may be evident in theheat capacity, and the breadth of the anomaly shown inFigure 1 may be indicative of just such inhomogeneity.29

Naturally, the above discussion relies on the interplaneresistivity being an accurate measure of the in-plane scat-tering rate, which may be true for the electron pocketsdue to their significant c-axis dispersion, but less likelyfor the hole pockets.

We now turn the discussion to the origin of the re-sistivity upturn observed in some crystals for temper-atures just above Tc. Similar upturns are observed inseveral other classes of unconventional superconductorsincluding many of the cuprates,30 several organics31,32

and other polycrystalline oxy-arsenides.33 However, in allthese classes of compounds one observes an enhancementof the anomaly with an applied magnetic field, whereas inthe present case we observe a suppression of the anomalywith field. In addition, we observe the upturn in somebut not all of our samples, implying that this behavior isintimately linked with the presence of disorder. Finally,the anomaly is observed regardless of the current orien-tation, whereas in other correlated materials the effectis only observed when the current is passed along thec-axis.30 In highly anisotropic materials with Josephsoncoupled planes, one expects dramatic differences in thebehavior of each current orientation in field. Specifically,near Tc in-plane currents are dissipated by the motionof pancake vortices under the Lorentz force while inter-layer currents are dissipated by the Josephson couplingbetween the layers, giving rise to a broad anomaly inρc.

30 We thus rule out such coupling as the source of theanomaly.

Given the relatively large concentration of Fe in themelts used to grow these crystals, it is not unreasonableto suggest that the resistivity upturn might be associatedwith Kondo scattering from magnetic impurities. How-ever, the strong anisotropy of the upturn’s suppressionwith field, together with the fact that samples exhibit-ing the upturn do not show a dramatically suppressed

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FIG. 10: (Color online) Temperature sweeps at constant fieldfor field directed parallel to the c-axis illustrating the effect ofapplied fields on the resistivity upturn observed at low tem-peratures for some samples. In (a) we show the interplaneresistivity for a sample with a small upturn and in (b) weshow the in-plane resistivity for a sample with a pronouncedup-turn. In both cases the anomaly is rapidly suppressed bymagnetic field, though clearly the more pronounced the up-turn, the higher the field required for the suppression.

Tc convincingly excludes this possibility. Another pos-sible scenario for the origin of the resistivity anomaly isweak localization due to elastic scattering defects, possi-bly also explaining the rapid suppression of the anomalywith field. Furthermore, in quasi-two-dimensional sys-tems, there can be a significant anisotropy in the field-induced suppression of weak localization.34 However, theupturn does not scale with the residual resistivity ρ0 (asshown in Figure 7 (b)), indicating that the effect doesnot correlate with the concentration of elastic scatteringcenters.

An intriguing alternative hypothesis for the origin ofthe resistivity anomaly is scattering from spin fluctua-

FIG. 11: (Color online) In-plane magnetoresistance for asample with a pronounced upturn. At low fields the magne-toresistance is negative until the anomaly is completely sup-pressed. (a) illustrates the suppression when field is appliedin-plane while (b) shows that the anomaly extends over amuch wider field range when the field is applied orthogonalto the c-axis. (c) Illustrates both these data set on the sameplot for direct comparison and (d) shows the data at 1.8 Kscaled by µ0H

abc2 for the in-plane data and µ0H

cc2 for the inter-

plane data.

tions associated with a competing magnetic phase. Nearperfect nesting of electron and hole pockets evidencedfrom dHvA measurements8 certainly raises the questionas to whether the spin density wave (SDW) observedin the isoelectronic compound LaFeAsO might be sta-bilized in LaFePO. In contrast, recent NMR results forLa0.87Ca0.13FePO indicate the presence of ferromagnetic

fluctuations,37 perhaps indicating that q ∼ 0 nestingbetween concentric FS sheets dominates for such highdoping levels. The same study also revealed anomalousbehavior of 1/T1T below Tc for that material, indicat-ing unusual spin dynamics in the superconducting state,though the origin of this effect is not yet clear. While theevidence points towards stoichiometric LaFePO being su-perconducting, one can speculate that, for example, mag-netic impurities, or even disorder-induced variation in theFe-P bond-length (which is believed to affect the magni-tude of the Fe moment36) might stabilize an incipientSDW in this material. However, there is no evidence fora magnetic or density wave transition in single-crystalsof LaFePO, and Tc is uncorrelated with the magnitudeof the resistivity upturn, at least for the range of val-ues that we have observed. Hence, for such a scenarioto be applicable, either the superconductivity must beinsensitive to the presence/absence of magnetic fluctu-ations, or there must be some degree of inhomogeneityin the crystals, such that parts of the sample that suffer

9

such fluctuations are physically separate from the major-ity superconducting phase. Unfortunately, although thispossibility is especially interesting due to the parallels toLaFeAsO, we cannot definitively establish whether it isappropriate from these measurements. Additional exper-iments are underway to determine the effect of stabilizingthe SDW on the normal and superconducting states inthis compound.

We note in closing that whatever the cause of the re-sistivity anomaly, it is reminiscent of an upturn seen byMcQueen et al. for polycrystalline samples which hadno superconducting transition.6 The residual resistivityratio of those polycrystalline samples was nearly two or-ders of magnitude lower than that of the single-crystalsamples described in this report, and the resistivity up-turn was significant. This raises the possibility that thelack of superconductivity in those samples might not bedue to differences in the oxygen content, but rather toa larger concentration of defects, potentially affecting acompeting density wave ground state.

V. CONCLUSIONS

We have studied transport and thermal properties ofsingle-crystals of LaFePO. These samples exhibit super-

conductivity, and the evidence suggests that stoichiomet-ric LaFePO is indeed a bulk superconductor, in contrastto other reports. Furthermore we find that the super-conducting gap is unrelated to non-magnetic disorderfor values of ξ/l ∼ 0.2(assuming that disorder is pro-portional to the interplane resistivity). This result isconsistent with an s-wave pairing symmetry, but is notdefinitive. Finally, we have investigated an anomalouslow-temperature resistivity upturn that appears in someof our samples through detailed temperature and fieldstudies. The feature is related to disorder, though thepresent measurements are insufficient to definitively es-tablish the origin of this effect.

VI. ACKNOWLEDGEMENTS

We would like to thank Ross McDonald, AmaliaColdea, J. D. Fletcher, Scott Riggs, Stephen Kivelson,Doug Scalapino, Zach Fisk, Ben Powell, D. H. Lu, MingYi, Z. X. Shen and Theodore Geballe for useful com-ments on this work prior to publication. This work issupported by the Department of Energy, Office of BasicEnergy Sciences under contract DE-AC02-76SF00515.

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