Spin excitations coupled with lattice and charge dynamics in La_{2-x}Sr_{x}CuO_4
K. Ikeuchi, S. Wakimoto, M. Fujita, T. Fukuda, R. Kajimoto, M. Arai
SSpin excitations coupled with lattice and charge dynamics in La − x Sr x CuO K. Ikeuchi, ∗ S. Wakimoto, M. Fujita, T. Fukuda, R. Kajimoto, and M. Arai
5, 6 Neutron Science and Technology Center, Comprehensive ResearchOrganization for Science and Society (CROSS), Tokai, Ibaraki 319-1106, Japan Materials Sciences Research Center, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan Institute for Materials Research, Tohoku University, Katahira, Sendai 980-8577, Japan Material Science Research Center, Japan Atomic Energy Agency (JAEA), Ko-to, Hyogo 679-5148, Japan Materials and Life Science Division (MLF), J-PARC Center, Tokai, Ibaraki 319-1195, Japan European Spallation Source ERIC, P.O. Box 176, SE-221 00 Lund, Sweden (Dated: February 17, 2021)Spin excitations of layered copper oxide show various characteristic features, depending on thecarrier concentration. In this study, we conducted inelastic neutron scattering (INS) measurementson La − x Sr x CuO (LSCO), with x = 0, 0.075, 0.18, and 0.30 and La − x Sr x NiO (LSNO) with1/3, to clarify the origin of the intensity enhancement in the excitation spectrum of LSCO atthe energy ( ω ) of 16–19 meV [Phys. Rev. B , 224404 (2015), ibid . , 094416 (2016)]. Weconfirmed the presence of a peak-structure in the ω -dependence of the local spin susceptibility χ (cid:48)(cid:48) ( ω ) of superconducting (SC) LSCO with a peak energy of 16–19 meV, where the spin excitationsintersect optical phonon branches. A comparable peak-structure is not observed in the insulatingLa CuO , LSNO, and heavily overdoped LSCO with x = 0.30. A dome-shaped x -dependence of theintegrated intensity around the peak energies is revealed for SC phase by summarizing the presentand previously reported results. Furthermore, our phonon calculation on LCO shows the existenceof two optical branches at ∼
19 meV that could stabilize stripe-alignment of carriers due to out-of-plane vibrations of Cu or O of the CuO planes. These results indicate the interplay among spin,charge, and lattice dynamics and suggest that the intensity enhancement is associated with theircomposite excitations. I. INTRODUCTION
The elucidation of spin excitations in superconducting(SC) cuprate oxides is an important research issue re-lated to doped Mott insulators. Extensive inelastic neu-tron scattering (INS) experiments have revealed a varietyof spin excitations in cuprate superconductors, depend-ing on the carrier concentrations . The undoped antifer-romagnet La CuO (LCO) shows spin-wave dispersion,which is well understood in the framework of spin-wavetheory . This excitation is replaced by the ”hourglass”-shaped excitations in SC La − x Sr x CuO (LSCO) , orig-inally observed in La . Ba . CuO and YBa Cu O (YBCO) . The hourglass excitations consist of a ver-tically standing low-energy incommensurate (IC) com-ponent and a high-energy outwardly dispersive compo-nent in a wide energy ( ω ) spanning the waist energy atapproximately 40 meV . The low-energy IC excita-tions evolve in the underdoped (UD) region upon dopingwith the increase in incommensurability ( δ ) and degradecoincidentally with the suppression of superconductiv-ity in the overdoped (OD) region . These experi-mental facts indicate an close relationship between theIC spin excitations and superconductivity. Intriguingly,corresponding measurements obtained by neutron and x-ray beams clarified a weak doping-dependence of thehigh-energy dispersion in LSCO and YBCO up to aheavily OD regime.Lipscombe et al. clarified the two-component char-acter of spin excitations for LSCO with x = 0.075, whichshows intensity maximums in the ω -dependence of local spin susceptibility ( χ (cid:48)(cid:48) ( ω )) at approximately ω = 19 and40 meV. Recently, Sato et al. reported the possible co-existence of IC and commensurate (C) excitations aroundthe waist energy of the hourglass excitations in UD x =0.10 and optimally-doped (OP) x = 0.16. An analysisbased on a two-component picture for the high-qualityINS data revealed evidence of the itinerant electron spinnature and localized magnetism for the low-energy ICand high-energy C excitations, respectively.Considering the one-dimensional alignment of spin andhole domains within a stripe model, the intensity max-imum at 40 meV is interpreted as the saddle pointcharacter of the gapped excitation from an even-legspin ladders system . For the excitations showingan intensity maximum at a lower ω (attributed as in-tensity enhancement), polarized INS measurements onLa . Sr . Cu . Ni . O confirmed that the enhancedspectral weight is magnetic in origin . More recently,Wagman et al. pointed out that the spin excitations atthe peak-energy of ∼
19 meV cross with optical phononbranches for La − x Ba x CuO (LBCO) with x = 0.035.They argued that the intensity enhancement was associ-ated with a modification of the exchange coupling con-stant J using a vibration mode of Cu-O-Cu bond. Asimilar peak-structure was also reported for the UD re-gion of LBCO and LSCO .Motivated studies presented above, the purpose of thisstudy is to gain insight into the relationship between in-tensity enhancement and superconductivity relating tospin excitations and clarifying the necessary conditionsfor intensity enhancement. To accomplish this, we per-formed INS measurements on LSCO with UD x = 0.075 a r X i v : . [ c ond - m a t . s up r- c on ] F e b (LSCO(7.5)) and slightly OD x = 0.18 (LSCO(18)), aswell as non-SC x = 0.30 (LSCO(30)). LSCO(30) showsno clear magnetic signal up to 40 meV , thus we mea-sured the phonons in this compound as the reference.The presence or absence of intensity enhancement wasalso examined for insulating systems of undoped antifer-romagnet LCO and stripe-ordered La − x Sr x NiO with x = 1/3 (LSNO(1/3)).We confirmed the enhancement of the magnetic spec-tral weight in LSCO(7.5) at 16 meV and LSCO(18)at 19 meV, where optical phonon branches are lying.Such enhancement is absent in the insulating LCO andLSNO(1/3), even though the same phonon branches ex-ist. The energy-integrated χ (cid:48)(cid:48) ( ω ) between the range of12 and 28 meV covering the peak energies ( E p ) exhibitsa dome-shaped x -dependence in the SC phase. To as-sign the optical phonons at approximately 19 meV thatcould couple with charge stripes, we performed a phononcalculation on LCO. Two possible modes containing out-of-plane oxygen vibration were clarified. These resultssuggest that the intensity enhancement is prone to ap-pear through the interplay among spin, charge, and lat-tice dynamics in cuprates.The remainder of this paper is organized as follows.Section II outlines the INS measurements, sample prepa-ration, and phonon calculations. The results are pre-sented in Section III. A discussion of the possible originof the intensity enhancement is presented in Section IV,and a summary is provided in Section V. II. EXPERIMENTS AND CALCULATIONS
Single crystals of LSCO and LSNO were grown usingthe traveling-solvent floating-zone method. The grownsingle crystals were 8 and 6 mm in diameter for LSCOand LSNO, respectively, with a length of 40 mm. Fiveto eight crystals used for the INS experiments wereco-aligned for each compound by either a backscatter-ing Laue method using an x-ray or a transparent Lauemethod using a γ -ray.The INS experiments were performed using 4SEA-SONS, a time-of-flight (TOF) Fermi chopper spectrom-eter, installed at the Materials and Life Science Experi-mental Facility (MLF) of J-PARC . Co-aligned sam-ples were mounted on a closed-cycle refrigerator so thatthe a - and c -axes of the orthorhombic crystallographicnotation were placed horizontally. The monochromatiz-ing chopper (Fermi chopper) was tuned to obtain theneutron incident energies of E i = 48 and 55.47 meV forLSCO and LSNO(1/3), respectively. The Fermi chop-per’s rotation frequency was set to 250 Hz, producing anenergy resolution of ∼ c -axis was parallel to theincident neutrons, k i || c ( k i : wave vector of incident neutrons) . This configuration effectively measuresthe spin excitations of LSCO in the energy and momen-tum ( Q = ( H , K , L )) spaces due to the low dimen-sionality of the spin correlations. In this study, neu-tron cross-sections were measured at this condition forLSCO(18). Additionally, the scattering intensities forLCO, LSCO(7.5), and LSCO(30) and LSCO(1/3) weremapped out in the four-dimensional Q - ω space. For thelatter case, the samples were rotated in the horizontal a - c plane from −
30 to +60 degrees with respect to theposition of k i || c . Data were collected at 2.5-degree stepsand for 20 minutes at each angle. We measured the neu-tron scattering intensity at 5 K for all samples and above200 K for LCO, LSCO(7.5), and LSCO(30). Hereafter,we present our data in the orthorhombic notation wherethe inplane antiferromagnetic zone center in LCO ( π , π )corresponds to ( H , K ) = (1, 0). We use the energy unitwith (cid:126) = 1 throughout the paper.INS provides the dynamical susceptibility as a functionof the three-dimensional momentum Q and ω , χ (cid:48)(cid:48) ( Q , ω ),by measuring the double differential cross-section definedas follows: d σd Ω dω = 2( γr e ) πg µ B k f k i | F ( Q ) | χ (cid:48)(cid:48) ( Q , ω )1 − exp( − βω )where ( γr e ) = 0 . − , ( k f /k i ) is the ratio ofthe final and incident neutron wave vector, | F ( Q ) | isthe anisotropic magnetic form factor for a Cu d x − y orbital, and 1 / (1 − exp( − βω )) is the Bose population fac-tor. We converted the magnetic intensity of LSCO(7.5),LSCO(18), and LSNO(1/3) in the absolute unit by an-alyzing the incoherent elastic scattering intensity. ForLCO and LSCO(30), the absolute intensity was esti-mated from the ratio of the phonon intensity at the zoneboundary (1, 0.5, 3) with that of LSCO(7.5). The ratioamong LCO, LSCO(7.5), and LSCO(30) was 0.33 : 1 :0.48.To assign phonon modes near (1, 0), we calculatedphonon dispersions for the parent LCO based on the shellmodel using the open source package OpenPhonon . III. RESULTS
Figure 1 presents the overall neutron scattering inten-sity in the absolute units measured at 5 K for: (a) LCO,(b) LSCO(7.5), (c) LSCO(30), and (g) LSNO(1/3). In-tensity maps at 200 K are also shown for (e) LSCO(7.5)and (f) LSCO(30). Data were integrated over the rangesof 0 . < H < . . < L < . K = 0 in LCOand LSCO(7.5), while similar magnetic signals were notobserved in LSCO(30). Due to the insufficient instrumen-tal resolution to resolve IC structure with a small value of δ , a broad single peak centered at K = 0 was detected forthe LSCO(7.5) sample. In contrast, LSNO(1/3) shows FIG. 1. (Color online) Dynamical susceptibility in the ω - K plane for La − x Sr x CuO with: (a) x = 0, (b) x = 0.075, (c) x =0.30 at T = 5 K, (e) x = 0.075, (f) x = 0.30 at T = 200 K, and (g) La − x Sr x NiO with 1/3 at T = 5 K. The intensities wereobtained by integrating over the ranges of 0 . < H < . . < L < .
5. The nuclear Bragg points and incommensuratemagnetic positions in the H - K plane for La − x Sr x CuO and La − x Sr x NiO are illustrated in panels (d) and (h), respectively.Shaded areas in (d) and (h) correspond to the integrated area in K and range in H of the horizontal axis for each intensitymap. well-defined IC signals due to the large δ . More impor-tantly, at a low temperature, relatively large intensitieswere observed for LSCO(7.5) at K = 0 and ω = 16–19meV, where optical phonon branches cross the spin ex-citations. This intensity enhancement disappears at 200K.In Fig. 2, the constant ω spectra at 19 meV are pre-sented for LCO, LSCO(7.5), and LSCO(30). The resultsfor LCO and the overlaid values of LSCO(30) are shiftedupward by 3. The phonon intensities are in good align-ment with each other. According to the INS studies re-porting the intensity enhancement in the magnetic sig-nal , we first evaluate the bare magnetic intensity bysubtracting the χ (cid:48)(cid:48) ( Q , ω ) of LSCO(30) from that of LCOand LSCO(7.5). Subsequently, we sliced the remnantmagnetic spectra after the subtracting procedure at con-stant ω and fit the spectra using a Gaussian functionto evaluate the Q -integrated intensity ( χ (cid:48)(cid:48) ( ω )). Detailsof this analysis are reported in Ref. 28. The evaluated χ (cid:48)(cid:48) ( ω ) for LCO and LSCO(7.5) are shown in Figs. 3(a)and (b), respectively. As seen in Fig. 3(b), we clarifythe presence of maximum χ (cid:48)(cid:48) ( ω ) in LSCO(7.5) near 16meV. We note that phonon spectra for orthorhombic x = 0 and 0.075 and those for tetragonal x = 0.30 may dif-fer from one another. However, the tilting mode of theCuO octahedron, which is strongly connected with thecrystal structure, is limited below ∼ . Therefore,the structural effects can be ignored when evaluating thebare magnetic signal above 10 meV, which is the focusedenergy range in the present study. Taking INS measurements while rotating the samplesenables us to draw intensity maps in a wide L range; thusthe subtraction analysis at various L from 0 to 7 r.l.u.could be carried out. As a result, we found that the baremagnetic spectra were independent from L although thephonon intensity varied strongly with L . Therefore, wesubsequently analyzed the data under the condition k i || c using a conventional method. In this measurement, the L value was a function of H , K , and ω . In Fig. 3(b),open circles represent χ (cid:48)(cid:48) ( ω ) with an unfixed L value ob-tained after analytically subtracting the phonon inten-sity. The results agree with those evaluated at a fixed L ,supporting the two-dimensional nature of χ (cid:48)(cid:48) ( ω ). Thus,the intensity enhancement is magnetic in origin.Based on these agreements, we analyzed the spectrameasured with k i || c for slightly OD LSCO(18). Asshown in Fig. 3(c), χ (cid:48)(cid:48) ( ω ) has an intensity maximumat ∼
19 meV, and the peak-structure vanishes at 250 K.These results are quite similar to those for LSCO(7.5),even though E p is higher than in LSCO(7.5). There-fore, the enhancement would be a characteristic featurein the SC phase at low temperatures. To further eluci-date the origin of intensity enhancement, we examinedLSNO(1/3), which has a diagonal stripe order. As theintensity map at L = 2 r.l.u. shows in Fig. 1(g), the spinexcitations vertically stand at the incommensurate posi-tion with K = ± / ∼
14 and ∼
20 meV. In Fig. 3(d),we present χ (cid:48)(cid:48) ( ω ) for LSNO, which was evaluated withthe same procedure as for LCO and LSCO(7.5). The en- FIG. 2. (Color online) The dynamical susceptibility ofLa − x Sr x CuO with x = 0, 0.075, and 0.30 sliced at 19 meVwith a width of ± x = 0 and overlaidvalues of x = 0.30 are shifted upward by 3. The intensity wasobtained by integrating over the ranges of 0 . < H < . . < L < . hancement of χ (cid:48)(cid:48) ( ω ) was not seen at energies where op-tical phonons intersected. Combined with the presenceof a peak-structure in χ (cid:48)(cid:48) ( ω ) for SC LSCO, the absenceof a similar structure in the doped LSNO(1/3) and un-doped LCO suggests that the metallicity, in addition tospin and lattice dynamics, is a fundamental factor for theintensity enhancement.Figure 4(a) summarizes the mean squared moment(
16 to ∼
19 meV at x ∼ IV. DISCUSSION
In this study, our INS measurements on several char-acteristic samples provided new insights into the inten-sity enhancement. First, no intensity enhancement ofphonons was observed for the OD LSCO(30) where low-energy IC magnetic fluctuations were absent . This ob- FIG. 3. (Color online) Energy-dependencies of the local spinsusceptibility χ (cid:48)(cid:48) ( ω ) of La − x Sr x CuO with: (a) x = 0, (b) x = 0.075, (c) x = 0.18, and (d) La − x Sr x NiO with x =1/3. Closed and open symbols in each figure represent theresults obtained at fixed and unfixed L values, respectively. E p represents the peak position. The colored hatch is the areaproducing the energy integral χ (cid:48)(cid:48) ( ω ) at low temperatures, asshown in Fig. 4. Dotted lines are guides to the eye. servation implies that phonons cannot solely induce theemergent phenomenon and supports the importance ofspin-phonon coupling for intensity enhancement . Next,we confirmed two more important points; (1) the pres-ence of a peak-structure of χ (cid:48)(cid:48) ( ω ) with the maximum at16 and 19 meV in UD and slightly OD LSCO, respec-tively, and (2) the absence of a peak-structure in theinsulating systems having either commensurate (LCOorincommensurate (LSNO(1/3)) low-energy spin excita-tions. By summarizing the present and previously re-ported χ (cid:48)(cid:48) ( ω ) in the absolute value, the dome-shaped x -dependence of the integrated intensity around the peakenergies was clarified. These results indicate that thepeak intensity increases when increasing the itineracy ofcarriers and decreases in the OD region, where the mag-netic correlation becomes weak . Therefore, the inten-sity enhancement reflects the coupling of spin fluctua-tions with both phonons and carrier degree of freedom.The entanglement with carrier mobility supports the re-lationship between superconductivity and composite ex-citations of these degrees of freedom. FIG. 4. (Color online) x -dependence of: (a) energy integratedlocal spin susceptibility from 12 to 28 meV at low (blue sym-bols) and high (pink symbols) temperatures, and (b) peak po-sitions in the energy-dependence of local spin susceptibility forLa − x Sr x CuO . The values for the open symbols were eval-uated from previously reported results . The greenarea represents the superconducting phase. Dotted lines areguides for the eye. One possible scenario for intensity enhancementthrough the interplay among spin, charge, and lattice dy-namics is as follows. Deformation of the electronic bandstructure near the Fermi level occurs through electron-phonon interaction. Moreover, the resulting changesin nesting conditions cause the intensity enhancementof magnetic signals. This scenario is valid for metal-lic phases but not for the insulating phase. Further-more, according to the Fermi surface nesting model , thepeak-structure could vanish at high temperatures wherethe anisotropic gap structure near the Fermi surface (thenesting condition) degrades. The evidence of an itiner-ant nature of the low-energy IC spin excitations of SCLSCO was reported by a recent neutron scattering ex-periment . This is consistent with our results, based onthe present findings that spin dynamics correlate withitinerant holes.An x-ray scattering measurement reported the exis-tence of dynamic short-ranged charge orders that couplewith phonons in LBCO with x = 1/8, even above theonset temperature of the static charge order . Develop-ment of a slow charge and lattice fluctuations upon cool-ing was more recently revealed by nuclear magnetic reso-nance measurements on LBCO with x = 1/8 . Assum-ing that the one-dimensional stripe alignment of dopedholes is essential for the coupling between phonons andholes, we consider possible phonons lying around 19 meV.Calculated phonons for the parent LCO, based on the FIG. 5. (Color online) (a) Intensity map of LSCO with x = 0 .
075 at 5 K in the L = 5 zone, together with phononbranches calculated by the shell model . The intensitymap was obtained by integrating H and L from 0.8 to 1.2 and4.5 to 5.5 r.l.u., respectively. (b) The displacement patternsof the CuO plane at (1, 0) for the three highlighted phononmodes, labeled A, B, and C in (a). shell model , are shown in Fig. 5 with the intensitymap in the L = 5 r.l.u. zone of LSCO(7.5). This L value is selected for a clear comparison, where phononshave higher intensities. Among the phonons crossing thespin excitations around 19 meV, we focus on three modeslabeled as A, B, and C in Fig. 5, which shows the sig-nificant motions of Cu and O atoms of the CuO plane.The motions of atoms for each mode are illustrated inthe right panel of Fig. 5. Phonon modes A and B are as-sociated with the out-of-plane motion of Cu or O atoms,producing a potential for trapping the charge stripesalong the Cu-O bond direction, and hence, could be cou-pled with charges. The presence of two E p ’s, shown inFig. 4(b), suggests that the two different phonons con-tribute to the intensity enhancement, which is consistentwith the result of the calculation. The variation of thestrength of the interplay between charge/spin dynamicsand these phonons could depend on the doping level, re-sulting in an increase in E p with doping. We note thatthe experimentally evaluated E p is slightly lower thanthe calculated energy of the two phonons at K = 0. Thisdifference is possibly due to the phonon softening causedby carriers in the doped system.Finally, we discuss the intensity enhancement in othercuprates. Angle-resolved photoemission spectroscopy(ARPES) measurements of cuprate superconductors re-vealed a kink structure in the electronic dispersion at60 and 40 meV as a result of electron-phonon cou-pling. The kinks at 40 and 60 meV originated fromthe coupling of holes with the oxygen buckling andhalf-breathing modes of the CuO plane, respectively .High-resolution ARPES measurements on the SC phaseof Bi Sr CaCu O δ revealed a new kink structure inthe electronic dispersion at ∼
16 meV and a decrease inanomaly strength upon doping . These results sup-port the existence of low-energy phonon modes that cou-ple with carriers and the doping evolution of the low-energy IC spin excitations. Meanwhile, the intensityenhancement of the magnetic signal was not reportedfor OP YBa Cu O δ and OP HgBa CuO δ us-ing INS measurements, possibly due to the opening ofa spin gap with large gap energy. That is, althoughoptical phonons exist, the intensity enhancement can-not occur due to the absence of a magnetic signal belowthe gap energy, similar to LSCO(30). Investigating thespin-phonon coupling in the electron-doped system is es-sential to understand the microscopic mechanism of theintensity enhancement and its relationship with super-conductivity. INS measurement on SC Nd − x Ce x CuO and (Pr, La) − x Ce x CuO , which exhibit low energy com-mensurate spin excitations and charge-density-waveorder , could provide vital information to test theo-retical works. V. SUMMARY
To clarify the origin of the peak-structure in the localmagnetic susceptibility χ (cid:48)(cid:48) ( ω ) at 16–19 meV of LSCO, we examined the spin excitations in LCO, LSCO(7.5),LSCO(18), LSCO(30), and LSNO(1/3). We confirmedthe peak-structure in SC LSCO(7.5) at ∼
16 meV andLSCO(18) at ∼
19 meV for 5 K, where the spin excitationssuperimposed on optical phonon branches. No inten-sity enhancement of the phonon and no peak-structurein χ (cid:48)(cid:48) ( ω ) were detected for LSCO(30), where low-energyspin excitations were absent as well as for the insulat-ing LCO and LSNO(1/3). Furthermore, the energy inte-grated χ (cid:48)(cid:48) ( ω ) covering the E p ’s showed a dome-shaped x -dependence similar to the x - T c relation in LSCO. Basedon the shell model, we determined that the candidatephonons coupled with the stripe-aligned holes. Theseresults suggest that the peak-structure is due to the in-terplay among spin, charge, and lattice dynamics. ACKNOWLEDGMENTS
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