NMR Investigation of the Quasi One-dimensional Superconductor K 2 Cr 3 As 3
NNMR Investigation of the Quasi One-dimensional Superconductor K Cr As H. Z. Zhi, T. Imai,
1, 2, ∗ F. L. Ning,
3, 4
Jin-Ke Bao,
3, 4 and Guang-Han Cao
3, 4 Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S4M1, Canada Canadian Institute for Advanced Research, Toronto, Ontario M5G1Z8, Canada Department of Physics, Zhejiang University, Hangzhou 310027, China Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing 210093, China (Dated: August 20, 2018)We report As NMR measurements on the new quasi one-dimensional superconductor K Cr As ( T c ∼ . , 011013 (2015)]. We found evidence for strongenhancement of Cr spin fluctuations above T c in the [Cr As ] ∞ double-walled subnano-tubes basedon the nuclear spin-lattice relaxation rate 1 /T . The power law temperature dependence, 1 /T T ∼ T − γ ( γ ∼ . /T just below T c suggests unconventional nature of superconductivity. PACS numbers: 74.70.Xa, 76.60.-k, 71.10.Pm
The surprising discovery of high T c superconductiv-ity in an iron-pnictide LaFeAsO − x F x [1] led to fran-tic search for superconductivity in iron-based pnictidesand chalcogenides [2]. The key building unit of theseiron-based high T c superconductors is the square latticeformed by Fe atoms. The mechanism of high T c super-conductivity in iron-pnictides remains as controversialas that in copper-oxides, which is also comprised of thesquare lattice of Cu atoms. The recent discovery of super-conductivity in helimagnetic CrAs with T c ∼ . ∼ . Cr As with the onset of T c = 6 . + ions with larger Rb + and Cs + ions lowers the T c to 4.8 K [6] and 2.2 K [7], respectively.In Fig. 1, we present the proposed crystal structure ofK Cr As with the most probable space group P Cr As is theone dimensional [(Cr As ) − ] ∞ double-walled subnano-tubes (DWSTs) with the outer diameter of 0.58 nm sepa-rated by columns of K + ions, in striking contrast with thetwo dimensional square lattice that forms iron-pnictideand copper-oxide high T c superconductors. Assumingthe standard ionic valence As − and ignoring vacanciesin the lattice, the nominal valence of the transition metalelement is Cr . , and hence each Cr has 3.7 3d electronson average. The short interatomic distance between Cratoms, 2.61 to 2.69 ˚A, suggests that the Cr-Cr bond-ing is metallic, while the bonding of Cr with As − ionsmay be considered ionic [5]. The bulk physical propertymeasurements on the critical field H c [5], the electronicspecific [5, 6], and the penetration depth [8] point towardthe presence of a node(s) in the superconducting energygap.Besides the generic interest in the mechanism of ex-otic superconductors, the novel linear chain structure of ∗ Electronic address: [email protected] (a)(c) (b)(d) K1 K2As1 As2Cr1 Cr1Cr1K2 K1 As1 As2a cAs1As2 As1 Cr1Cr2 cCr2 Cr2Cr2As2b
FIG. 1: (Color online) The crystal structure of quasi 1Dsuperconductor K Cr As [5]. (a) Top view of four unit cells.A complete [Cr As ] ∞ DWST is in the middle. (b) Angledview of a unit cell, and (c)-(d) DWST. the [Cr As ] ∞ DWSTs provides us with a unique oppor-tunity to investigate the fundamental physics of a quasione dimensional (1D) inorganic metal, and its relationwith superconductivity [5]. Theoretically, it is well es-tablished that Fermions confined in 1D, commonly calledthe Tomonaga-Luttinger liquid (TLL), behave very dif-ferently from the two or three dimensional analogues, be-cause electron-electron interactions completely alter theelectronic properties near the Fermi energy no matterhow weak the interactions are [9–11]. As a consequence,a simple Fermi liquid theory based on Landau’s quasi-particle picture breaks down. The peculiar influence ofinteractions between two particles in the TLL could beunderstood intuitively, if we realize that two particlesmust always meet each other head on in 1D; they cannotavoid each other by moving side ways. A fingerprint ofthe TLL is the power-law behavior arising from the singu-larity at the Fermi energy that manifest in various physi-cal properties. Past explorations of the exotic propertiesof the TLL focused on organic conductors (see, for exam- a r X i v : . [ c ond - m a t . s up r- c on ] M a r ple, discussions in [12–14] and references therein), semi-conductor nano structures [15], carbon nanotubes [16–20]and their superconductivity [21, 22], or quasi-1D Heisen-berg model systems [23–25]. Does the [Cr As ] ∞ DWSTin K Cr As indeed exhibit the signatures expected forthe TLL above T c ? If so, is the superconducting statebelow T c also exotic?In this paper, we report the first microscopic AsNMR investigation of K Cr As by fully taking advan-tage of the versatile nature of the NMR techniques. Weprobed the electronic and superconducting properties atdifferent As sites separately by measuring their nuclearspin-lattice relaxation rate 1 /T . We found evidencefor strong enhancement of Cr spin fluctuations toward T c . The dynamical electron spin susceptibility χ (cid:48)(cid:48) of theDWST obeys a characteristic temperature dependence, χ (cid:48)(cid:48) ∝ /T T ∼ T − γ ( γ = 0 . ± . ] [13] and carbon nanotubes [17–20],and is consistent with the TLL. Moreover, we show thatthe Hebel-Slichter coherence peak of 1 /T [26], commonlyobserved for conventional BCS s-wave superconductorswith isotropic energy gaps, is absent in the present case.In view of the low symmetry of the As sites inK Cr As , the EFG (electric field gradient) at the Assites originating from K + , Cr . , and As − ions in theirvicinity must be large. Since the nuclear quadrupole in-teraction frequency ν Q of the As nuclear spins ( I = 3 / γ n / π = 7 . ν Q inK Cr As should be much larger than ν Q ∼ T c superconductor Ba(Fe − x Co x ) As [27]. (The As site in Ba(Fe − x Co x ) As is more sym-metrical and surrounded by Ba and Fe ions.) Wefirst searched for the As NMR signals in our randomlyoriented powder sample in high magnetic fields, and iden-tified two distinct As NMR signals with ν Q ∼
40 MHz[28]. Such large values of ν Q would readily allow us todetect As NQR (Nuclear Quadrupole Resonance) be-tween the (nominal) I z = ± / ± / B = 0. NQR is advan-tageous in probing the intrinsic superconducting prop-erties, because we do not perturb the superconductingstate with the applied magnetic field.Armed with the preliminary knowledge of ν Q , wesearched for the As NQR signals between 33 and 55MHz. We show representative As NQR spectra in Fig.2. The lineshape observed at 200 K indicates the pres-ence of two sets of sharp NQR peaks: the A line near39 MHz and the B line near 44 MHz, both accompaniedby smaller side peaks. Since the integrated intensity ofthe NQR signals below 43 MHz is equal to that above43 MHz, these two sets of NQR signals must arise fromAs1 and As2 sites. Notice that the local arrangementsof K + ions near As1 and As2 sites are different, as read-ily seen in Fig.1(a,b). Therefore ν Q should be somewhatdifferent, too, between As1 and As2 sites. Unless we con-duct single crystal NMR measurements, we are unable to
36 38 40 42 44 46 48 50 As NQR (B = 0) S p i n E c ho I n t en s i t y [ a r b . un i t s ] Frequency [Mhz](a) 200 K(b) 6.5 K A A B B B B ν Q ( M H z ) T (K) AB B FIG. 2: (Color online) As NQR spectra measured at (a)200 K and (b) 6.5 K. We divided the raw NQR signal intensityby the square of the frequency to take into account variationof the sensitivity. We marked three distinctive peaks as A,B , and B . Inset: the temperature dependence of the AsNQR peak frequency, ν Q . All solid curves are guides for theeye. determine which of the A and B lines arise from As1 andAs2 sites, but none of our discussions below depend onthe details of the site assignments.The presence of smaller side peaks and broad contin-uum suggests the influence of K + defects on ν Q , as of-ten observed in alloys and disordered materials. Accord-ing to the energy-dispersive X-ray spectroscopy (EDS)analysis, the composition of the present material is ac-tually close to K . ± . Cr As . ± . [5]. Generally,defects would locally alter the magnitude of ν Q throughthe change of the EFG tensor (see [29] for a recent ex-ample of Cu substitution effects on ν Q in the BaFe As high T c superconductor). Since the side peak of the Bline is separately observable even at low temperatures,we distinguish the main and side peaks by calling themB and B , respectively. The temperature dependence ofthe NQR frequency ν Q is very similar at A, B and B sites as shown in the inset to Fig. 2. The decrease of ν Q from 2 K to 295 K is anomalously large, 3 ∼ ν Q , however, rules out the presence of Peierls instability.Next, let us examine the electronic properties of the[(Cr As ) − ] ∞ DWSTs. In Fig. 3, we plot the tempera-ture dependence of 1 /T measured by inversion recoverytechniques [28] at As sites in a log-log scale. We alsopresent 1 /T T in Fig. 4. Quite generally, 1 /T T probesthe wave-vector q -integral in the first Brillouin zone ofthe imaginary part of the dynamical electron spin suscep-tibility, χ (cid:48)(cid:48) ( q , ν Q ), where ν Q is the NQR frequency usedto measure 1 /T . In other words, 1 /T T probes the lowfrequency spin dynamics of electrons integrated over theBrillouin zone. If the underlying electronic states of theDWSTs may be described by a simple Fermi liquid the- As NQR (B = 0) / T ( s - ) T (K)T c ~T ~T ~T AB B FIG. 3: (Color online) As nuclear spin-lattice relaxationrate 1 /T measured by NQR techniques in B = 0 for A, B ,and B sites. The solid line above T c is the best fit for the Asites with a power-law, 1 /T ∼ T − γ ( γ = 0 . ± . T c represents 1 /T ∼ T . Thedotted line is the best linear fit of the normal state data forthe B peak, 1 /T = 0 . · T s − . ory and the electron-hole pair excitations dominated thelow energy excitations at the Fermi surface, we expect1 /T ∝ T · N ( E F ) , where N ( E F ) is the electronic den-sity of states at the Fermi energy E F . That is, Korringarelation holds, 1 /T T ∼ constant, for Fermi liquids witha broad band(s). The strong increase of 1 /T T toward T c observed for the main A and B sites clearly con-tradicts with such an expectation. Without relying onany theoretical assumptions, we conclude that Cr spinfluctuations grow toward T c prior to the onset of super-conductivity at a certain wave vector(s).The magnitude of 1 /T T in Fig. 4 is comparable tothat of the iron-pnictide high T c superconductors suchas Ba(Fe − x Co x ) As [30–32]. If we assume that thehyperfine coupling of As nuclear spins with Cr 3d elec-tron spins in the present case is comparable to that withFe 3d electron spins in iron-pnictides, our results in Fig.4 imply that the dynamical spin susceptibility of Cr isenhanced near T c as much as the case of the supercon-ducting Ba(Fe . Co . ) As near its T c ∼
25 K [30]. Atfirst glance, the gradual growth of 1 /T T (and hence χ (cid:48)(cid:48) )toward T c in the present case also seems similar to typ-ical iron-pnictide high T c superconductors [30–32]. Thegrowth of χ (cid:48)(cid:48) near T c within the FeAs planes of iron-pnicides could be successfully fit with a Curie-Weiss law,1 /T T ∼ C/ ( T + θ ), where C and θ are constants, in / T T ( s - K - ) T (K)AB B T c As NQR (B = 0)
040 100 200 300 T T ( s K ) T (K)T c A FIG. 4: (Color online) 1 /T T for A, B , and B sites. Thesolid curve through the normal state data of the A sites rep-resents the power-law fit, 1 /T T ∼ T − γ , with the same γ asin Fig. 3. The dotted straight line through the data points ofthe B peak is the Korringa fit, 1 /T T = 0 .
27 s − K − above T c . Inset: Temperature dependence of T T for the A peakabove T c , with the best fit, T T ∼ T + γ . the temperature range where the electrical resisitivityshows a linear temperature dependence [30–32]. TheCurie-Weiss behavior is theoretically anticipated for two-dimensional electron gas systems with antiferromagneticspin correlations [33, 34].In contrast with the case of quasi two-dimensional iron-pnictide high T c superconductors, the fundamental struc-tural unit of quasi 1D K Cr As is a metallic DWSTformed by [Cr As ] ∞ . Recent theoretical calculationspredicted the existence of two quasi 1D bands and onethree dimensional band [35, 36], and very strong an-tiferromagnetic correlations along the DWST with thenearest-neighbor Cr-Cr exchange interaction as large as ∼ T c .As explained above, the 1D electron gas with electron-electron interactions forms a TLL that gives rise to apower law behavior in various physical observables. Ear-lier theoretical calculations showed that the TLL wouldshow a power-law behavior, 1 /T T ∼ T − γ , where the ex-ponent γ is a non-universal constant that depends on thedetails of the system, such as the band structure, nest-ing wave vector 2 k F , and the strength of interactions[12, 17, 19]. Analogous power-law behavior was previ-ously reported for TTF[Ni(dmit) ] with γ ∼ . γ ∼ .
66 [20].Close examination of our 1 /T data in Fig. 3 indeedreveals that all of our 1 /T data points for the A (andB ) sites above T c are on a straight line in a log-logplot, implying a power-law, 1 /T ∼ T − γ , or equivalently, χ (cid:48)(cid:48) ∝ /T T ∼ T − γ . The best fit yields γ = 0 . ± . γ in Fig. 4, which nicely reproduces the mysteriouslystrong divergent behavior of χ (cid:48)(cid:48) near T c . Our findingsare similar to earlier reports on quasi 1D materials withthe TLL behavior [12–14, 18–20, 24, 25]. The observedvalue of γ = 0 .
25 in the present case suggests that theelectron-electron interactions are repulsive, and the dom-inant channel of the spin correlations is antiferromag-netic for the wave vector 2 k F [12]. Our conclusion isconsistent with the large antiferromagnetic exchange cou-pling ∼ Cr As based on ARPES and other techniques.Having established the characteristic quasi 1D behav-ior of Cr spin fluctuations above T c , let us turn our at-tention to the superconducting state. In conventionalisotropic BCS s-wave superconductors, 1 /T exhibits ahump just below T c due to the sharp density of states atthe edge of the energy gap, where the low energy quasi-particle excitations contribute constructively to 1 /T dueto the coherence factor predicted by the BCS theory[26, 37]. The observation of such a Hebel-Slichter co-herence peak of 1 /T is a crucial test for the validityof the description of the superconducting state based onthe conventional isotropic BCS s-wave model. In addi-tion, 1 /T decreases exponentially far below T c , 1 /T ∼ exp ( − ∆ /k B T c ), in isotropic BCS s-wave superconduc-tors, where ∆ is the isotropic energy gap at the Fermisurface [37, 38]. For contemporary examples of the con-ventional BCS s-wave superconductors, see [39, 40].In the present case, our 1 /T data for the A and B sites in Fig. 3 show a steep drop just below T c withoutexhibiting the coherence peak. Moreover, the tempera-ture dependence of 1 /T below T c is consistent with apower law, 1 /T ∼ T n with n ∼
4. These results below T c are similar to the case of unconventional superconduc-tors, such as the high T c superconductor YBa Cu O − δ with d-wave pairing symmetry [41]. We are not aware ofany theoretical prediction of 1 /T below T c for the TLL;if we apply the conventional wisdom for exotic supercon-ductivity in two- or three-dimensional correlated electronsystems, our findings strongly suggest that the supercon- ducting state is not an isotropic s-wave state. Instead,an unconventional superconducting ground state with anode in the energy gap seems realized in K Cr As . Thisconclusion is consistent with other reports of the possi-ble presence of the nodes in the energy gap based on themeasurements on the bulk properties [5, 6, 8].Finally, we comment on the nature of the broad sidepeak B in Fig. 2. 1 /T T at the B sites is comparableto that of A and B sites near room temperature, butremains constant, 1 /T T = 0 .
27 s − K − , in the entiretemperature range above T c with no signature of the TLLbehavior. As shown in Fig. 3, all the 1 /T data pointsof the B sites in the superconducting state are below anaive extrapolation of the corresponding T-linear behav-ior. This is consistent with a viewpoint that the B sitessense a small energy gap, suggesting the intrinsic natureof the B sites. In this scenario, the broad line shapeof the B sites must be a consequence of the defects intheir vicinity, which may explain why the TLL behavioris suppressed above T c and the energy gap is very smallbelow T c . We cannot rule out, however, an alternativepossibility that the B sites originate from a secondaryphase with slightly different K concentration, and the B peak is merely superposed on the broad tail of the B sites accounting for ∼ Cr As toward T c , obeying acharacteristic power-law predicted theoretically for theTLL. 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