75As NMR-NQR study in superconducting LiFeAs
Seung-Ho Baek, Hans-Joachim Grafe, Franziska Hammerath, Madeleine Fuchs, Christian Rudisch, Luminita Harnagea, Saicharan Aswartham, Sabine Wurmehl, Jeroen van den Brink, Bernd Büchner
aa r X i v : . [ c ond - m a t . s up r- c on ] M a y EPJ manuscript No. (will be inserted by the editor) As NMR-NQR study in superconducting LiFeAs
Seung-Ho Baek , a , Hans-Joachim Grafe , Franziska Hammerath , Madeleine Fuchs , Christian Rudisch , LuminitaHarnagea , Saicharan Aswartham , Sabine Wurmehl , Jeroen van den Brink , and Bernd B¨uchner Leibniz Institute for Solid State and Materials Research IFW-Dresden, PF 270116, 01171 Dresden, GermanyReceived: date / Revised version: date
Abstract.
We report results of As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance(NQR) experiments as well as Li NMR on different samples of self flux grown LiFeAs and 5% Co dopedLiFeAs single crystals, and a polycrystalline LiFeAs sample. We were able to distinguish the samples bytheir slightly different quadrupole frequencies, ν Q , which is a direct measure of the electric field gradient(EFG) at the As site. Interestingly, samples with a large quadrupole frequency appear to show a differentKnight shift and spin lattice relaxation in the superconducting state from those with a lower ν Q , yet allthe samples are clearly superconducting. For sample S1 which has the largest ν Q , we find constant Knightshift K across T c for a certain direction of the magnetic field and a peculiar upturn of the NQR spin latticerelaxation rate ( T T ) − below T c . In contrast, samples with a lower ν Q exhibit the expected behavior fora singlet superconductor: a drop of K and ( T T ) − for both NMR and NQR below T c . Our results showthat already tiny changes in stoichiometry uncovered by slightly different NQR frequencies lead to verydifferent behavior of the NMR parameters in the superconducting state of LiFeAs. Different possibilitieswill be discussed which may explain the contrasting behavior. PACS.
XX.XX.XX No PACS code given
Among the recently discovered superconducting iron pnic-tides [1,2], LiFeAs is a rare member exhibiting supercon-ductivity with T c ∼
18 K in a stoichiometric form withoutdopants or pressure. Yet, the Li content in this compoundis difficult to control and seems to have a large influenceon the physical properties. For example, Li deficiencies ofonly ∼
1% greatly suppress superconductivity [3]. Proba-bly related to the sensitivity of the Li concentration, thesuperconducting ground state of LiFeAs and the pairingmechanism are still under debate.Small angle neutron scattering (SANS) and angle re-solved photoemission spectroscopy (ARPES) [4,5,6] sug-gest that LiFeAs could be a weakly electron-phonon cou-pled conventional-type superconductor. However, a recentRaman scattering study did not find evidence for substan-tial electron-phonon-coupling and no superconductivity-induced phonon anomalies [7]. Furthermore, while the spindensity wave (SDW) state is absent in LiFeAs, there is ev-idence that weak local moments [8] and magnetic fluctua-tions are still present in the normal state, putting LiFeAsclose to a magnetic instability [9,10]. Theoretical analysesof the electronic band-structure find a superconductingorder parameter of s ± type driven by collinear antiferro-magnetic fluctuations [11]. The fully gapped s ± supercon- a e-mail: [email protected] ductivity is also suggested by heat transport [12], mag-netic penetration depth measurements [13], and inelasticneutron scattering (INS) study [14]. On the other hand,Brydon et al. [15] proposed spin-triplet p -wave pairing inthis system. Being in agreement with the theoretical ar-gument, vortex properties [16] and H c measurements [17]for H k ab show a very similar behavior as in the suppos-edly triplet superconductor Sr RuO , and quasi particleinterference (QPI) patterns measured by scanning tunnel-ing microscopy (STM) [18] supports an elementary p -wavesymmetry, rather than singlet pairing symmetries ( s ± - or d -wave).The so far reported NMR measurements of LiFeAspowder samples indicate the existence of magnetic correla-tions from the analysis of the Korringa relation [19,20]. Inthe superconducting state, the Knight shift shows a sharpdrop at T c which is suggestive of spin-singlet superconduc-tivity. In the only NMR study on single crystals Ma et al. argue that the absence of the spin density wave ordering inLiFeAs is due to off-stoichiometry and/or lattice defects,and find two different Li sites in their superconductingsamples [21].Here, we report detailed NMR and NQR results onthree single crystal LiFeAs samples, as well as on a 5% Codoped single crystal, and a polycrystalline LiFeAs sam-ple. We show that the NQR frequency is highly sensi-tive to the Li content, and that samples with tiny differ-ences in stoichiometry can be distinguished by their differ- Seung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs ent quadrupole frequencies. A doping dependence of thequadrupole frequency has already been found in other ironpnictides [22], and similar changes of ν Q with Co doping inLiFeAs indicate that also Li deficiencies change the dop-ing level of the samples. Interestingly, samples with a largequadrupole frequency appear to show a different Knightshift and spin lattice relaxation in the superconductingstate from those with a lower ν Q . Sample S1 which hasthe largest ν Q , exhibits a constant Knight shift K across T c for a certain direction of the magnetic field and a pe-culiar upturn of the spin lattice relaxation rate ( T T ) − below T c . In contrast, samples with a lower ν Q exhibit adrop of K and ( T T ) − below T c . Our results show that al-ready tiny changes in stoichiometry uncovered by slightlydifferent NQR frequencies lead to very different behaviorof the NMR parameters in the superconducting state ofLiFeAs. The tiny differences in stoichiometry and theirlarge impact on the superconducting properties may alsoaccount for the contradicting results reported so far. The LiFeAs single crystals were grown by a self-flux methodusing a molar ratio of Li:Fe:As = 3:2:3 similar to ref. [23].The stoichiometry of the samples has been checked by in-ductively coupled plasma mass spectroscopy (ICPMS). 20mg of the LiFeAs single crystal were dissolved in a leak freeglass ampoule in nitric acid. The molar ratio Li:Fe:As isfound to be 0.99:1.00:1.00, consistent with a stoichiomet-ric LiFeAs composition [23]. ARPES measurements per-formed on a LiFeAs single crystal from the same batchwere found to be in agreement with an exact stoichiome-try [5].The susceptibility of our samples exhibits a sharp su-perconducting transition at T c ∼
18 K [23,4]. A clearanomaly at T c in the specific heat measurement [24], andthe large residual resistance ratio (RRR) [23,25], with thelowest residual resistivity observed so far in iron pnic-tides [26,27,28] indicate that the samples are clean su-perconductors. Furthermore, STM measurements yield adefect concentration < I z = − / ↔ − / I z = +1 / ↔ +3 /
2) of a NMRspectrum, because those measure directly the distributionof the electric field gradient (EFG) which is caused bydisorder or defects in the sample, while the broadeningof the central transition ( I z = − / ↔ +1 /
2) is domi-nantly magnetic in origin. As we will show below, all sam-ples exhibit very narrow linewidth of both As NQR linesand Li NMR satellites which prove the absence of largeamounts of defects in our samples and a stoichiometry ofclose to 1:1:1. As (nuclear spin I = 3 /
2) NMR/NQR, and Li ( I =3 /
2) NMR measurements were carried out in five differ-ent LiFeAs samples: four single crystalline samples: S1, S2,S3, and Co 5%-doped LiFeAs, and a polycrystalline sam-ple, where the single crystals S1, S2, and S3 are from the same batch. Due to the extreme sensitivity of the samplesto air and moisture, all the samples were carefully sealedinto quartz tubes filled with Ar gas. It could happen thatthermal cycling damages the sealing of the quartz tubesthat contain the sample, so that, if the sample probe has tobe taken out of the cryostat, the sample is easily degradedby contact with air. For this reason we could not obtainfull data sets for all of the samples since the NMR andNQR signals become negligibly weak in a sample whichhad contact with air.Since the local symmetry at the As is axial (tetrag-onal), the nuclear quadrupole frequency ν Q can be deter-mined directly from the resonance frequency of the NQRspectrum for the As and by the splitting of the satellitesfor the Li. The Knight shift was obtained by measuringthe central transition. The nuclear spin-lattice relaxationrates T − were measured by saturation and inversion re-covery methods. For exact orientation of the crystals withrespect to the static magnetic field a single axis goniome-ter has been used for most of the measurements. As NQR
For the As in a non-cubic environment, the four-fold de-generacy of the nuclear spin of I = 3 / Q and the surrounding EFG, eq , which allows a NQR res-onance at a frequency given by ν Q ≡ e qQ/h where h isPlanck’s constant and e the electron charge. We find a verynarrow NQR line near 21.5 MHz at room temperature, asshown in the inset of Fig. 1. The As NQR spectra havea width ranging from 60 kHz (S2) to 80 kHz (S1) at roomtemperature, which is a factor of 2-3 narrower than 170kHz reported earlier in powder samples of LiFeAs [20],and even significantly smaller than the values reportedfor other undoped (non-superconducting) iron pnictides:100 kHz from NMR satellites in BaFe As [29], 308 kHzand 385 kHz in La- and SmOFeAs, respectively [22], and480 kHz in CaFe As [30]. This is even more surprisingregarding the high quadrupole frequency of LiFeAs withrespect to the other iron pnictides, and indicates the highhomogeneity of all of our single crystals.The temperature dependences of the nuclear quadrupolefrequency ν Q of the As are shown in Fig. 1. The re-sults obtained in the polycrystalline sample and the 5%Co doped single crystal sample are also compared. We findthat ν Q , or the EFG eq , varies with the samples investi-gated. Despite the different ν Q at a given temperature,the temperature dependences of ν Q of all the samples arevery similar among one another, i.e., ν Q decreases withdecreasing T , being saturated at low temperatures. Sucha strong temperature dependence of ν Q is commonly ob-served in iron pnictides [29,31], and is attributed to mostlyelectronic effects due to complicated multi-orbitals of theiron ion (3 d ), since the lattice (thermal vibration) con-tribution, usually, leads to an opposite (and very weak)temperature dependence. However, we can distinguish the eung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs 3
Fig. 1.
The quadrupole frequency, ν Q , decreases with decreas-ing temperature and almost saturates at low temperatures.While the temperature dependences of ν Q of all the samplesare similar, the values of the sample S1 are noticeably largerthan those of the samples S2 and S3, as clearly shown in theinset. For comparison, ν Q ( T ) for polycrystalline and Co-dopedsamples are shown, too. Note that the linewidth is also stronglysample-dependent, yielding 80, 60, and 40 kHz for S1, S2, andS3, respectively at room temperature. samples clearly by their different values at a given tem-perature, which resembles a doping dependence similarto other pnictides [22,32] even though samples S1-S3 arefrom the same batch, and should have the same compo-sition according to ICPMP and ARPES [23,5]. Interest-ingly, we observe that ν Q ( T ) of the polycrystalline sampleis very similar to that of S1, while ν Q ( T ) of the Co-dopedsample is even below those of S2 and S3. It appears thatsamples with a larger ν Q reveal a peculiar temperature de-pendence of the relaxation rates and/or the Knight shiftin the superconducting state, as shown below, whereassamples with a lower ν Q show more normal behaviors, asexpected in typical spin-singlet superconductors. We notethat ν Q ( T ) of the powder samples obtained by Li et al.[20] appears to be close to our Co-5% doped single crystal.Fig. 2 shows the As NQR measurement of the spinlattice relaxation rate divided by temperature, ( T T ) − .For all samples, ( T T ) − slightly decreases with decreas-ing T and approaches a constant value below ∼
150 Kdown to T c . Below T c , however, the temperature depen-dence of ( T T ) − varies among the samples. Due to theopening of the superconducting gap, the electron densityof states at the Fermi level to which ( T T ) − is propor-tional, is reduced rapidly, and thus ( T T ) − is expectedto decrease accordingly. While S3 exhibits such a rapiddrop at T c , S1 does not. Nevertheless, the fact that theupturn occurs at T c suggests that the unusual behavioris associated with superconductivity, as will be discussedbelow in comparison to the NMR ( T T ) − . For the Co- Fig. 2. As NQR spin-lattice relaxation rates divided by T ,( T T ) − , as a function of T in zero field. While ( T T ) − of allfour samples are essentially the same above T c , those changedrastically below T c . For both the single crystal S1 and thepolycrystalline sample, ( T T ) − rises below T c . 5% Co-dopingsuppresses the enhancement below T c , but still without a de-crease. On the contrary, data from another single crystal S3reveals a rapid drop, as expected in the superconducting state. doped sample, the enhancement of ( T T ) − is suppressed,while maintaining the constant value from above T c . Thepolycrystalline sample also shows a strong enhancement of( T T ) − below T c , similar to that of S1. In all cases, su-perconductivity has been confirmed at the same time bya strong change in the resonance frequency of the NMRcircuit, which is proportional to the ac susceptibility ofthe sample. We note that both S1 and the polycrystallinesample which reveal a similar behavior of ( T T ) − possesslarger ν Q values than the other samples, as shown in Fig.1. Tentatively, this trend may suggest that the strengthof the EFG has a relationship with the underlying physicswhich may cause the different behaviors of ( T T ) − in thesuperconducting state. Li NMR spectra
Fig. 3 shows Li NMR spectra including the two satellitesobtained for the crystal S3. At 200 K, the spectra for bothdirections along c and ab reveal very sharp lines which al-low us to determine ν Q = 33 kHz accurately. This value isalso consistent with the value of ν Q = 34 kHz estimatedby Jegliˇc et al. [19] by an echo decay measurement. Thealmost identical linewidth of cental and satellite lines indi-cates that the broadening mechanism is mainly magnetic,and the distribution of the EFG is negligibly small. At lowtemperatures, the Li spectra broaden significantly, unlikethe As NMR-NQR spectrum whose linewidth increasesonly for S1 at low temperatures. This indicates that the
Seung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs
Fig. 3. Li NMR spectra at 200 K and 20 K at H = 4 . Li quadrupole frequency, ν Q = 33 kHz. The sep-aration between the satellite lines for H k c corresponds to2 ν Q , as expected in the tetragonal symmetry (the asymmetryparameter η = 0). The linewidth, which is the same for centraland satellite lines, for H k ab ( H k c ) increases from 9 kHz (11kHz) at 200 K to 20 kHz (40 kHz) at 20 K. Li nuclei experience quasi-static spin fluctuations at lowtemperatures, particularly for H along the c axis.We emphasize that our Li NMR spectra assure thatthere is only one single Li site in our crystals. This isin stark contrast with the crystals used by Ma et al. [21]where two Li resonances are observed, indicating the pres-ence of inequivalent Li sites in their crystals. Therefore ourresults are not consistent with the claim that the absenceof magnetism is due to the off-stoichiometry or defects.Rather, we argue in this paper that the stoichiometry is acritical parameter governing the nature of magnetism andsuperconductivity in LiFeAs. As NMR Knight shifts
Fig. 4 (a) shows the T -evolution of the As NMR centralline of the single-crystal S1 measured with H parallel tothe ab -plane. At high temperatures, the spectrum shiftsdown with decreasing T , and approaches a constant fre-quency below ∼
50 K. Unexpectedly, we observed that thespectrum (drawn with thick lines below T c ) maintains theresonance frequency in the superconducting state downto 4.2 K. This behavior drastically changes when H is ro-tated out of the ab -plane by ∼ ◦ – now the As NMR lineshows visible shifts below T c , see Fig. 4 (b). Nevertheless,this indicates that the sample is superconducting.Due to the large NQR frequency ν Q , there should bea substantial shift of the central transition for H k ab that is strongly angle dependent, due to the second orderquadrupole effect. In an uniaxial symmetry, which we con-firmed by Li NMR spectra, the second order quadrupole
Fig. 4. As NMR spectra of the central transition ( I z =1 / ↔ − /
2) at an external field of H = 7 . H k ab . Note that the resonance frequency of the spectra doesnot change upon going through T c . (b) Same as in (a), butwith tilting the sample by 2 ◦ . Although the temperature de-pendence of the shift above T c is similar to the case of theexact alignment, the resonance frequency drops at T c ( H ) ∼ shift for a nucleus with spin I = 3 / ∆ν ( θ ) = 3 ν Q γ n H (1 − cos θ )(1 − θ ) , (1)where θ is the angle between the tetragonal c axis and H . ∆ν ( θ ) has been subtracted from the total shift of theNMR lines to extract the Knight shift shown in Fig. 5. Inour case, the extreme sensitivity of ∆ν to θ caused by thelarge ν Q is indeed a benefit since one can take advantageof it in order to align the sample with great accuracy. Inparticular, it is very useful for H k ab , since ∆ν is simplythe maximum when θ = 90 ◦ . Furthermore, we confirmedby exact diagonalization of the nuclear Hamiltonian thevalidity of the second order correction.The resulting Knight shift K shown in Fig. 5(a) de-creases slowly upon lowering the temperature, flatteningout at around 50 K, being in agreement with the results re-ported previously [20,19], as already reflected in the rawdata (see Fig. 4). The total Knight shift K consists ofa spin and an orbital contribution, K = K spin + K orb ,where the latter involves the orbital motion of the con-duction electrons and is usually temperature independent.Here, K spin is directly proportional to the spin suscepti- eung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs 5 bility, K spin = Aχ spin , where A is the hyperfine couplingstrength. Therefore, K should vanish at T ≪ T c if thespin state of Cooper pairing is singlet. Usually, the hyper-fine coupling constant is extracted from plots of K versusthe bulk susceptibility, χ . We extracted the hyperfine cou-pling constants for temperatures T >
170 K, because be-low the temperature the Knight shift does not scale withthe susceptibility χ due to a magnetic impurity contribu-tion which affects only χ . For H k ab we obtain A ab = 6 . µ B , and for H k c A c = 0 .
95 T/ µ B . These values ap-pear to be strongly anisotropic, compared to other ironpnictides, e.g., A ab = 3 .
87 T/ µ B and A c = 2 .
61 T/ µ B for isostructural NaFeAs [34] and A ab = 2 .
64 T/ µ B and A c = 1 .
88 T/ µ B for BaFe As [29].A scaling of the Knight shifts measured for differentorientations and for different nuclei would indicate that allnuclei probe the same component of the spin susceptibil-ity. Such a behavior has been found for optimally dopedLaO . F . FeAs [35]. Instead, we find that for As K ab does not give a linear relation with K c . Likewise, theKnight shift of the Li nucleus does not scale with theKnight shift measured at the As for both directions.Since there are several bands crossing the Fermi level inthe iron pnictides, one can expect each band to make adifferent contribution to the total spin susceptibility withdifferent hyperfine couplings to different bands. Such isthe case for O NMR in Sr RuO , where the oxygensimultaneously couples to multiple bands with differenttemperature-dependent susceptibilities [36]. The strong an-gular dependence of K is also observed for the O Knightshift in Sr RuO , whose sign changes with angle at lowtemperatures as in our case. While the spin susceptibil-ity χ spin is always positive, the Knight shift can be nega-tive since K spin can be decomposed into two components: K spin = A s χ s + A cp χ non- s where A s is the direct Fermi con-tact hyperfine coupling to s -electrons and A cp arises fromcore polarization of inner s -shells due to non- s electrons( p or d ) [37]. Here, A s is always positive whereas A cp isalways negative. Thus, if χ non- s is strongly angle and tem-perature dependent, K will change accordingly, possiblyreversing its sign. Although this may catch the essentialfeatures, the whole T - and angle-dependencies of our dataobtained in LiFeAs are not correctly understood quantita-tively within this simple picture. This is likely due to themulti-band structure as mentioned above. In this case, thespin susceptibility from each band may have quite differ-ent response to temperature and field direction, dependingon the overlap with p -orbitals of the As ion, resulting inthe observed angular and temperature dependencies of theKnight shift.Now, we focus on the temperature dependence of K at low temperatures, which is shown in Fig. 5(b). Upon We do not show K c here, because we measured our sam-ples only with a single axis goniometer. Therefore, while onecan reach a perfect alignment for H k ab , there may be smalldeviations for H k c which lead to additional second orderquadrupole correction. This affects only the absolute value of K c , but not the temperature dependence which can be com-pared with K ab . going through the superconducting T c , the Knight shift K ab for the sample S1 does not show any change, whichwas already manifested in the raw data [Fig. 4(a)].Furthermore, in the superconducting state the behav-ior of K changes when the field H is tilted by just 2 ◦ outof the ab plane: there is a clear drop of K at T c and itapproaches to a finite value as T → ◦ , K is small and even upturns slightly below T c , but approaches a similar value for 2 ◦ -off case, too, as T →
0. The temperature dependence of K for a tilting of2 ◦ is similar to the data measured in the polycrystallinesample [19,20], and further indicates that our crystals aresuperconducting. In polycrystalline samples, however, onemay argue that whether K ab is constant for precisely in-plane field is very difficult to be confirmed due to the in-evitable ambiguity in assigning the singularity for H k ab in a powder pattern.However, the results measured in another single crystalS2 exhibit totally different behavior. K for S2 is slightlylarger than for S1 above T c , and K ab shows a clear drop at T c . With tilting the crystal by 3 ◦ , a similar behavior of K was observed, unlike the strong angle dependence obtainedfor S1. Such a strong variation of K in two samples grownin the same batch is surprising, and we interpret this asan indication that LiFeAs is located in the vicinity of aninstability which may cause the extreme sensitivity of thephysical properties. As NMR and NQR linewidth
Fig. 6 shows the temperature dependence of the full widthat half maximum (FWHM) for the NMR and NQR spec-tra. For sample S1, FWHM increases with decreasing tem-perature, indicating a growing of magnetic fluctuations. Incontrast, FWHM of sample S2 is nearly temperature inde-pendent. Note that for technical reasons we could obtainonly limited high temperature NMR data for S2 (see alsoSection 2). The T independent NQR FWHM supports thefact that the NMR FWHM is also T independent, espe-cially since its absolute value is very small even at lowtemperatures.In general, the sample quality is one of the factors de-termining the linewidth of NMR and NQR spectra. Wheninterpreting the linewidth one has to distinguish intrinsiceffects such as broadening from local magnetic momentsfrom the effect of impurities. This can be done by com-paring the temperature dependence of the linewidth ofNMR and NQR spectra where the broadening from de-fects (mainly quadrupole effects) and local magnetic mo-ments (magnetic effects) appear differently. In the para-magnetic phase, the local moments are fluctuating. If theinverse correlation time, 1 /τ c of the fluctuations is muchhigher than the NMR linewidth, each nucleus sees only thetime-averaged local field and the NMR line should be nar-row (motional narrowing). As the fluctuations slow down,the nuclei will start to feel a distribution of local fieldswhich broadens the NMR/NQR lines. Note that even atiny moment size can broaden the NMR line consider-ably. For example, if we assume a moment size of only Seung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs
Fig. 5. (a) The Knight shift ( K ) as a function of temperaturefor sample S1 for different orientations, and for S2 for H k ab .(b) K at low temperatures. For S1 and H k ab , K is constantacross T c , whereas it decreases below T c as soon as the fieldis tilted out of the ab plane. In contrast, for the crystal S2, K drops below T c even for H k ab , and the angle dependence of K is not as strong as that of S1. − µ B , it will lead to a linewidth on the order of ∼ ∆ν ∼ H int ∼ Aµ , using the hy-perfine coupling A = 6 . µ B as extracted in Section3.3. The temperature dependence of FWHM (Fig. 6) cor-roborates the magnetic broadening. Disorder or defects inthe sample can also lead to an enhanced magnetic broad-ening, but the effect of disorder is much stronger on thequadrupole broadening, and would not lead to the ob-served temperature dependence. However, the influenceof quadrupole effects can be directly measured by NQRor by the satellite transitions ( I z = − / ↔ − / I z = +1 / ↔ +3 /
2) of the NMR spectrum, whereas thecentral transition ( I z = − / ↔ +1 /
2) is only affectedby second order quadrupole effects. Any small deviationsfrom a homogeneous charge distribution or lattice anoma-
Fig. 6.
FWHM as a function of temperature. For sampleS1, FWHM measured by NMR and NQR increases with de-creasing temperature, and shows a strong angle dependence.In contrast, for the crystal S2, FWHM is smaller than for S1and the NQR FWHM is temperature independent. The NMRand NQR FWHM of S2 seem to be T independent as indicatedby the dashed line. In the superconducting state, FWHM forS1 decreases, whereas it increases for S2. lies such as deficiencies or defects will lead to a distri-bution of EFGs at the nucleus which contribute to thequadrupole linewidth. Therefore, while the narrow NQRlines of our LiFeAs single crystals is related with high ho-mogeneity, the increase of the linewidth when approaching T c , regardless of the rotation angle, signals that magneticcorrelations progressively gain in strength upon loweringthe temperature in the sample S1, whereas S2 does notshow such a behavior.We observe that the narrow line for H k ab rapidlybroadens when H rotates out of the plane. A tilting an-gle of 2 ◦ already causes a noticeable broadening (Fig. 6)and for 5 . ◦ the line broadens by a factor of three. Forabout 8 ◦ the width exceeds 200 kHz and K is very small.Such an angle dependence could arise from a magnetic ef-fect, where anisotropic, probably momentum-dependent,spin fluctuations are present, which are closely relatedto the anisotropic Knight shift K . This would be in linewith the presence of incommensurate, nearly ferromag-netic, spin fluctuations that emerge in microscopic calcu-lations [15], the character of which can be strongly affectedby a magnetic field. Or the angle dependence arises froma quadrupolar effect. In this case, a distribution of anglesbetween the external magnetic field H and the direction ofthe principle axis of the EFG tensor V zz would be neededto explain the angle dependent broadening, yet narrowNQR resonance line.In the superconducting state, the linewidth for sampleS1 unexpectedly decreases below T c . This feature is alsoobserved in the NQR spectra. Usually the NMR linewidthincreases in the superconducting state due to vortex-related eung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs 7 broadening as is observed for sample S2. The origin of thedecreasing linewidth just below T c is not yet clear. Nev-ertheless, it indicates that the magnetic properties of thesample change at the superconducting transition temper-ature, namely that the spin fluctuations which lead to thebroadening above T c are strongly reduced in the super-conducting state. As spin-lattice relaxation rates in external field By As NQR, we have shown that the As ( T T ) − isstrongly sample dependent in the superconducting state.In order to check how an external field affects the low en-ergy spin dynamics in the superconducting state, we mea-sured ( T T ) − by As NMR in the two single crystals S1and S2. As shown in Fig. 7, for the crystal S1, we observethat ( T T ) − even in the normal state is enhanced com-pared to the NQR results (solid horizontal line). Since itis expected that the NMR results for H k c are equivalentto NQR ones for which the nuclei are also quantized alongthe c axis, the behavior is somewhat surprising, suggestingthe presence of unusual, field dependent low energy spindynamics in the system. For H k ab , ( T T ) − is furtherenhanced, as denoted by the dotted line. Regardless of thedirection of H , the strong enhancement of ( T T ) − below T c observed in the NQR measurement (i.e., in zero field)is substantially suppressed in a magnetic field, although asharp drop is still absent for sample S1. A similar behav-ior has been found in La . Ca . FePO [38], where P( T T ) − increases just below T c in low magnetic fields,while high magnetic fields of about 6 T suppress this in-crease (see also the discussion in Section 4).For the crystal S2, we observe contrasting results, as inthe Knight shift (Fig. 5). In the normal state ( T T ) − datafor H k ab are considerably smaller than those of S1. SinceNQR results were the same among all of the samples, thisindicates that the spin dynamics even in the normal statebecome material-specific in field. In the superconductingstate, a sharp drop at T c is observed for S2, as in NQRcase for S3.An interesting observation is that ( T T ) − of S1 re-veals a weak but clearly visible maximum just above T c for both directions of H . Together with the enhanced nor-mal state ( T T ) − in an external field, one can argue thatthe normal state spin dynamics are strongly influencedby an external field, signaling a nearby critical instabilitywhose nature is unclear yet. Furthermore, the presence ofthe local maximum of ( T T ) − just above T c in field aswell as the mysterious upturn of ( T T ) − below T c in zerofield may indicate unusual superconductivity in LiFeAs. Our single crystals S1, S2, and S3 of LiFeAs which weregrown in the same environment, exhibit significantly dif-ferent static ( ν Q and K ) and dynamic [( T T ) − ] prop-erties, particularly, in the superconducting state. Never-theless, all the crystals are found to be of good quality Fig. 7. As NMR ( T T ) − as a function of T measured at7 T for the sample S1 and at 8.5 T for the sample S2. Above T c we observe a small but visible enhancement compared toNQR results (horizontal solid line), particularly for S1. Below T c , only the sample S2 exhibits a drop of ( T T ) − . Sample S3exhibits similar temperature dependence as sample S2. and high homogeneity as evidenced by the narrow AsNQR line and the almost equal linewidth of central andsatellite Li NMR lines. Although the NQR FWHM of S1( ∼
80 kHz) is much larger than that of S3 ( ∼
40 kHz), itis still a factor of more than 2 narrower than reported forpowder LiFeAs samples [20] and significantly smaller thanreported for other undoped iron pnictides (see above).Therefore, our results suggest that pure LiFeAs is locatednear a critical point so that its physical properties are ex-tremely sensitive to very small perturbations such as tinyvariations in stoichiometry. A similar critical doping de-pendence has also been reported in literature [3], whereone percent of Li deficiencies largely suppress supercon-ductivity. However, we emphasize that all of our crystalsare superconducting with similar T c . We confirmed theonset of superconductivity by a strong change in the reso-nance frequency of the NMR sample probe below T c whichis caused by the change of the surface resistance of thesample. Furthermore, a drop of the Knight shift for smallangles off H k ab and the anomalous change of both thelinewidth and ( T T ) − below T c indicate that sample S1is also superconducting.First, we discuss the different behavior of the Knightshift K in the superconducting state. When a supercon-ducting condensate consists of singlet Cooper pairs, a mag-netic field cannot polarize these paired electrons unlesspairs are broken up. Consequently the spin susceptibility χ spin and thus K vanishes [39] below T c when T →
0. Thismay explain the behavior that we observe in sample S2,and that is reported for powder samples of LiFeAs [19,20]
Seung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs so far. In contrast, the constant Knight shift across T c insample S1 for H k ab exhibits a behavior that would beexpected for a spin-triplet superconductor where pairingdoes not interfere with the magnetic response of the elec-trons and χ spin remains constant across T c down to zerotemperature. For small angles off H k ab , however, theKnight shift decreases below T c , suggesting that a smallcomponent of the magnetic field along the c direction leadsto a transition into a state with a superconducting or-der parameter of different symmetry in the orbital and/orspin sector. Note that the so far reported Knight shiftmeasurements of LiFeAs [19,20] have been performed inpolycrystalline samples in which the broadening due tolarge second order quadrupole shift may hinder determin-ing the intrinsic spin shift if there is a strong angle depen-dence of the Knight shift. Another explanation would bethat the nature of superconductivity may strongly dependon the effective doping level of the samples, even thoughLiFeAs is considered to be a stoichiometric compound.The differences in the doping level could be visualized bythe slightly different quadrupole frequencies: those sam-ples with a high quadrupole frequency reveal the constant K across T c , whereas those samples with a lower ν Q , in-cluding the powder sample reported in ref. [20], show amore normal behavior.A measurement of the intrinsic spin susceptibility inthe superconducting state via the Knight shift is oftennot straightforward and other reasons may lead to a con-stant K ab . First of all, the correction for the large secondorder quadrupole shift could mask a decreasing Knightshift. However, we observe that the quadrupole frequencyexhibits only an insignificant temperature dependence atlow T , and the constant K ab is already recognizable inthe raw data without quadrupole correction in Fig. 4 (a).Also demagnetization effects are negligible for H k ab dueto the plate-like shape of the crystals. Furthermore, de-magnetization effects reduce the actual field in the super-conductor and therefore should lead to a further decreaseof the total shift K below T c . A simple heating effect ofthe sample by the radio frequency pulses can be excludedsince we observed the decreasing Knight shift for smallangles off H k ab and for sample S2 under similar condi-tions. Another reason for a constant K in a singlet super-conductor could be an enhanced magnetic susceptibilityvia strong orbital magnetism [40] or via spin-orbit scat-tering in the presence of disorder [41]. Such a scenarioappears rather unlikely. First, the strong angular depen-dence of the Knight shift in the superconducting state (seeFig. 5) is incompatible with a large non-spin contributionto K ab , such as strong orbital magnetism. For the samereason the unchanged Knight shift through T c cannot beexplained by an impurity-based scenario. Moreover, oursamples appear to be clean single crystals, even thoughtiny differences between the crystals have to exist.In LiFeAs the ( π , π )-nesting and static antiferromag-netism are absent [5]. Investigating theoretically the mag-netic and pairing instabilities in an electronic model thatincorporates the poor nesting properties and unusuallyshallow hole pockets of LiFeAs, Brydon and coworkers [15] find ferromagnetic fluctuations to drive an instabilitytoward spin-triplet p -wave superconductivity. These mag-netic fluctuations are related to LiFeAs being in the vicin-ity of nearly ferromagnetic, incommensurate, long-rangespin ordered phases, the stability of which is governed bythe detailed electronic density and interaction parameters.Such a spin-triplet scenario may be supported by the con-stant spin susceptibility across T c observed for H k ab and the increasing linewidth with decreasing temperaturein sample S1, although samples S2 and S3 clearly showa spin-singlet behavior. As we have discussed above, theexperimental results in single crystals S1–S3 should resultfrom intrinsic properties rather than extrinsic ones. Thissuggests that different phases are competing in LiFeAswhere relatively small changes due to external fields, struc-ture or stoichiometry can cause transitions between un-conventional and more conventional superconducting groundstates, and may also explain other contradicting experi-mental results in literature (see also Section 1).Another anomalous behavior is the strange upturn of( T T ) − in sample S1 and in the polycrystalline sample.Nakai et al. [38] suggest four different possibilities for asimilar upturn in La . Ca . FePO: (i) impurity contri-butions which can be excluded for both compounds, as ar-gued above. Furthermore, the relaxation curves are singleexponential in LiFeAs, too, whereas impurities would leadto a multiexponential behavior of the relaxation curves.(ii) Vortex contributions to ( T T ) − which can be ex-cluded for LiFeAs since the upturn occurs in zero mag-netic field (NQR). (iii) Slowing of magnetic fluctuationsdue to the opening of the superconducting gap. In thiscase, scattering of local magnetic moments with conduc-tion electrons in the normal state enhances the energyscale of the fluctuations. In the superconducting state thescattering is suppressed due to the formation of Cooperpairs, and the local magnetic moments may slow down. Asargued by Nakai et al., such a behavior has not been re-ported yet. (iv) Collective modes of the spin-triplet pairscould give rise to novel spin dynamics in the SC state [38,42]. In particular, we note that the possibility (iv) may ex-plain the observed constant Knight shift in the very samesample S1.In order to reconcile the two different results even inthe single crystals grown under the same conditions, weconjecture that the nature of spin fluctuations, which isgenerally thought to mediate Cooper pairs in non-BCSunconventional superconductors, could be either antifer-romagnetic or ferromagnetic depending on the proximityto a ferromagnetic instability in an extremely sensitivefashion. It is also interesting to note that there is a seem-ing trend that the EFG and thereby the NQR frequency ν Q are larger, when the Knight shift and ( T T ) − exhibitthe peculiar behaviors. This indicates a possible connec-tion between the doping level, which could be propor-tional to the EFG as in other iron pnictides, and a fer-romagnetic instability. Consistently, Co doping leads toa lower quadrupole frequency (EFG), and to a reductionof ( T T ) − in the superconducting state, putting the Codoped sample further away from the ferromagnetic insta- eung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs 9 bility. This observation is also consistent with theory [11,15], where the small hole pocket at the Γ point drives theferromagnetic fluctuations. Regarding Co doping as elec-tron doping, the hole pocket should shrink upon doping,thereby weakening the ferromagnetic fluctuations [43]. We have used NMR and NQR to investigate differentLiFeAs samples. We find that tiny differences in the sto-ichiometry of the samples exist which lead to differentnormal state properties as well as to different supercon-ducting properties. A possibility to distinguish the sam-ples is the quadrupole frequency, ν Q . Sample S1 yields aslightly higher ν Q than sample S2, whereas ν Q of a Codoped sample is even below that of S2. At the same time,the Knight shift of sample S1 is constant across T c for H k ab . Although this may suggest spin triplet supercon-ductivity, we find that the Knight shift drops below T c forsmall angles off the ab plane. On the other hand the Knightshift of sample S2 decreases in the SC state regardless ofthe angle which is compatible with standard singlet pair-ing of the Cooper pairs. The temperature dependence ofthe linewidth varies also with the crystals. The linewidthof sample S1 increases with decreasing temperature, indi-cating a growing of magnetic fluctuations, while that ofsample S2 is temperature independent. Consistent withthe observation of K ab = const. across T c could be theincreasing ( T T ) − in the SC state of sample S1 as wellas of the polycrystalline sample which also yields a higher ν Q . The increase of ( T T ) − below T c could originate fromnon-vanishing spin degree of freedom in the SC state whichgive rise to novel spin dynamics. Acknowledgement
We are deeply grateful to K. Kitagawa and M. Takigawafor invaluable experimental collaboration and for sharingtheir data with us. The authors also thank G. Lang, C.Nacke, I. Morozov, M. Daghofer, C. Timm, and P. M. Bry-don for discussion and M. Deutschmann, J. Werner, A.Voss, J. Eckert, and R. Vogel for technical support. Thiswork has been supported by the Deutsche Forschungsge-meinschaft through FOR 538 (Grant No. BU887/4) andSPP1458 (Grant No. GR3330/2 and BE1749/13). SW ac-knowledges support by DFG under the Emmy-Noetherprogram (Grant No. WU595/3-1).
References
1. Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono.
J. Am. Chem. Soc. , 130:3296–3297, 2008.2. M. Rotter, M. Tegel, and D. Johrendt.
Phys. Rev. Lett. ,101:107006, 2008.3. M. J. Pitcher, T. Lancaster, J. D. Wright, I. Franke, A. J.Steele, P. J. Baker, F. L. Pratt, W. T. Thomas, D. R.Parker, S. J. Blundell, and S. J. Clarke.
J. Am. Chem.Soc. , 132:10467–10476, 2010. 4. D. S. Inosov, J. S. White, D. V. Evtushinsky, I. V. Moro-zov, A. Cameron, U. Stockert, V. B. Zabolotnyy, T. K.Kim, A. A. Kordyuk, S. V. Borisenko, E. M. Forgan,R. Klingeler, J. T. Park, S. Wurmehl, A. N. Vasiliev,G. Behr, C. D. Dewhurst, and V. Hinkov.
Phys. Rev. Lett. ,104:187001, 2010.5. S. V. Borisenko, V. B. Zabolotnyy, D. V. Evtushinsky,T. K. Kim, I. V. Morozov, A. N. Yaresko, A. A. Kordyuk,G. Behr, A. Vasiliev, R. Follath, and B. B¨uchner.
Phys.Rev. Lett. , 105:067002, 2010.6. A. A. Kordyuk, V. B. Zabolotnyy, D. V. Evtushinsky,T. K. Kim, I. V. Morozov, M. L. Kuli´c, R. Follath, G. Behr,B. B¨uchner, and S. V. Borisenko.
Phys. Rev. B , 83:134513,2011.7. Y. J. Um, J. T. Park, B. H. Min, Y. J. Song, Y. S. Kwon,B. Keimer, and M. Le Tacon.
Phys. Rev. B , 85:012501,2012.8. S. J. Zhang, X. C. Wang, R. Sammynaiken, J. S. Tse, L. X.Yang, Z. Li, Q. Q. Liu, S. Desgreniers, Y. Yao, H. Z. Liu,and C. Q. Jin.
Phys. Rev. B , 80:014506, 2009.9. F. L. Pratt, P. J. Baker, S. J. Blundell, T. Lancaster, H. J.Lewtas, P. Adamson, M. J. Pitcher, D. R. Parker, and S. J.Clarke.
Phys. Rev. B , 79:052508, 2009.10. N. Qureshi, P. Steffens, Y. Drees, A. C. Komarek, D. Lam-ago, Y. Sidis, L. Harnagea, H.-J. Grafe, S. Wurmehl,B. B¨uchner, and M. Braden.
Phys. Rev. Lett. , 108:117001,2012.11. C. Platt, R. Thomale, and W. Hanke.
Phys. Rev. B ,84:235121, 2011.12. M. A. Tanatar, J.-Ph. Reid, S. Ren´e de Cotret, N. Doiron-Leyraud, F. Lalibert´e, E. Hassinger, J. Chang, H. Kim,K. Cho, Y. J. Song, Y. S. Kwon, R. Prozorov, and L.Taillefer.
Phys. Rev. B , 84:054507, 2011.13. K. Hashimoto, S. Kasahara, R. Katsumata, Y. Mizukami,M. Yamashita, H. Ikeda, T. Terashima, A. Carring-ton, Y. Matsuda, and T. Shibauchi.
Phys. Rev. Lett. ,108:047003, 2012.14. A. E. Taylor, M. J. Pitcher, R. A. Ewings, T. G. Per-ring, S. J. Clarke, and A. T. Boothroyd.
Phys. Rev. B ,83:220514, 2011.15. P. M. R. Brydon, M. Daghofer, C. Timm, and J. van denBrink.
Phys. Rev. B , 83:060501, 2011.16. A. K. Pramanik, L. Harnagea, C. Nacke, A. U. B. Wolter,S. Wurmehl, V. Kataev, and B. B¨uchner.
Phys. Rev. B ,83:094502, 2011.17. K. Cho, H. Kim, M. A. Tanatar, Y. J. Song, Y. S. Kwon,W. A. Coniglio, C. C. Agosta, A. Gurevich, and R. Pro-zorov.
Phys. Rev. B , 83:060502, 2011.18. T. H¨anke, S. Sykora, R. Schlegel, D. Baumann, L. Har-nagea, S. Wurmehl, M. Daghofer, B. B¨uchner, J. van denBrink, and C. Hess.
Phys. Rev. Lett. , 108:127001, 2012.19. P. Jegliˇc, A. Potoˇcnik, M. Klanjˇsek, M. Bobnar,M. Jagodiˇc, K. Koch, H. Rosner, S. Margadonna, B. Lv,A. M. Guloy, and D. Arˇcon.
Phys. Rev. B , 81:140511, 2010.20. Z. Li, Y. Ooe, X.-C. Wang, Q.-Q. Liu, C.-Q. Jin, M.Ichioka, and G.-q. Zheng.
J. Phys. Soc. Jpn. , 79:083702,2010.21. L. Ma, J. Zhang, G. F. Chen, and Weiqiang Yu.
Phys.Rev. B , 82:180501, 2010.22. G. Lang, H.-J. Grafe, D. Paar, F. Hammerath, K. Man-they, G. Behr, J. Werner, and B. B¨uchner.
Phys. Rev.Lett. , 104:097001, 2010.0 Seung-Ho Baek et al.: As NMR-NQR study in superconducting LiFeAs23. I. Morozov, A. Boltalin, O. Volkova, A. Vasiliev, O.Kataeva, U. Stockert, M. Abdel-Hafiez, D. Bombor, A.Bachmann, L. Harnagea, M. Fuchs, H.-J. Grafe, G. Behr,R. Klingeler, S. Borisenko, C. Hess, S. Wurmehl, and B.B¨uchner.
Cryst. Growth Des. , 10:4428–4432, 2010.24. U. Stockert, M. Abdel-Hafiez, D. V. Evtushinsky, V. B.Zabolotnyy, A. U. B. Wolter, S. Wurmehl, I. Morozov,R. Klingeler, S. V. Borisenko, and B. B¨uchner.
Phys. Rev.B , 83:224512, 2011.25. O. Heyer, T. Lorenz, V. B. Zabolotnyy, D. V. Evtushinsky,S. V. Borisenko, I. Morozov, L. Harnagea, S. Wurmehl,C. Hess, and B. B¨uchner.
Phys. Rev. B , 84:064512, 2011.26. J. H. Tapp, Z. Tang, B. Lv, K. Sasmal, B. Lorenz, P. C. W.Chu, and A. M. Guloy.
Phys. Rev. B , 78:060505, 2008.27. X.C. Wang, Q.Q. Liu, Y.X. Lv, W.B. Gao, L.X. Yang, R.C.Yu, F.Y. Li, and C.Q. Jin.
Solid State Commun. , 148:538– 540, 2008.28. Y. J. Song, J. S. Ghim, B. H. Min, Y. S. Kwon, M. H.Jung, and J.-S. Rhyee.
Appl. Phys. Lett. , 96:212508, 2010.29. K. Kitagawa, N. Katayama, K. Ohgushi, M. Yoshida, andM. Takigawa.
J. Phys. Soc. Jpn. , 77:114709, 2008.30. N J Curro, A P Dioguardi, N ApRoberts-Warren, A CShockley, and P Klavins.
New J. Phys. , 11:075004, 2009.31. S.-H. Baek, N. J. Curro, T. Klimczuk, E. D. Bauer, F. Ron-ning, and J. D. Thompson.
Phys. Rev. B , 79:052504, 2009.32. S.-H. Baek, H.-J. Grafe, L. Harnagea, S. Singh,S. Wurmehl, and B. B¨uchner.
Phys. Rev. B , 84:094510,2011.33. G. C. Carter, L. H. Bennett, and D. J. Kahan.
Metallicshift in NMR . Pergamon, New York, 1977.34. Kentaro Kitagawa, Yuji Mezaki, Kazuyuki Matsubayashi,Yoshiya Uwatoko, and Masashi Takigawa.
J. Phys. Soc.Jpn. , 80:033705, 2011.35. H-J Grafe, G Lang, F Hammerath, D Paar, K Manthey,K Koch, H Rosner, N J Curro, G Behr, J Werner, N Leps,R Klingeler, H-H Klauss, F J Litterst, and B Buchner.
NewJ. Phys. , 11:035002, 2009.36. T. Imai, A. W. Hunt, K. R. Thurber, and F. C. Chou.
Phys. Rev. Lett. , 81:3006–3009, 1998.37. A. Abragam.
The Principles of Nuclear Magnetism . Ox-ford University Press, 1961.38. Y. Nakai, K. Ishida, Y. Kamihara, M. Hirano, and H.Hosono.
Phys. Rev. Lett. , 101:077006, 2008.39. Kei Yosida.
Phys. Rev. , 110:769–770, 1958.40. A. M. Clogston, A. C. Gossard, V. Jaccarino, and Y. Yafet.
Rev. Mod. Phys. , 36:170–175, 1964.41. W. A. Hines and W. D. Knight.
Phys. Rev. B , 4:893–903,1971.42. D. Vollhardt and P. W¨olfe.
The Superfluid Phase of Helium3 . Taylor and Francis, New York, 1990.43. S. Aswartham, G. Behr, L. Harnagea, D. Bombor, A. Bach-mann, I. V. Morozov, V. B. Zabolotnyy, A. A. Kordyuk,T. K. Kim, D. V. Evtushinsky, S. V. Borisenko, A. U. B.Wolter, C. Hess, S. Wurmehl, and B. B¨uchner.