Nanoscopic coexistence of magnetic and superconducting states within the FeAs layers of CeFeAsO1-xFx
S. Sanna, R. De Renzi, T. Shiroka, G. Lamura, G. Prando, P. Carretta, M. Putti, A. Martinelli, M.R. Cimberle, M. Tropeano, A. Palenzona
NNanoscopic coexistence of magnetic and superconducting stateswithin the FeAs layers of CeFeAsO − x F x S. Sanna, ∗ R. De Renzi, T. Shiroka,
3, 4
G. Lamura, G. Prando,
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P. Carretta, M. Putti, A. Martinelli, M.R. Cimberle, M. Tropeano, and A. Palenzona Dipartimento di Fisica “A. Volta” and Unit`a CNISM di Pavia, I-27100 Pavia, Italy Dipartimento di Fisica and Unit`a CNISM di Parma, I-43124 Parma, Italy Laboratorium f¨ur Festk¨orperphysik, ETH-H¨onggerberg, CH-8093 Z¨urich, Switzerland Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland CNR-SPIN and Universit`a di Genova, via Dodecaneso 33, I-16146 Genova, Italy Dipartimento di Fisica “E. Amaldi”, Universit`a di Roma3-CNISM, I-00146 Roma, Italy CNR-SPIN Corso Perrone 24, I-16146 Genova, Italy CNR-IMEM, via Dodecaneso 33, I-16146 Genova, Italy (Dated: November 8, 2018)We report on the coexistence of magnetic and superconducting states in CeFeAsO − x F x for x = 0 . T m = 30 K and T c = 18 K, respectively.Zero and transverse field muon-spin relaxation measurements show that below 10 K the two phasescoexist within a nanoscopic scale over a large volume fraction. This result clarifies the nature ofthe magnetic-to-superconducting transition in the CeFeAsO − x F x phase diagram, by ruling out thepresence of a quantum critical point which was suggested by earlier studies. The recent discovery of high- T c superconductivity (SC)close to the disruption of magnetic (M) order in Fe-basedcompounds has stimulated the scientific community tofurther consider the role of magnetic excitations in thepairing mechanism. In order to address this point it isnecessary to understand how the ground state evolvesfrom the M to the SC phase within each family of Fe-based superconductors. In the REFeAsO − x F x family(hereafter RE1111, with RE=La or a rare earth) earlyexperiments have suggested that the M-SC crossover isRE-dependent. For instance, a smooth reduction of themagnetic and superconducting ordering temperatures, T m and T c respectively, was found for RE=Ce, sug-gesting the presence of a quantum critical point. ForRE=Sm a partial coexistence of the M and SC stateswas found, while a first order transition seems to oc-cur for RE=La. Successive studies have shown thatthe doping region where T m and T c are both non-zerois virtually point-like in Sm1111, demonstrating thatthe cases of RE=La and Sm can be reconciled undera unique behavior. Recently, nanoscale electronic in-homogeneities have been shown to be present in bothRE=La and Sm in a wide range above the crossoverregion. Actually also the case of RE=Ce is susceptibleto further investigation concerning the presence of elec-tronic inhomogeneities in the superconducting dome oreven the possible microscopic coexistence of magnetic or-dering and superconductivity in the FeAs layers, whichmight have eluded previous neutron diffraction studies. In fact, contrary to diffraction techniques, which can-not detect short range magnetic order, muons act as lo-cal magnetic probes, hence making muon spectroscopy( µ SR) an ideal tool for this sort of investigations. Forthis reason µ SR has long been employed to study the M-SC coexistence in cuprates as well as in other super-conducting compounds, such as the ruthenocuprates, or the heavy-fermion superconductors. Here we report on zero- (ZF) and transverse-field (TF) µ SR measurements on a sample of CeFeAsO − x F x whichunambiguously show the coexistence of superconductiv-ity and short range magnetic order on a nanoscopiclength scale. While in contradiction with previous ex-perimental findings on the same compound, this resultclosely resembles the behavior of Sm1111 at the M-SCcrossover. The investigated polycrystalline CeFeAsO − x F x sam-ple was synthesized by a solid-state reaction method fol-lowing the procedure reported in Ref. 18. The total fluo-rine content was evaluated from intensity measurementsof the F nuclear magnetic resonance echo signal, ascompared to that of a SmOF reference compound. Suc-cessive Rietveld analysis of the powder x-ray diffractionpattern excluded the presence of fluorine in other sec-ondary phases, except for a tiny minority (3% vol.) of aspurious CeOF phase. The combined result of the aboveanalysis gives a best estimate of x = 0 . − x F x .The temperature dependence of magnetic suscepti-bility, χ ( T ), was measured on the powder sample us-ing a dc Superconducting Quantum Interference Device(SQUID), and it is shown in Fig. 1. Two key features areevident from the data: a sizeable diamagnetic responsebelow T c = 18 K due to SC shielding, and a cusp at T Ce N = 2 . A similar behavior is found in anoptimally doped Ce1111 sample. To empirically sepa-rate the contributions due to the electrons in FeAs bandsfrom the ones of Ce , the susceptibility was fitted tothe sum of two functions: an erf[( T − T c ) / ( √ T c witha width ∆), and a Curie-Weiss term, which accounts forthe behavior of the Ce sublattice. The two contributionsare shown in Fig. 1 by dashed and dotted lines, respec-tively. From the low-temperature limit of the first term, a r X i v : . [ c ond - m a t . s up r- c on ] J u l FIG. 1. (Color online) Magnetic susceptibility in zero-fieldcooling of CeFeAsO − x F x with x = 0 . T Ce N . The superconducting (dashed line)and the Curie-Weiss (dotted line) contributions are also dis-played (see text for details). χ sc ( T → (cid:39) . ∼
50% superconducting volume fraction.This fraction could be even larger, since at low dopingthe field penetration depth increases considerably, andbecomes comparable to the grain size (1–10 µ m). Hencethe shielding volume is effectively reduced within eachgrain. The SC fraction could also be smaller if supercon-ductivity were limited to the grain surface, but we shallshow this not to be the case by TF- µ SR.To probe the local magnetic state in Ce1111 we per-formed a series of ZF- µ SR measurements. Figure 2shows the time dependence of the ZF muon asymmetry, A ZF ( t ), normalized to its room temperature value a ZF (a marginal muon fraction of 5%, due either to muonsstopped in the cryostat walls or in a non magnetic impu-rity phase, was subtracted as a constant background).Solid lines show the best fit to the measured sampleasymmetry using the following normalized ZF function: A ZF ( t ) a ZF = f L e − λ L t + f T · ( w e − σ t / + w e − σ t / ) (1)Here we distinguish a slowly decaying ( λ L ∼ . µ s − )muon fraction, f L , whose amplitude increases from 1/3at low temperature to a unitary value at high T , and asecond muon fraction, f T , which vanishes at high temper-ature. One can easily identify them with the longitudinal( B i (cid:107) S µ ) and transverse ( B i ⊥ S µ ) components of theasymmetry, respectively, with B i the internal magneticfield and S µ the initial muon-spin direction.The very fast relaxing transverse components repre-sent the signature of a sizeable distribution of internalfields B i . Best fits at low temperature yield two Gaus-sian contributions with weights w = 0 .
85 and w = 0 . FIG. 2. (Color online) Time dependence of the normalizedzero-field muon asymmetry with best fits to Eq. (1), measuredat four different temperatures. and standard deviations σ/ πγ =( B i − B i ) / (cid:39)
60 mTand 12 mT, respectively. Internal fields of this size aretypically found at the muon site when the magnetic or-dering occurs in the FeAs layers of samples close to a M-SC crossover. Indeed, since we find both the transversecomponents to disappear at the same temperature, theyshould reflect the same electronic environment. Thesetwo transverse components most probably come from twodifferent muon stopping sites as suggested by a previous µ SR study in undoped Ce1111 samples. By consider-ing that simple geometric arguments predict f L = 1 / V mag = 3(1 − f L ) / V mag is reported inFig. 3a. It shows that the magnetic transition has itsonset already at T m (cid:39)
30 K and that the whole samplebecomes magnetic below T (cid:46)
10 K, hence proving thepresence of ordered magnetic moments throughout theFeAs layers of the whole sample volume. This does notnecessarily imply that all the muons are implanted insidea magnetically ordered domain. The distance betweenadjacent antiferromagnetic domains (i.e. with vanishingmacroscopic moment) can be estimated by simply consid-ering the dipolar interaction between the S µ = muonspin and a domain moment with the value of the orderedmoment, m ≈ . µ B , which at a distance d produces alocal field B i = µ π md − . Since in ZF- µ SR a rough detec-tion limit for the spontaneous internal fields is ca. 1 mT,one can estimate to d ∼ FIG. 3. (Color online) a) Temperature dependence of themagnetic (triangles) and non-superconducting (solid line) vol-ume fractions as seen by ZF- µ SR and magnetization measure-ments, respectively. The onset of superconducting and mag-netic transitions, T c and T m , is indicated by vertical arrows.b), c) and d) panels display the fraction, the decay rate andthe relative field shift for the j = 1 fraction of the TF- µ SRasymmetry (Eq. 2). the FeAs layer for T (cid:46)
10 K (see Fig. 3a), one can con-clude that the maximum distance between magneticallyordered domains is of the order of a few nanometers.Combined with the above SQUID measurements, the ZF µ SR results clearly demonstrate that at low temperaturethe SC and M states coexist within a nanoscopic lengthscale in at least 50% of the sample volume, as shown bythe hatched area of Fig. 3a. This coexistence implies thatthe superconductivity must survive within a few nanome- ters, a condition which is satisfied in this material, wherethe typical coherence length is of the order of ξ ∼ To further investigate the M-SC coexistence state wecarried out TF- µ SR measurements, whereby the samplewas cooled in an externally applied field H ⊥ S µ equalto µ H = 20 mT, i.e. higher than the lower supercon-ducting critical field H c , expected in the range 0–10mT. Accordingly, a flux-line lattice is generated below T c . In this experiment muons probing the pure flux-linelattice experience the diamagnetic shift of the local field B µ = µ H (1 + χ ), with χ < On the other hand, thosemuons implanted in the magnetically ordered phase willprobe a magnetic field B µ = | µ H + B i | , whose magni-tude in a powder sample is B µ (cid:38) µ H . The amplitudesof these frequency-distinct signals are proportional to thevolume fractions where the corresponding order param-eter is established. Based on these considerations, wecould describe the time evolution of the TF- µ SR nor-malized asymmetry using: A TF ( t ) a TF = (cid:88) j =1 , f TF j e − λ j t cos(2 πγB j t ) + f TF3 e − λ t , (2)with γ = 135 . a TF , the total asymmetry measured at high temperature.Equation (2) fits the TF data very well over the en-tire 3–300 K temperature range ( χ ≈ ÷ . µ H + B i ) (cid:107) S µ , expected below T m . The second ofthe oscillating terms (the one labeled with j = 2 — notshown), is present only below T m . It reflects an environ-ment with spontaneous magnetic order, characterized byparamagnetic field shifts at the muon site B ≈
23 mT( > µ H ), and by fast ( λ ∼ µ s − ) relaxation rates dueto the disordered distribution of spontaneous local fields B i , in agreement with previous ZF- µ SR results.Let us now focus on the parameters describing thefirst ( j = 1) oscillating term. Figure 3b shows the frac-tion f TF1 that is close to one at high temperatures (with f TF2 = f TF3 = 0), since the whole sample is in a singlephase for
T > T m . Interesting insights come from therelative field shift sensed by implanted muons (shown inFig. 3d). In this high- T regime the absence of a shift char-acterizes a sample which is neither in a superconducting,nor in a magnetically ordered state. Here the Lorentziancharacter of relaxation, with small λ (cid:46) . µ s − values(see Fig. 3c), reflects the presence of very small fluctuat-ing dipolar fields, probably due either to the Ce magneticmoments or to some minor phase of diluted Fe clusters. Once the sample is cooled below T m a reduction of f TF1 is observed, specular to the increase in magnetic volumefraction detected by ZF- µ SR, as clearly seen in panels aand b of Fig. 3. However, no appreciable variations in λ or B are detected across T m , suggesting that no elec-tronic changes occur in the f TF1 volume fraction downto T c . Only below T c there is a sizeable increase of thediamagnetic shift (panel d), which denotes an expulsionof the externally applied field, as well as the increase ofthe relaxation rate (panel c), which reaches values typicalof the superconducting pnictides. Notice that the muonfraction in the superconducting environment is f TF1 > . < T < T c , which demonstrates that the corre-sponding volume is more than 50%. By further coolingbelow 10 K (hatched area in panels b–d) one finds that f TF1 reduces drastically to ∼ λ anda progressive vanishing of the diamagnetic shift B . Allthese facts imply that the magnetic environment probedby muons is far more complex than the initially pureflux-line lattice, with internal fields B i of the order of µ H developing throughout the whole volume within ananoscopic length scale. This picture fully agrees withthat from ZF- µ SR, also consistent with the presence ofcoexisting magnetic order in the FeAs layers.In summary, both ZF- and TF- µ SR experiments showthat a superconducting Ce1111 sample becomes fullymagnetic within the FeAs layers below 10 K. Below T c a sizeable fraction of muons detect a pure superconduct-ing volume, which seems to progressively vanish as the fully ordered magnetic state develops. This, however,does not imply that superconductivity is destroyed, asclearly proved by susceptibility measurements, which de-tect a practically unchanged SC volume fraction (oncethe unrelated paramagnetic behavior of Ce is properlyaccounted for).These results demonstrate that in Ce1111 the super-conductivity may coexist at the nanoscopic scale withmagnetically ordered moments in the FeAs layers. 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