The 27Al and 63Cu spin-lattice relaxation rates were found to contain a large T2 term over a wide temperature range below 400 K in several thermodynamically stable quasicrystalline alloys, including i-AlCuRu, i-AlPdRe, i-AlCuFe, and the crystalline approximant phase a-AlMnSi. The relaxation mechanism is proven to be electronic in origin. Such nonlinear temperature dependence is shown to be a clear signature of sharp features in the density of states at the Fermi level. The estimated width of this sharp feature is on the order of 20 meV

Hill, E.A.

Poon, S.J.

Tang, X.-P.

Wonnell, S.K.

Wu, Y.

Carolina Digital Repository

VOLUME 79, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 11 AUGUST 1997255gbeof1070Sharp Feature in the Pseudogap of Quasicrystals Detected by NMRX.-P. Tang,1 E. A. Hill,1 S. K. Wonnell,1 S. J. Poon,2 and Y. Wu11Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-32Department of Physics, University of Virginia, Charlottesville, Virginia 22901(Received 13 January 1997)The 27Al and 63Cu spin-lattice relaxation rates were found to contain a largeT2 term over a widetemperature range below 400 K in several thermodynamically stable quasicrystalline alloys, includini-AlCuRu, i-AlPdRe, i-AlCuFe, and the crystalline approximant phasea-AlMnSi. The relaxationmechanism is proven to be electronic in origin. Such nonlinear temperature dependence is shown toa clear signature of sharp features in the density of states at the Fermi level. The estimated widththis sharp feature is on the order of 20 meV. [S0031-9007(97)03655-7]PACS numbers: 61.44.Br, 71.20.–b, 76.60.–ktnRionhotesap-p-usn-eionQuasicrystals possess novel structures with long-ranorder and point group symmetry incompatible with perodicity [1]. Structurally ordered quasicrystalline metalic alloys also exhibit novel transport properties, includinvery high electrical resistivity and semi-insulating behaior [2,3]. A pseudogap of about 0.5–1.0 eV in width athe Fermi levelEF was shown both experimentally [4–8and theoretically [9] to be a generic property of quasicrytals and approximants. Such a pseudogap could contribsignificantly to the thermodynamic stability of quasicrystals, but it is too broad to account for the novel tranport properties [9]. Band structure calculations show thspiked peaks and valleys of density of states (DOS) wwidths of 10–50 meV are present in the broad pseudgap, and such sharp features could be related to the notransport properties [9]. High resolution photoemissiospectroscopy (PES) reveals a broad pseudogap in sevquasicrystalline alloys; however, no sharp DOS featurare observed [6,7]. Since PES only probes the near surflayers, sharp features in the pseudogap could be remoby subtle structural deviations near the surface from thathe bulk. Subtle structural deviations near the surface habeen observed by scanning tunneling microscopy studof annealed quasicrystal surfaces [10]. However, tunning spectroscopy studies of quasicrystals have providevidence of a sharp DOS valley atEF with a width of about50 meV [8] even though this technique is also sensitivesurface structures. In contrast to PES and tunneling sptroscopy, magnetic susceptibility [11] and nuclear manetic resonance (NMR) [12] studies probe bulk propertiesignatures of sharp DOS features atEF could be revealedby these techniques. In this work, novel NMR resultsthe quasicrystalline and approximant phases are preseand explained, demonstrating unambiguously the preseof a sharp DOS valley at the Fermi level.Icosahedral quasicrystals Al65Cu20Ru15 (i-AlCuRu),Al 62.5Cu24.5Fe13 (i-AlCuFe), Al70Pd20Re10 (i-AlPdRe), andthe crystalline approximant Al72.5Mn17.4Si10.1 (a-AlMnSi)were investigated. For comparison, two crystallinnonapproximants, the metallicv phase Al7Cu2Fe (v-AlCuFe) and the semiconducting Al2Ru, were also studied.0031-9007y97y79(6)y1070(4)$10.00gei-l-gv-t]s-ute-s-atitho-velneralesacevedofveiesel-edtoec-g-s;intednceeSamples were vacuum sealed in quartz tubes for NMexperiments. The27Al, 63Cu, and 65Cu NMR measure-ments were performed selectively on the central transitat 9.4 T. The signal was detected by the Hahn ectechnique, and the nuclear spin-lattice relaxation rawere obtained by the inversion recovery method [12].Figure 1(a) shows27Al spectra ofi-AlPdRe at 9.4 Twhich are characteristic of Al-based quasicrystals andproximants. The shifts in the quasicrystals and the aproximant are very small with respect to the aqueoAl(NO3)3 solution and are noticeably temperature depedent, as illustrated in Fig. 1(a).If the spin lattice relaxation is dominated by hyperfincouplings between nuclear and electron spins, the inversFIG. 1. (a) the27Al spectra ofi-AlPdRe. (b) The inversionrecovery curves of magnetizationM versust which is scaledby T 2 at the corresponding temperature in-AlPdRe andMp ; fMs`d 2 MstdgyfMs`d 2 Ms0dg.© 1997 The American Physical SocietyVOLUME 79, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 11 AUGUST 1997neca,es-onhe-.-ron-l.iththelestoe-n-htvethe.recovery of the magnetizationMstd associated with thecentral transition for spin-52 nuclei is governed byMstd ­ M`f1 2 0.057 exps22W1td2 0.356 exps212W1td2 1.587 exps230W1tdg , (1)where t is the recovery time after the magnetizatioinversion. The spin-lattice relaxation rate is defineas 1yT1 ; 2W1. Figure 2 shows the temperature dependence of1yT1 obtained by a least-squares fit othe inversion-recovery curve with Eq. (1). The fits, ashown in Fig. 1(b), deviate from the measured curvat long t as observed before [13,14]. However, thtemperature dependence of1yT1 can also be confirmedby scaling t for each temperature, as demonstratedFig. 1(b); this procedure is independent of the funFIG. 2. (a) 1y27T1 versus T in v-AlCuFe and i-AlCuRu,10y27T1 versusT in Al 2Ru, and1y63T1 versusT in i-AlCuRu.The corresponding curves are fits with1y27T1 ~ T for v-AlCuFe and 1yT1 ~ T 2 for i-AlCuRu. (b) 1y27T1 versusT in v-AlCuFe, a-AlMnSi, i-AlPdRe, andi-AlCuFe. Thecorresponding curves are fits discussed in the text. The inshows1y27T1 data in i-AlPdRe fitted with´ ­ 1 and ´ ­ 2,as discussed in the text. Errors not indicated by error barscomparable to the sizes of the symbols.d-fssein-setretional form of Mstd. The 1y27T1 data of i-AlCuRu[Fig. 2(a)] andi-AlPdRe [Fig. 2(b)] (the superscripts 2763, and 65 refer to27Al, 63Cu, and 65Cu, respec-tively) show a striking feature below 400 K;1y27T1 isproportional to T 2 rather than toT as observed inv-AlCuFe. Furthermore,1y63T1 in i-AlCuRu is alsoproportional toT 2 below 400 K [Fig. 2(a)]. Significantdeviations from1y27T1 ~ T are also clearly visible ini-AlCuFe anda-AlMnSi [Fig. 2(b)].The nature of the relaxation mechanism can be invtigated by studying the spin-lattice relaxation of63Cu and65Cu in i-AlCuFe andi-AlCuRu. In addition to the contri-bution via hyperfine couplings, the spin-lattice relaxatiof these quadrupolar nuclei could also originate from tquadrupolar interaction [15]. Since63Cu and 65Cu arespin-32 nuclei with different quadrupolar momentsQ andgyromagnetic ratiosgn, the two mechanisms can be distinguished by measuring the ratio65T1y63T1. The quadrupo-lar mechanism leads to65T1y63T1 ­ s63Qy65Qd2 ­ 1.14[15], and the hyperfine interaction leads to65T1y63T1 ­s63gny65gnd2 ­ 0.87 [15]. At room temperature (RT), themeasured65T1y63T1 ratio is 0.80–0.87 ini-AlCuFe and0.83–0.90 ini-AlCuRu, similar to the previous report [14]Thus,1y63T1 and 1y65T1 are dominated by hyperfine interactions below RT. Since27Al possesses very similaQ andgn values as the Cu isotopes, the quadrupolar ctribution to 1y27T1 is expected to be negligible as welFurthermore, the quadrupolar contribution associated wphonons can also be estimated from the study of Al2Ruwhich has a Debye temperature comparable to allsamples investigated here [2]. Since1y27T1 in Al 2Ru isat least 100 times smaller than that in all other sampinvestigated here (Fig. 2), the quadrupolar contribution1y27T1 is again expected to be negligible.In metallic systems, the Fermi contact interaction btween conductions-electron spins and nuclear spins geerally dominates the spin-lattice relaxation and the Knigshift [15]. Assuming that the characteristics of the wafunction do not change significantly overkBT aroundEF ,the Knight shift can be expressed as [15]Ks ­ as1kBTZdE gsEdfsEd f1 2 fsEdg , (2)where fsEd is the Fermi-Dirac distribution,gsEd is theDOS associated with a single spin orientation,as ­s4py3d"2g2e kju2ks0djlEF , where kju2ks0djlEF is the densityof the wave function at the nucleus averaged overFermi surface, andge is the electron gyromagnetic ratioThe spin-lattice relaxation rate is given by [15]s1yT1ds ­ bsZdE g2sEdfsEd f1 2 fsEdg , (3)wherebs ­ s64y9dp3"3g2eg2nkju2ks0djl2EF . SincefsEd f1 2fsEdg ­ 2kBT≠fsEdy≠E vanishes asE deviates fromEF by a fewkBT , the temperature dependences ofKs ands1yT1ds are determined by the energy dependence ofgsEdnearEF. In typical metals the DOS variation nearEF is1071VOLUME 79, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 11 AUGUST 19971072TABLE I. A, B, k, and K0 are obtained from fitting1y27T versusT . The heat capacityconstantg, obtained from Ref. [2], is in units of mJs g atomd21 K22.A ssK sd21y2d B ssK eV sd21y2d k K0 (ppm) gi-AlPdRe ,1.0 3 1022 0.57 6 0.05 0.4 6 0.1 86 6 10 0.10i-AlCuRu ,1.0 3 1022 0.43 6 0.03 0.3 6 0.1 100 6 10 0.11i-AlCuFe s3.2 6 0.9d 3 1022 0.32 6 0.03 20.2 6 0.1 86 6 10 0.31a-AlMnSi s6.5 6 0.4d 3 1022 0.32 6 0.05 20.9 6 0.1 138 6 10 0.6v-AlCuFe s2.3 6 0.1d 3 1021 · · · 1.0 6 0.1 40 6 10 · · ·dfltous-ceightin-tosmall. Thus, Ks is temperature independent ans1yT1ds ~ T . The observed significant deviations from1yT1 ~ T below 400 K indicates that the variation othe DOS nearEF is not small overkBT aroundEF inquasicrystals and approximants.Assuming thatgsEd ­ g0 1 g1jE 2 EF j´, whereg0 isthe residual DOS atEF, Eq. (2) leads toKs ­ asf g0 1 2Cs´dg1skBT d´g , (4)whereCs´d ­R`0 dx x´exys1 1 exd2, and Eq. (3) leads tos1yT1ds ­ bskBT f g20 1 4Cs´dg0g1skBT d´1 2Cs2´dg21skBT d2´g . (5)For skBT d´s g1yg0d ¿ 1, Eqs. (4) and (5) show thatKs ~ T ´ and s1yT1ds ~ T 112´, whereas the conventionatemperature dependences ofKs and s1yT1ds are satisfiedfor skBT d´s g1yg0d ø 1. The temperature dependence o1yT1 in i-AlCuRu and i-AlPdRe indicates that́ ø 12 .As shown in Fig. 2, the temperature dependence1yT1 below 400 K can be fit very well with1yT1 ­T fA2 1 4Cs0.5dABskBT d1y2 1 2Cs1dB2kBT g (´ ­ 12 )where the fitting parametersA andB are listed in Table I.Since sByAd skBT d1y2 is significantly larger than one ini-AlCuRu, i-AlPdRe, andi-AlCuFe near RT, the thirdterm (which was neglected previously in a perturbatiotreatment [12]) is comparable or larger than the secoterm in Eq. (5). Thus, the previously reported analys[12] of 1yT1 data ini-AlCuRu with ´ ­ 2 is inaccurate.As an example, the inset of Fig. 2(b) shows that the1yT1data ofi-AlPdRe cannot be fit with́ ­ 2 using Eq. (5).Reducing thé value below one results in reasonable fias shown in the inset of Fig. 2(b). Overestimation ofAvalues would result from assuming1yT1 ~ T ; this couldbe responsible for the disagreement of some previoureportedA values [14] with that shown in Table I. Theabsence of the third term in Eq. (5) and the assumption´ ­ 2 are responsible for the differentA value reportedpreviously for i-AlCuRu [12]. The A values obtainedwith ´ ­ 12 are in good agreement with the measurespecific heat constantg which is also proportional tog0(Table I). The square-root power law could be found fthe DOS at Van Hove–type singularities [6]; it was alspredicted by the model of hierarchical packing of atomclusters in quasicrystals [1].The Korringa relation [15],sT1dsTK2s ­ Cs with Cs ­s"y4pkBd sg2eyg2nd, is also satisfied by Eqs. (4) and (5) foskBT d´s g1yg0d ø 1. For skBT d´s g1yg0d ¿ 1, Eqs. (4)fofnndissslyofdroicrand (5) givesT1dsTK2s ­ f2C2s´dyCs2´dgCs. Thus,Ks ­pCsypsT1dsT should be followed within 10% accuracyover the entire temperature range below 400 K for´ ­ 12and within 25% accuracy foŕ ­ 1. Figure 3 shows thetemperature dependence of the shift as well as fitsing K ­ K0 1 kpCsypT1T , where the parameterK0 ac-counts for the orbital contribution [15] and the isotropisecond-order quadrupolar shift, and the parameterk char-acterizes the deviation from the Korringa relation. Thgood fits withK ­ K0 1 kpCsypT1T below 400 K indi-cate that the novel temperature dependences of the Knshift and 1yT1 are both caused by the sharp featurethe DOS at the Fermi level. Above 500 K, ­ K0 1kpCsypT1T overestimates theT dependence of the shiftbecause of the contribution of the atomic motion to1yT1[12]. In i-AlCuRu andi-AlPdRe the shifts are positive andincrease with increasingT [Fig. 3(a)]; the parameterk isabout 13 (Table I). Such deviation from the Korringa relation can be explained by core polarization contributionsK and1yT1, denoted byKd ands1yT1dd , respectively. InFIG. 3. (a) The measured27Al shift versus T in i-AlPdRe(o), i-AlCuRu shd, and the fits ofK based on the measuredT1data in i-AlPdRe s3d and i-AlCuRu s1d, as discussed in thetext. (b) The measured27Al shift versusT in i-AlCuFe (o),a-AlMnSi shd, and the fits ofK based on the measuredT1data ini-AlCuFe s3d andi-AlMnSi s1d.VOLUME 79, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 11 AUGUST 1997leyiescends...D.,,i,l.,.,s..i,tt..B,n,o,e,s.. I.Al alloys with transition elements, thed band at the Fermilevel could induce a core polarization hyperfine interactiogiving rise toK ­ K0 1 Ks 1 Kd with Kd being nega-tive for 27Al. Assuming that thed-band DOS,gdsEd, isgiven bygdsEd ­ g0d 1 g1d jE 2 EFj´ nearEF, expres-sions similar to Eqs. (4) and (5) can be obtainedKd ands1yT1dd, respectively. The deviation from the Korringarelation in i-AlCuRu andi-AlPdRe can be explained byassumingKd ø 20.8Ks. In a-AlMnSi [Fig. 3(b)], K de-creases asT increases, indicating thatKs , jKdj, whichis consistent with the observed negativeK values. Ini-AlCuFe [Fig. 3(b)], the smallK values and the weakTdependence ofK are consistent with nearly equal contributions ofKs andjKdj.Precise estimation of the width of the DOS valley aEF is hampered by uncertainties such as the relative cotributions of hyperfine interactions caused by conductios-electron spins and core polarization. Nevertheless,approximate value can be estimated. Since NMR proban energy range of aboutkBT aroundEF, a measure ofDE, wheregsEF 6 DEy2d ø 2g0, is kBTp andTp is thetemperature above which1yT1 exhibits significant devia-tions from 1yT1 ~ T . In i-AlCuFe, Tp is about 150 Kwhich leads tokBTp ­ 13 meV. This estimate agreeswith the estimation ofDE based on theA and B val-ues listed in Table I. Since the ratioByA in i-AlCuFeis 10 eV21y2, gsEd ­ g0 1 g1jE 2 EFj1y2 increases to2g0 atE ­ EF 6 10 meV. Ini-AlCuFe, the specific heatmeasurement shows thatg0 is about one-third of the esti-mated free-electron value, which serves as an upper liof DOS atEF without the DOS valley [2,3]. Thus,DE ø20 meV can serve as an estimated width of the sharp DOfeature in i-AlCuFe. In i-AlPdRe andi-AlCuRu, spe-cific heat measurements show thatg0 is about one-tenthof the estimated free-electron value [2]. The estimatwidths of the DOS valley ini-AlPdRe andi-AlCuRu areof the same order of magnitude as ini-AlCuFe basedon the ByA ratio of about50 eV21y2 (Table I). Tunnel-ing experiments reveal a similar width of about 50 mefor the sharp feature in the DOS at the Fermi level [8however, the form of the narrow gap obtained heregsEd ­ g0 1 g1jE 2 EF j´ with ´ ø 1.8 2 rather than12 # ´ # 1. Given the uncertainties in both the NMR anthe tunneling experiments, such a discrepancy could notclarified based on the currently available information.In conclusion, the novel temperature dependences1yT1 and the Knight shift in quasicrystalline alloys reveathe presence of a sharp DOS valley aroundEF; the widthof this sharp feature is on the order of 20 meV. Thsharp feature is much narrower than the broad pseudon-tn-nanesmitSedV];isdbeoflisgapof about 0.5–1.0 eV. The observed sharp DOS valcould have significant influence on the transport propertof quasicrystals.This work was supported by the National ScienFoundation under Contracts No. DMR-9520477 aNo. DMR-9319084.[1] C. Janot, Quasicrystals: A Primer(Clarendon, Oxford,1994).[2] B. D. Biggs, S. J. Poon, and N. R. Munirathnam, PhyRev. Lett.65, 2700 (1990); B. D. Biggs, Y. Li, and S. JPoon, Phys. Rev. B43, 8747 (1991); S. J. Poon, AdvPhys. 41, 303 (1992); F. S. Pierce, S. J. Poon, and B.Biggs, Phys. Rev. Lett.70, 3919 (1993); F. S. 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Sharp feature in the pseudogap of quasicrystals detected by NMR

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Sharp feature in the pseudogap of quasicrystals detected by NMR

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