Two energy scales in the spin excitations of the high-temperature superconductor La 2 x Sr x CuO 4

Transcription

1 Two energy sles in the spin exittions of the high-temperture superondutor L x Sr x CuO 4 B. VIGNOLLE,S.M.HAYDEN *,D.F.MMORROW,, H. M. RØNNOW 4,B.LAKE 5,C.D.FROST AND T. G. PERRING H. H. Wills Physis Lortory, University of Bristol, Tyndll Ave., Bristol BS8 TL, UK London Centre for Nnotehnology nd Deprtment of Physis nd Astronomy, University College London, London WCE 6BT, UK ISIS Fility, Rutherford Appleton Lortory, Chilton, Didot OX QX, UK 4 Lortory for Neutron Sttering, ETH-Zürih nd Pul Sherrer Institut, 5 Villigen, Switzerlnd 5 Hhn-Meitner Institut, Berlin D-49, Germny *e-mil: s.hyden@ris..uk Pulished online: 8 Ferury 7; doi:.8/nphys546 The exittions responsile for produing high-temperture superondutivity in the opper oxides hve yet to e identified. Two promising ndidtes re olletive spin exittions nd phonons. A reent rgument ginst spin exittions is sed on their inility to explin strutures oserved in eletroni spetrosopies suh s photoemission 5 nd optil ondutivity 6,7. Here, we use inelsti neutron sttering to demonstrte tht olletive spin exittions in optimlly doped L x Sr x CuO 4 re more strutured thn previously thought. The exittions hve two-omponent struture with lowfrequeny omponent strongest round 8 mev nd roder omponent peking ner 4 7 mev. The seond omponent rries most of the spetrl weight nd its energy mthes strutures oserved in photoemission 5 in the rnge 5 9 mev. Our results demonstrte tht olletive spin exittions n explin fetures of eletroni spetrosopies nd re therefore likely to e strongly oupled to the eletron qusiprtiles. Sine their disovery, onsiderle progress hs een mde in understnding the properties of the high-ritil-temperture, T, uprte superondutors. We know, for exmple, tht the superondutivity involves Cooper pirs, ut with d-wve rther thn the s-wve piring of onventionl Brdeen Cooper Shrieffer (BCS) superondutors. One outstnding issue is the piring mehnism itself. For onventionl superondutors, identifying the osoni exittions tht strongly ouple to the eletron qusiprtiles plyed pivotl role in onfirming the phonon-medited piring mehnism 8,9. In the se of the opper oxide superondutors, eletroni spetrosopies suh s ngle-resolved photoemission (ARPES) nd infrred optil ondutivity mesurements 6,7 hve reveled strutures in the lowenergy eletroni exittions, whih my reflet oupling to osoni exittions. ARPES mesurements on Bi Sr CCu O 8,Bi Sr CuO 6 nd L x Sr x CuO 4 hve shown rpid hnges or kinks in the qusiprtile dispersion, E(k), for energies in the rnge 5 8 mev (refs 5). These fetures in ARPES hve een interpreted in terms of oupling to phonon modes 5. However, the ARPES mesurements do not distinguish etween oupling to lttie nd spin exittions. Identifying phonons s the strongly oupled osons is not without its diffiulties: we must explin wht is speil out the phonons in the uprtes; intertions with phonons do not nturlly explin other importnt properties of the uprtes, suh s the lrge liner temperture dependene of the norml-stte resistivity t optiml doping nd the origin of d-wve symmetry of the superonduting gp itself. The interprettion of the kinks nd other fetures in eletroni spetrosopies 7 in terms of oupling to olletive spin exittions hs een hmpered y the lk of mgneti spetrosopy dt. Most neutron sttering dt refer to YB Cu O 6+x, ompound for whih ARPES dt re sre. Although ARPES kinks hve lso een reported in L x Sr x CuO 4, omprison with neutron sttering is restrited y the ft tht high-resolution studies in this ompound hve only een mde for energies elow the relevnt 5 8 mev energy window 4. At these nd higher energies of relevne, only orsely verged dt re ville 5, preluding detiled omprison with eletroni spetrosopies. Here, we report highresolution neutron sttering study of the mgneti exittions in optimlly doped L x Sr x CuO 4 (x =.6,T = 8.5 K) designed to fill this gp in our knowledge. For our experiments, we hve grown new single rystls y floting-zone tehnique nd ssemled smple with totl mss of 48.5 g (see the Supplementry Informtion). The experiments were rried out using the MAPS spetrometer t the ISIS splltion neutron soure, Rutherford Appleton Lortory. MAPS hs n order of mgnitude etter momentum resolution thn the MARI instrument used for the previous high-energy study 5. The prent ompound L CuO 4 of the L x Sr x CuO 4 superonduting series exhiits ntiferromgneti order with n ordering wvevetor of Q D = (/, /). Doping indues superondutivity nd uses low-frequeny inommensurte flututions, to develop with wvevetors Q D = (/,/ ± δ) nd (/ ± δ,/). These exittions roden nd disperse inwrds initilly towrds (/, /) (ref. 4) with inresing energy. Neutron spetrosopy provides diret proe of the mgneti response funtion χ (Q,ω). Figure h shows wvevetordependent imges of the mgneti response t vrious energies demonstrting how it evolves with energy. At low energies, nture physis VOL MARCH 7 6

2 .8 ± mev ± mev ± mev 4 d. 4 ± mev e. 5 ± 5 mev 5 f. 9 ± mev 4 g. ± mev. h. 5 ± mev i.8 ± mev 4 j.8 8 ± mev 4 k.8 5 ± mev 4 l. 4 ± mev m. 5 ± 5 mev 5 n. 9 ± mev 4 o. ± mev. p. 5 ± mev Figure Imges of the mgneti exittions in L.84 Sr.6 CuO 4. h, The mesured χ (Q,ω) is plotted in units of μ B ev f.u. s funtion of wvevetor for vrious energies in the superonduting phse t T = K., The emergene nd dispperne of the omponent t (/± δ,/) nd (/,/± δ), whih is most intense t lower energies. d h, The higher-energy omponent, whih emerges round 4 mev nd disperses outwrds with inresing energy. i p, Model fits to the imges of the mgneti exittions shown in h. The phenomenologil model (eqution ()) provides good desription of the experimentlly mesured mgneti exittions nd n therefore e used to prmeterize the dt. At higher energies (n p), the dt re est fitted with the model χ (Q,ω) rotted 45 in the h k plne. The nisotropy is strongest for pnel n. Wvevetors re lelled y their positions in reiprol spe Q = h + k + l. A kground of the form α + β Q hs een sutrted from thedteforeonversiontoχ (Q,ω). E = mev (Fig. ), we oserve the low-energy inommensurte exittions 4. As the energy is inresed, E = 8 mev (Fig. ), the response eomes stronger, the pttern fills in long the line onneting the nerest-neighour inommensurte peks nd the inommensurility δ dereses. For E = 5 mev (Fig. ), the intensity of the pttern is notiely ttenuted. On further inresing to E = 4 mev (Fig. d), the response reovers, eoming more intense gin, ut is now peked t the ommensurte wvevetor (/, /). At higher energy E = 9 mev (Fig. f), the struture resemles squre ox with the orners pointing long the ()-type diretions, tht is, towrds the Brillouin zone entre. Thus, the squre pttern is rotted 45 with respet to the low-energy response (for exmple, Fig. ). A similr high-energy response hs een oserved in underdoped YB Cu O 6+x (refs 6,7) nd the stripe-ordered omposition L.875 B.5 CuO 4 (ref. 8). Thus, rotted ontinuum seems to e universl feture of the uprtes. To mke our nlysis quntittive, we fitted modified lorentzin ross-setion previously used to desrie the uprtes nd other systems 9 to the dt: with R(Q) = κ 4 (ω) χ (Q,ω)= χ δ (ω) () [κ (ω)+ R(Q)] [ (h ) + (k ) δ ] +l(h ) (k ) 4δ 64 nture physis VOL MARCH 7

3 E = mev E = 8 mev E = 4 mev d E = 5 mev e. E = 9 mev f.5 E = mev Figure Mgneti exittions in L.84 Sr.6 CuO 4. f, The vrition of the sttered intensity with wvevetor for vrious fixed exittion energies t T = K. The trjetory of the ut is shown y the dshed line in Fig.. nd show the inommensurte low-frequeny omponent of the response. The high-frequeny omponent is strongest for 4 5 mev ( f). Two distint peks re seen t higher energies (e,f ), these disperse wy from (/, /) in similr mnner to the spin-wve exittions in the prent ompound L CuO 4. The error rs re determined from the numer of neutrons ounted. where κ(ω) is n inverse orreltion length, the position of the four peks is speified y δ, nd l ontrols the shpe of the pttern (l = 4 orresponds to four distint peks nd l = orresponds to pttern with irulr symmetry). Further detils of the experimentl method nd nlysis re given in the Supplementry Informtion. Figure i p shows plots of the fitted model response for the sme energies s Fig. h. Another wy of displying the results is to tke onstnt energy uts through our dt set. Figure shows uts long the dshed trjetory in Fig. for vrious energies together with fits of our model response (eqution ()) onvolved with the experimentl resolution. The good greement etween the dt nd fits llows us to use the prmeters derived from the fits (Fig. ) to interpret our results. To distinguish etween mgneti nd phonon sttering, the experiment ws rried out t numer of inident energies. This mens tht the sme in-plne momentum (h,k) ould e proed with vriety of l (momentum perpendiulr to plne) vlues nd strong phonons isolted. The ft tht dt olleted with different inident energies yield similr results onfirms the vlidity of our nlysis. We hve expressed the strength of the spin flututions in terms of the lol or wvevetorverged suseptiility χ (ω)= χ (Q,ω)d Q/ d Q determined from the fitted ross-setion. The lol suseptiility, χ (ω), is mesure of the density of mgneti exittions for given energy. Figure shows one of the key results of this work: the mgneti response of L.84 Sr.6 CuO 4 hs two-omponent struture. The lower-energy pek orresponds to the inommensurte struture tht is rpidly ttenuted ove mev. The nture physis VOL MARCH

4 χ ( ω ) ( μ B ev f.u. ) (r.l.u.) κ χ ( ω ) K K δ (r.l.u.) Figure Mgneti exittion spetrum nd evolution of the form of the mgneti response with energy., The wvevetor-verged suseptiility, χ (ω), shows pek-dip-hump struture suggesting tht the mgneti response hs two omponents., The emergene of the higher-frequeny omponent ove out 4 mev orresponds to rodening of the response in the wvevetor s demonstrted y the rpid inrese in κ., There is strong dispersion of the pek positions in onstnt exittion-energy uts s shown y the energy dependene of the inommensurility δ(ω). The high-energy dispersion indites the persistene of residul ntiferromgneti intertions. The symols in the min pnels indite different inident energies: E i = (dimond), 55 (open squre), 9 (filled squre), 6 (filled irle), 4 mev (open irle). The inset in shows tht the low-energy pek is strongly suppressed t T = K onfirming tht it is mostly mgneti in origin. The error rs re sttistilly determined from lest-squres fitting. higher-energy struture is peked t (/, /) for E 4 5 mev nd rodens out with inresing energy ove this. Although the wvevetor-verged suseptiility, χ (ω), of the higher-frequeny omponent is peked round 5 mev, it hs long til with mesurle response t the highest energies proed (E = 55 mev) in this experiment. It is interesting to ompre the present results with those otined on L.875 B.5 CuO 4 (ref. 8). L.875 B.5 CuO 4 is stripe ordered with Brgg peks orresponding to spin nd hrge order nd is only wekly superonduting with T < 6K, wheres L.84 Sr.6 CuO 4 is superonduting with T = 8.5 K nd hs no oservle spin or hrge order. For given energy, oth ompositions show rodly similr strutures in their χ (Q,ω) ptterns. The energy dependene of the response s hrterized y χ (ω) is very different in the two ompositions. L.875 B.5 CuO 4 (ref. 8) shows pek in χ (ω) entred on zero energy, whih is proly onneted to exittions owing to the mgneti order present in this ompound. For E > 5 mev, χ (ω) inreses to rod mximum t out 6 mev. In ontrst, in L.84 Sr.6 CuO 4,sE is inresed from zero, χ (ω) rises from zero to shrp mximum t 8 mev, followed y dip t 5 mev nd seond roder mximum t 5 mev. Aove out 6 mev, oth ompositions show similr responses, with χ (ω) deresing slowly with ω. The differene in the responses of the two mterils elow 6 mev is not surprising given tht L.875 B.5 CuO 4 is mgnetilly (nd hrge) ordered nd therefore must hve exittions refleting this ordered stte. Given the mrkedly different hrteristis of the two omponents tht mke up the mgneti response in L.84 Sr.6 CuO 4, it is likely tht they hve different origins. One possile interprettion is tht the lower-energy inommensurte struture is due to qusiprtile (eletron hole) pir retion, whih might e lulted from n underlying nd struture,, wheres the higher-energy struture is due to the residul ntiferromgneti intertions. It is instrutive to ompre the mgneti response t optiml doping with tht of the ntiferromgneti prent ompound L CuO 4 (ref. ). In L CuO 4, χ (ω) is pproximtely onstnt over the energy rnge proed here ( 6 mev) with χ (ω).7 μ B ev f.u.. Thus, the effet of doping is to suppress the high-energy response ( hω >5 mev) nd enhne the response t lower frequenies, reting doule-pek struture. Figure shows tht the highenergy prt of the response disperses with inresing energy. Constnt energy uts through the dt yield two peks (see Fig. ) tht re reminisent of spin wves in the prent ompound L CuO 4. We my use the high-energy dispersion to estimte n effetive Heisenerg exhnge onstnt, J, whih quntifies the strength of the oupling etween the opper spins. Using the fitted vlues of δ in Fig. for E > 4 mev, we estimte the grdient to e de/dδ = 5 ± 5 mev Å. This my then e ompred with the stndrd expression for the spin-wve veloity in squre lttie ntiferromgnet, hv s = Z 8SJ,whereZ, S nd re the quntum renormliztion, spin nd lttie prmeter respetively. We find tht the effetive exhnge onstnt for L.84 Sr.6 CuO 4 is J = 8 ± 9 mev. This is sustntilly redued ompred with tht of the prent ompound L CuO 4,whereJ = 46±4 mev (ref. ). We now ompre our mesurements of the mgneti exittions with eletroni spetrosopy rried out on uprte superondutors with the sme energy sle. The energy of the 5 mev pek mthes the energy rnge (4 7 mev) where ARPES mesurements 5 in the sme ompound L x Sr x CuO 4 show rpid hnges or kinks in the qusiprtile dispersion E(k). Theory hs no diffiulty in explining kinks nd relted fetures round the underlying Fermi surfe through oupling to spin exittions tht re strongest ner (/, /). In the lterntive senrio where phonons re the most strongly oupled oson modes, we would expet priori tht there would e series of kinks orresponding to different phonons. Coupling to the spin exittions seems to provide more nturl explntion 66 nture physis VOL MARCH 7

5 for the kink, euse there is single feture in the spin exittions with the required energy sle. At higher energies, ARPES mesurements suggest tht the qusiprtiles re oupled to osoni exittions with energies up to t lest mev (ref. 4). This would mth the high-energy til of the olletive spin exittions in Fig.. These energies re well ove the phonon utoff of out 85 mev. Other eletroni spetrosopy dt re not ville for L x Sr x CuO 4. However, we my mke omprisons with other systems. Infrred optil ondutivity mesurements on YB Cu O 6+x (ref. 5) nd Bi Sr C.9 Y.8 Cu O 8+δ (ref. 6) provide evidene of oupling to high-energy osons in the rnge of the 5 mev exittions reported here. The infrred optil ondutivity mesurements lso suggest the existene of osons t higher energies, onsistent with the present experiment. It should e noted tht the mgneti exittions reported here do not seem to e relted to the lttie modes reently oserved y snning tunnelling mirosopy 7 in Bi Sr CCu O 8+δ. These lttie modes re ssoited with the wvevetor q (.,), rther thn q (/,/). Reeived 9 August 6; epted Jnury 7; pulished 8 Ferury 7. Referenes. Chuukov, A. V., Pines, D. & Shmlin, J. in The Physis of Superondutors Vol. (eds Bennemnn, K. H. & Ketterson, J. B.) (Springer, Berlin, ).. Bogdnov, P. V. et l. Evidene for n energy sle for qusiprtile dispersion in Bi Sr CCu O 8. Phys.Rev.Lett.85, ().. Kminski, A. et l. Renormliztion of spetrl line shpe nd dispersion elow T in Bi Sr CCu O 8+δ. Phys.Rev.Lett.86, 7 7 (). 4. Johnson, P. D. et l. Doping nd temperture dependene of the mss enhnement oserved in the uprte Bi Sr CCu O 8+δ. Phys.Rev.Lett.87, 777 (). 5. Lnzr, A. et l. Evidene for uiquitous strong eletron phonon oupling in high-temperture superondutors. Nture 4, 5 54 (). 6. Bsov, D. N. & Timusk, T. Eletrodynmis of high-t superondutors. Rev. Mod. Phys. 77, (5). 7. Dordevi, S. V. et l. Extrting the eletron oson spetrl funtion α F(ω) from infrred nd photoemission dt using inverse theory. Phys.Rev.B7, 459 (5). 8. MMilln, W. L. & Rowell, J. M. Led phonon spetrum lulted from superonduting density of sttes. Phys.Rev.Lett.4, 8 (965). 9. Stedmn, R., Almqvist, L. & Nilsson, G. Phonon-frequeny distriutions nd het pities of luminum nd led. Phys. Rev. 6, (967).. Chuukov, A. V. & Normn, M. R. Dispersion nomlies in uprte superondutors. Phys.Rev.B7, 7455 (4).. Shirne, G. et l. Temperture dependene of the mgneti exittions in L.85Sr.5CuO 4 (T = K). Phys.Rev.Lett.6, (989).. Cheong, S. W. et l. Inommensurte mgneti flututions in L xsrxcuo 4. Phys.Rev.Lett.67, (99).. Mson, T. E., Aeppli, G. & Mook, H. A. Mgneti dynmis of superonduting L.86Sr.4CuO 4. Phys.Rev.Lett.68, (99). 4. Christensen, N. B. et l. Dispersive exittions in the high-temperture superondutor L xsrxcuo 4. Phys.Rev.Lett.9, 47 (4). 5. Hyden, S. M.et l. Comprison of the high-frequeny mgneti flututions in insulting nd superonduting L xsrxcuo 4. Phys.Rev.Lett.76, (996). 6. Hyden, S. M., Mook, H. A., Di, P. C., Perring, T. G. & Dogn, F. The struture of the high-energy spin exittions in high-trnsition-temperture superondutor. Nture 49, 5 54 (4). 7. Stok, C. et l. From inommensurte to dispersive spin-flututions: The high-energy inelsti spetrum in superonduting YB Cu O 6.5. Phys.Rev.B7, 45 (5). 8. Trnqud, J. M. et l. Quntum mgneti exittions from stripes in opper oxide superondutors. Nture 49, (4). 9. Sto, H. & Mki, K. Theory of inelsti neutron sttering from Cr nd its lloys ner the Néel temperture. Int. J. Mgn. 6, 8 9 (974).. Fujit, M., Gok, H., Ymd, K., Trnqud, J. M. & Regnult, L. P. Stripe order, depinning, nd flututions in L.875B.5CuO 4 nd L.875B.75Sr.5CuO 4. Phys.Rev.B7, 457 (4).. Si, Q. M., Zh, Y. Y., Levin, K. & Lu, J. P. Comprison of spin dynmis in YB Cu O 7 δ nd L xsrxcuo 4 effets of fermi-surfe geometry. Phys.Rev.B47, (99).. Littlewood, P. B., Znen, J., Aeppli, G. & Monien, H. Spin flututions in -dimensionl mrginl fermi-liquid. Phys.Rev.B48, (99).. Colde, R. et l. Spin wves nd eletroni intertions in L CuO 4. Phys.Rev.Lett.86, (). 4. Kordyuk, A. A. et l. Constituents of the qusiprtile spetrum long the nodl diretion of high-t uprtes. Phys.Rev.Lett.97, 7 (6). 5. Bsov, D. N. et l. Pseudogp nd hrge dynmis in CuO plnes in YBCO. Phys.Rev.Lett.77, (996). 6. vn der Mrel, D. et l. Quntum ritil ehviour in high-t superondutor. Nture 45, 7 74 (). 7. Lee, J. et l. Interply of eletron-lttie intertions nd superondutivity in Bi Sr CCu O 8+δ. Nture 44, (6). Aknowledgements We knowledge finnil support from the EPSRC. Correspondene nd requests for mterils should e ddressed to S.M.H. Supplementry Informtion ompnies this pper on Competing finnil interests The uthors delre tht they hve no ompeting finnil interests. Reprints nd permission informtion is ville online t nture physis VOL MARCH