Progress in Neutron Scattering Studies of Spin Excitations in High-Tc Cuprates
Masaki Fujita, Haruhiro Hiraka, Masaaki Matsuda, Masato Matsuura, John M. Tranquada, Shuichi Wakimoto, Guangyong Xu, Kazuyoshi Yamada
JJournal of the Physical Society of Japan
FULL PAPERS
Progress in Neutron Scattering Studies ofSpin Excitations in High- T c Cuprates
Masaki Fujita , Haruhiro Hiraka , Masaaki Matsuda, Masato Matsuura , John M. Tranquada, Shuichi Wakimoto, Guangyong Xu, and Kazuyoshi Yamada , Institute for Materials Research, Tohoku University, Katahira, Sendai 980-8577, Japan Neutron Scattering Science Division, Oak Ridge National Laboratory,Oak Ridge, Tennessee 37831, USA Condensed Matter Physics & Materials Science Department, Brookhaven National Laboratory, Upton,NY 11973-5000, USA Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan WPI Advanced Institute for Materials Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-8577,Japan
Neutron scattering experiments continue to improve our knowledge of spin fluctuations in layeredcuprates, excitations that are symptomatic of the electronic correlations underlying high-temperature su-perconductivity. Time-of-flight spectrometers, together with new and varied single crystal samples, haveprovided a more complete characterization of the magnetic energy spectrum and its variation with carrierconcentration. While the spin excitations appear anomalous in comparison with simple model systems,there is clear consistency among a variety of cuprate families. Focusing initially on hole-doped systems, wereview the nature of the magnetic spectrum, and variations in magnetic spectral weight with doping. Weconsider connections with the phenomena of charge and spin stripe order, and the potential generality ofsuch correlations as suggested by studies of magnetic-field and impurity induced order. We contrast thebehavior of the hole-doped systems with the trends found in the electron-doped superconductors. Return-ing to hole-doped cuprates, studies of translation-symmetry-preserving magnetic order are discussed, alongwith efforts to explore new systems. We conclude with a discussion of future challenges.
KEYWORDS: superconductivity, neutron scattering, cuprates
1. Introduction
It is now 25 years since the remarkable discoveryof high-temperature superconductivity by Bednorz andM¨uller, and this year is also the centennial anniversaryof the original discovery of superconductivity in the labof Kammerlingh Onnes. Possible polaronic effects moti-vated the initial decision to look at cuprates, but a rolefor magnetism soon became clear. Anderson pointedout that undoped cuprates should be Mott insulators,with antiferromagnetism driven by superexchange, andantiferromagnetic order in La CuO y was quickly iden-tified by neutron diffraction. The possibility that anunconventional pairing mechanism involving antiferro-magnetic spin fluctuations
5, 6) might be driving high-temperature superconductivity quickly became an im-portant research theme.Over the last quarter century, a great deal of progresshas been made in characterizing the magnetic corre-lations in cuprate superconductors. Our focus here ison neutron scattering studies, but there has also beenmuch complementary work with techniques such as nu-clear magnetic resonance (NMR) and muon spin rota-tion ( µ SR). Much of the progress in neutron work isdue to the gradual improvement in sample quality, andespecially the growth of large, high-quality single crys-tals. Another factor has been the development at spal-lation sources of time-of-flight spectroscopy with two-dimensional, position-sensitive detectors, which comple-ments the use of triple-axis spectrometers at reactor sources. There have already been a number of reviews of neu-tron scattering work on cuprates, as well as on rel-evant theoretical work.
Two of us were involved ina review published in this same venue five years ago.
Here we will emphasize work done since then.The rest of this article is organized as follows. Thenext section provides some relevant background infor-mation. For the class of hole-doped cuprates, we dis-cuss the magnetic excitation spectrum in §
3, we drawconnections with the phenomenology of stripe order in §
4, and we consider the impact of impurities on theCu site in §
5. Section 6 covers electron-doped cuprates,Pr − x LaCe x CuO δ (PLCCO) in particular. In §
7, wereview evidence for exotic magnetic order associated withthe pseudogap phase, and efforts to search for magneticexcitations in new systems, such as Bi x Sr − x CuO δ .We conclude in §
2. Background
The common structural feature of all cuprates is theCuO plane. Within these layers, the Cu atoms form anapproximately square lattice, with O atoms at the bridg-ing positions between nearest-neighbor Cu’s. It is oftensufficient to consider a tetragonal, or pseudo-tetragonal,coordinate system, with a ∼ . a r X i v : . [ c ond - m a t . s up r- c on ] N ov . Phys. Soc. Jpn. FULL PAPERSFig. 1. (Color online) Representative phase diagrams for hole-doped La − x Sr x CuO and electron-doped Pr − x LaCe x CuO δ ,showing antiferromagnetic (AFM), superconducting (SC), andspin-glass (SG) phases. Below the crossover line labelled T ∗ is thepseudogap regime. units (rlu) (2 π/a, π/a, π/c ).Figure 1 shows representative phase diagrams for hole-and electron-doped cuprates. In the undoped state, wehave an antiferromagnetic insulator. Each Cu atom hasa half-filled 3 d x − y orbital, corresponding to a spin S = 1 /
2. The nearest-neighbor spins are coupled by thesuperexchange interaction, with magnitude J ∼ . Q AF =( , , a set to 1, so that Q AF = ( π, π ) in two dimen-sions.] Inelastic neutron scattering studies of La CuO show that the magnetic excitations are fairly well de-scribed by spin-wave theory, with the excitationsextending over a band width of ∼ J . For YBa Cu O x ,which has a CuO bilayer in each unit cell, one distin-guishes between spin excitations that are in-phase be-tween neighboring layers (acoustic mode) or out-of phase(optical mode).There are some cases where we have to take ac-count of structural deviations from tetragonal. ForLa − x Sr x CuO (LSCO), the structure over much ofthe phase diagram is the so-called low-temperature or-thorhombic (LTO) phase, in which the unit cell volumeis doubled, with a rotation of the in-plane principal axesby 45 ◦ . In this structure, the not-quite-orthogonal Cu-Obonds are equivalent to one another, but the antiferro-magnetic wave vectors (1 , , o and (0 , , o are not.(We will label wave vectors in the LTO coordinate sys-tem with a subscript “o”.) It is important to distinguishthe LTO phase of LSCO from the orthorhombic struc-ture of superconducting YBa Cu O x (YBCO). In thelatter, the unit cell size is the same as that of the tetrag-onal, but Cu-O bonds along the a axis are shorter thanthose along the b axis.Looking at Fig. 1, one can see that long-range antifer-romagnetic (AF) order is destroyed by a very small con- centration (2%) of doped holes. With further doping, aspin-glass phase develops at low temperatures and coex-ists with the superconducting (SC) phase for x (cid:38) .
06 inLSCO.
8, 18)
The doping level corresponding to the max-imum SC transition temperature, T c , is referred to as“optimal”. Below the crossover line indicated as T ∗ , onehas the so-called pseudogap phase. With electron-dopingthe situation is somewhat different. The AF orderingtemperature, T N , decreases more slowly with carrier con-centration, and the superconducting phase appears withmaximum T c near the point where T N → T c . A spingap opens, and weight appears in a “resonance” peakabove it.
9, 23–26)
It has been argued that the ratio ofthe resonance energy to the superconducting gap energyhas a universal value of 1.3.
3. Magnetic excitations
The inelastic-neutron-scattering (INS) technique usinghigh-flux pulsed neutrons has unveiled the overall spindynamics of hole-doped cuprates, which extends over alarge energy scale, comparable to the bandwidth of ∼ J found for the AF parent phase. While doping causes sub-stantial changes to the magnetic spectrum, a consistentpattern has been identified, as the “hour-glass” disper-sion was first established in the acoustic magnetic excita-tions of YBa Cu O . and in La . Ba . CuO . A comparison of the effective magnetic dispersions about Q AF for several different cuprate families is shown inFig. 2.The spectrum can be thought of in terms of two com-ponents, separated by an energy E cross at the waist ofthe hour glass. (We note that, while the q width of themagnetic scattering is smallest at E cross , it is a matterof taste whether one describes the q dependence thereas a single commensurate peak or a set of unresolved in-commensurate peaks.) The upwardly dispersing portion,above E cross , looks similar to what one would expect fromAF spin fluctuations with a finite gap, and it is relevantto note that the results for different cuprate families ap-pear to scale with J for the parent AF insulators. If oneconsiders a fixed excitation energy and looks at the distri-bution of spectral about Q AF , it is rather isotopic, with a possible diamond shape having points orientedalong [110] and [1¯10] directions.
28, 29, 34, 35)
Below E cross ,there appears to be a downward dispersion. A series ofstudies on detwinned single crystals of YBa Cu O x indicate that, at least for underdoped samples, the dis-tribution of spectral weight is quite anisotropic, with thedispersion effectively occurring only along the [100] direc-tion.
34, 36–39)
Such an anisotropy cannot be identified inunderdoped LSCO within the superconducting regime,as there is no structural anisotropy between the twoCu-O bond directions; however, the low-energy excita-tions disperse down to the incommensurate wave vectors( ± δ, ,
0) and ( , ± δ,
0) at E = 0. We will consider
2. Phys. Soc. Jpn.
FULL PAPERSFig. 2. (Color online) Magnetic dispersion relation along (0 . h, . , tetra in various cuprates, corresponding to wave vectorsparallel to the Cu-O bonds. Data are for La . Ba . CuO , La . Sr . CuO , YBa Cu O . , YBa Cu O . , andBi Sr CaCu O δ . The energy is scaled by J for the AF parentmaterial. the connection with stripe order in § Sr CaCu O δ (Bi2212) is of particular interest, as it is the prototyp-ical system for studies with angle-resolved photoemis-sion spectroscopy (ARPES) and scanning tunneling spec-troscopy (STS). The challenge has been to grow crystalsof sufficient size for inelastic neutron scattering studies.Initial experiments on smaller crystals allowed one toobserve the temperature-dependent development of theresonance peak below T c , but identifying the dis-persion was a challenge. Recently, large crystals ofoptimally-doped were successfully grown, enabling thedirect measurement of the magnetic excitations.
Theeffective dispersion is indicated by the open circles inFig. 2. The good consistency with the other systems sug-gests that this behavior is universal.
While the excitations dispersing upwardly from E cross appear to evolve into the AF spin waves as doping isreduced, the downwardly-dispersing excitations clearlyreflect the impact of the doped holes, as they have nosimple correspondence with any features of the parentAF. The temperature dependence of the spectral weightdistribution also reflects the behavior of the itinerantcharges. The development of a spin gap and the pile upof weight into a resonance peak are generally associatedwith cooling through T c .If the low-energy spin fluctuations are associated with particle-hole excitations near the Fermi level, then itis natural for a spin gap to develop when supercon-ductivity occurs and gaps out the low-energy electronicstates.
48, 49)
Interactions can pull magnetic weight belowtwice the superconducting gap energy, resulting in theresonance peak. This has been a very popular interpre-tation.
There are some results that the particle-hole excita-tion picture has difficulty explaining. For example, inLSCO the resonance occurs at an incommensurate wavevector,
24, 25) whereas the calculations tend to put it at Q AF . Also, the calculated spectra for T < T c havethe lower energy excitations dispersing in the directionsalong ( ± δ, ± δ ) and ( ± δ, ∓ δ ) (due to the nodalstructure of the superconducting d -wave gap),
48, 50–52) which is inconsistent with experiment.
As we discuss in § § The incommensurabil-ity of the low-energy excitations is then a direct resultof the doped holes. The development of a spin gap andresonance indicates a coherent response of the momentsto the superconductivity, but a thorough explanation interms of a stripe picture has yet to be provided.
How does the magnetic dispersion change as one goesfrom the AF to the SC phase? In LSCO, there is an in-tervening spin-glass regime, characterized by incommen-surate spin order, with the ordering wave vectors rotatedby 45 ◦ from those in the superconducting regime. Inorthorhombic notation, the spin ordering wave vectorsare (0 , ± δ, o , with δ ∼ x . Despite the rotation, themagnetic excitations exhibit a dispersion quite similar tothe hour-glass of the superconducting regime. Figure 3shows the dispersion determined for LSCO x = 0 . An interesting feature is that the low-energy spin fluc-tuations La . Sr . CuO disperse only along the [010]direction and not along [100], similar to the nematic-like response of YBCO x = 0 .
3, 0.35, and 0.45.
37, 38)
This dynamical anisotropy is present even above the on-set temperature of the static order. A theoretical studysuggests that the nematic-like response originates fromfluctuating spin stripes driven by the charge nematic or-dering.
The phenomenological model reproduces theobserved magnetic excitation spectra.The excitations at energies above E cross have beencharacterized by time-of-flight measurements on LSCO x = 0 . The original data have been reanalyzed by
3. Phys. Soc. Jpn.
FULL PAPERS La x Sr x CuO x =0.04 x =0.05(Zn0.03) x =0.04 ( T =290 K) x =0.05LBCO( x =1/8) h (cid:1) ( m e V ) q (r.l.u.) T <10 K Fig. 3. (Color online) Magnetic dispersion relation along q K in La . Sr . CuO (filled circles) below 10 K and at 290K (filled diamonds) (Ref. ). For comparison, magnetic dis-persion relations in other related compounds are also shown.The filled triangles, filled squares, and open squares are dataof La . Sr . Cu . Zn . O , La . Sr . CuO (Ref. ), andLa . Ba . CuO (Ref. ), respectively. It is noted that thepeak positions are 45 ◦ rotated in La . Ba . CuO . The thickshaded bars represent the full width at half maximum of the ex-citation peaks in La . Sr . CuO . The broken lines are visualguides. Hiraka et al. , and the dispersion is presented in Fig. 4.The high-energy dispersion is consistent with the spinwaves of the x = 0 phase, though with a slightly reduced J . Curves for LSCO x = 0 .
085 and 0.16 are also shown inFig. 4, and we can see that there is a gradual softeningof the high-energy excitations, which can be describedby a decrease in the effective J describing the disper-sion. At the same time, the low-energy, long-wavelengthexcitations disperse from the incommensurate wave vec-tors. Hole doping clearly reorganizes the excitations be-low E cross , but has a more modest effect on the effectivedispersion above it.Returning to Fig. 3, it is intriguing that the slope ofthe effective low-energy dispersion, which corresponds toa velocity, shows little variation with doping. If the veloc-ity is independent of doping, while the incommensurabil-ity is linear in x for x (cid:46) , then one would expect E cross to be proportional to x .
58, 59)
In Fig. 5, values for E cross extracted from neutron scattering studies
29, 32, 33, 60, 61) are plotted. Each symbol represents an estimate frominterpolating a parabola through the low-energy disper-sion, while the error bars indicate the energy range overwhich constant-energy cuts are consistent with a single ω ( m e V ) (1+ q , 0) (r.l.u.) x = 0 ( J = 132 meV) Spin-glass La x Sr x CuO ( x = 0.05), T = 10 K x = 0.0850.16 -0.2 0.40.2 Fig. 4. (Color online) Magnetic dispersion of spin-glass LSCOwith x = 0 .
05 determined by time-of-flight spectroscopy. The thickhorizontal bars (light blue) represent peak width from constant- ω cuts. For reference, results from LSCO with x = 0 (antiferro-magnetic insulator), 0 .
085 (underdoped superconductor), and 0 . peak of minimum width. The results are consistent with E cross ∼ x for x (cid:46) . This trend is opposite to the grad-ual decrease observed for high-energy, antiferromagnetic-like spin excitations, which we will discuss shortly.Given the continuous evolution of E cross with doping,providing a connection with La . Ba . CuO wherecharge and spin stripe order is known to occur, it isconsidered that charge stripes and moment modulationare likely to be an important part of the incommensurateresponse in the diagonal incommensurate phase. In termsof a stripe picture, the dominant magnetic interactionwould be superexchange within locally antiferromagneticdomains. There is still a challenge to understand whythe dispersion of the low-energy excitations is not sig-nificantly affected by the rotation in stripe orientation.One possibility suggested by Granath is that a diag-onal stripe might consist of a staircase pattern of bond-parallel stripes, in which case local interactions wouldbe independent of average stripe orientation. Granath found that such a pattern is necessary in order to obtainconsistency with the photoemission experiments. The magnetic excitations have been studied theoreti-cally in a wide range of doping on the basis of the Hub-bard model by Seibold and Lorenzana.
64, 65)
The mag-netic excitation spectra from the stripes almost repro-duce the overall feature of the hour-glass excitations.However, the calculations predict much larger values for E cross in the region of x < Furthermore, it is notedthat, while spin-wave calculations for a diagonal-stripemodel
59, 66) provide a good description of the magneticspectrum observed in insulating La − x Sr x NiO ,
67, 68)
4. Phys. Soc. Jpn.
FULL PAPERSFig. 5.
Plot of E cross vs. x in LSCO (filled circles),La − x Sr x Cu − y Zn y O (open triangle), and La − x Ba x CuO (open circle) (Refs. ). The dashed line is a guideto the eye. they have difficulty in reproducing the hour-glass-likespectrum in LSCO. Besides the dispersion, it is also important to considerhow the frequency-dependent magnetic spectral weightevolves with doping. Neutron scattering directly mea-sures the dynamical structure factor, S ( Q , ω ), which isproportional to χ (cid:48)(cid:48) ( Q , ω ) / (1 − e − (cid:126) ω/k B T ), where χ (cid:48)(cid:48) ( Q , ω )is the imaginary part of the dynamical susceptibility. Byintegrating χ (cid:48)(cid:48) ( Q , ω ) over Q (within a Brillouin zone)one obtains the local susceptibility, χ (cid:48)(cid:48) ( ω ). There is asum rule for S ( Q , ω ); integrating S over Q and ω yields (cid:104) S (cid:105) , corresponding in the present case to the mean-squared spin per Cu atom. The thermal factor connect-ing S and χ (cid:48)(cid:48) goes to unity as T →
0, so integrating thelow-temperature local susceptibility over ω also gives ameasure of the mean-squared spin.We begin by considering χ (cid:48)(cid:48) ( ω ) in LSCO x = 0 .
05, asshown in Fig. 6.
56, 57)
In the range of 50 to 150 meV, themagnitude is comparable to that for spin waves in theordered antiferromagnet at x = 0. There is a substantialupturn at low frequency, which appears to correspond tothe weight that correspond to the static order parameterin the AF. Thus, in the spin-glass phase, the frustrationof AF order by the doped holes causes the low-energycorrelations to remain dynamic. Comparing with the re-sults for LSCO x = 0 . indicated by the red curvein Fig. 6, we see that the enhanced low-energy weightappears to be suppressed as one moves into the super-conducting regime.We can also see from Fig. 6 that χ (cid:48)(cid:48) ( ω ) for x = 0 . x = 0 result for (cid:126) ω (cid:38)
200 meV. For x = 0 . et al. were the first to iden-tify this trend, and to show that it occurs in several dif-ferent cuprate families. In particular, they estimated theenergy (cid:126) ω ∗ at which χ (cid:48)(cid:48) ( ω ) falls to half of that for thatAF phase. In the top of Fig. 7, we have reproduced theirplot, together with a point for the LSCO x = 0 .
05 sam-ple. Further evidence for a universal trend of reduction ω (meV) χ ” ( ω ) ( μ B e V - C u - ) Spin-glass La x Sr x CuO ( x = 0.05), T = 10 K
110 0 100 200 300( x = 0)( x = 0.085) x = 0.05 E i E i E i Fig. 6. (Color online) χ (cid:48)(cid:48) ( ω ) at 10 K determined by pulsed-neutron scattering experiments. The line (light-blue) through thedata points is a guide to eyes. Results from LSCO with x = 0and 0 .
085 are indicated by solid lines (green and red, respec-tively). in magnetic bandwidth with doping is provided by Ra-man measurements of two-magnon scattering.
Stock etal. also pointed out that this energy scale is quite sim-ilar to the pseudogap energy that has been determinedfrom a number of electronic probes, such as ARPES andSTS.
We note that this energy scale is also virtuallyidentical to the energy gap determined from an analy-sis of the temperature dependence of the Hall effectin LSCO, and it has the same doping dependence asthe mid-infrared gap determined by optical reflectivitymeasurements on YBCO.
Why would magnetic spectral weight disappear abovethe pseudogap energy? Consider first the parent insula-tor phase. The AF order and spin-waves are well-definedthere because they occur at energies well below the gap( ∼ The superexchange en-ergy that drives the AF correlations is a consequence ofthe competition between the strong onsite Coulomb re-pulsion between Cu 3 d electrons and the kinetic energyof these electrons, which can be reduced by hopping be-tween neighboring sites. For this magnetic mechanismto survive hole doping, it should be favorable to main-tain a particle-hole excitation gap. When magnetic exci-tations exceed that gap, they may no longer be defined,a connection noted by Stock et al.
It has been estab-lished from ARPES studies that the pseudogap has astrong dependence on the electronic momentum k . For k oriented at ∼ ◦ to the Cu-O bonds (nodal direction),there is no gap, but the pseudogap is large for k paral-lel to the Cu-O bonds (antinodal direction). If we thinkabout charges in an AF background,
76, 77) then an elec-tron near the Fermi energy moving in the nodal direction
5. Phys. Soc. Jpn.
FULL PAPERS
Hole doping, p ω ( m e V ) I n s u l a t o r Z χ (a)(b) ω cross ω * LSCO ( x =0.05)LSCOYBCOfrom Matsuda et al. LSCOLBCOBSCCOYBCO from Stock et al.
LSCO ( x =0.05) Fig. 7. (Color online) (a) ω ∗ plot following Stock et al. , whereopen symbols indicate for a number of cuprates the energy at which χ (cid:48)(cid:48) ( ω ) becomes half of that of undoped La CuO . Stock et al. have pointed out that the p dependence (cid:126) ω ∗ is quite similar to thatof (cid:126) ω pg determined by various electronic probes. The crosses in-dicate E cross , from Fig. 5. The filled symbols are the correspondingpoints for LSCO x = 0 . (b) Plot of Z χ vs. hole doping forLSCO, where Z χ is the ratio of the frequency-integrated local sus-ceptibility to that predicted by spin-wave theory for a 2D AF. Filled symbol is for LSCO x = 0 .
05; open squares, LSCO; open circles, YBCO. can hop on the same AF sublattice; no spin flips are in-volved, so there is no conflict with the AF correlations.In contrast, an electron hopping in the antinodal direc-tion, along Cu-O bonds, can only do so by flipping spinsand disrupting the AF correlations. Thus, it is physicallyreasonable that the antinodal pseudogap sets an upperlimit for the existence of locally-AF spin correlations.There is also interesting structure and temperature de-pendence in the spectral weight for (cid:126) ω (cid:46) E cross . As men-tioned in §
2, near optimal doping and above, a spin gapopens below T c and weight moves into a resonance peakabove it. In YBCO and Bi2212, the resonance energy issimilar to E cross . In LSCO, the spin gap is much smallerthan E cross ; for optimal doping, the resonance energy is ∼
18 meV,
24, 32) and there is still a feature there justabove T c . Lipscombe et al. have followed the tem-perature evolution of the the structures in χ (cid:48)(cid:48) ( ω ) below E cross on cooling from 300 K to low temperature. Wehave plotted the doping dependence of E cross for the theLSCO-related samples with red crosses in Fig. 7 to con-trast it with (cid:126) ω ∗ . It is comparable to the upper limitsfor 2∆ sc , where ∆ sc is the effective superconducting gapdetermined at the edge of the Fermi arc, as identified ina recent ARPES study. The overdoped regime provides another opportunityto probe the relationship between spin fluctuations andsuperconductivity. The evidence for depressed magneticspectral weight at low frequencies has been discussed S ( ω ) ( μ B e V –1 f. u . –1 ) ω ( meV ) La Sr x CuO LBCO1/8(Ref. [2])
LBCO 1/8 Ei=140meVLSCO 25% Ei=140meVLSCO 25% Ei=80meVLSCO 30% Ei=140meV
Fig. 8. (Color online) S ( ω ) spectra of overdoped La − x Sr x CuO with x = 0 .
25 and 0.30 compared with La − x Ba x CuO with x =1 /
8, from Ref. previously.
More recently, Wakimoto et al. havemeasured the magnetic excitations of La − x Sr x CuO (LSCO) with x = 0 .
25 and 0.30 up to 100 meV usingpulsed neutrons at ISIS. They found that χ (cid:48)(cid:48) ( ω ) is di-minished over the entire energy range compared to un-derdoped samples. In particular, magnetic excitationsat ω <
60 meV have completely vanished in the non-superconducting x = 0 .
30 sample, as shown in Fig. 8.In related work, Lipscombe et al. reported a qualita-tively similar spin excitation spectrum in the overdoped x = 0 .
22 sample, with a strong depression of the localsusceptibility in the range of 40–70 meV. These resultsare consistent with a gradual suppression of AF spectralweight with overdoping, and in parallel with the reduc-tion in T c .The bottom panel of Fig. 7 shows Z χ , the ratio ofthe frequency-integrated χ (cid:48)(cid:48) ( ω ) relative to the spin-wavetheory prediction for a two-dimensional AF, obtainedfor LSCO. It demonstrates that doping causes a grad-ual decrease of the mean-square magnetic moment asone moves away from the AF phase. There are exper-imental indications for a similar trend in YBCO.
13, 81, 82)
Therefore it is likely to be a universal trend in the hole-doped cuprate superconductors that the antiferromag-netic spectral weight decreases with doping, especiallyin the overdoped regime. We note, however, that a re-cent resonant inelastic x-ray scattering (RIXS) study ofspin fluctuations in YBCO has interpreted the measure-ments as indicating rather little renormalization of J orreduction of spectral weight with doping. Further com-parisons of RIXS and neutron measurements on similarsamples are needed to resolve this discrepancy.Uemura has reviewed evidence that a reduced frac-tion of the normal-state carriers participate in the su-perfluid density for overdoped samples. He has arguedthat there may be a short length scale phase separa-tion between normal and superconducting regions. If AFspin correlations are important to the superconductivity,such a phase separation and the reduced superfluid den-sity in overdoped samples would be compatible with the
6. Phys. Soc. Jpn.
FULL PAPERS La Ba x CuO T SO LTLO LTLO+LTT T CO SO CO bulk SC
LTO T c T LT bulk SC LTT T e m p e r a t u r e ( K ) hole doping (x) Fig. 9. (Color online) Phase diagram for La − x Ba x CuO as afunction of temperature and doping as determined from single crys-tals. Transitions are indicated as follows: structural transition, T LT , (gray) squares; charge stripe order (CO), T CO , (blue) circles;spin stripe order (SO), T SO , (red) circles; bulk superconducting T c , (green) diamonds. The low-temperature phase is either low-temperature tetragonal (LTT), low-temperature less orthorhombic(LTLO), or a coexistence of the two. reduced magnetic spectral weight.
4. Stripes and superconductivity
The downward-dispersing excitations of the hour-glassspectrum connect (in the case of LSCO and LBCO), orextrapolate (in the case of YBCO), to the incommen-surate wave vectors associated with spin-stripe order.For 214 cuprates with a lattice symmetry that makes or-thogonal Cu-O bonds inequivalent, both charge and spinstripe order have been experimentally identified.
85, 86)
The role of charge and spin stripes has been controver-sial.
12, 13, 87)
Much of the focus has been in terms of a typeof order that competes with superconductivity; however,recent observations of two-dimensional (2D) supercon-ducting correlations coexisting with stripe order
88, 89) have led to suggestions of a more intimate connectionwith pairing and the phase of the superconducting orderparameter.
Several groups have explored the doping dependenceof stripe order in La − x Ba x CuO with neutron and x-ray scattering. A phase diagram for stripe orderin La − x Ba x CuO , as reported by H¨ucker et al. , isshown in Fig. 9. As one can see, the onset of chargestripe order is limited by the structural transition fromthe low-temperature orthorhombic (LTO) phase to thelow-temperature tetragonal (LTT); static spin stripe or-der develops at a lower temperature. When compar-ing the results from various studies, there are somequantitative discrepancies regarding stripe ordering tem-peratures at particular doping levels; however, theseare likely due to uncertainties in the Ba concentra-tion. It has been shown that the discrepancies canbe resolved by calibrating the composition through thedoping-dependent transition temperature from the high-temperature tetragonal phase (HTT) to the LTO, with the assumption that the transition temperature varieslinearly with x . Note that Dunsiger et al. have alsoconfirmed the rotation in stripe direction from verticalto diagonal on reducing x from 0.08 to 0.05 and 0.025.As demonstrated by Abbamonte et al. , charge stripeorder can also be detected by resonant soft x-ray diffrac-tion. That technique has now been used by Fink etal. to determine the phase diagram for charge or-der in La . − x Eu . Sr x CuO . The Eu-doped system isof interest because the charge-ordering transition is wellseparated from the structural transition, from LTO toLTT, whereas the structural transition appears to limitthe onset of charge stripe order in La − x Ba x CuO , asindicated in Fig. 9. The occurrence of spin stripe orderin La . − x Eu . Sr x CuO was previously determined bymuon spin-rotation spectroscopy and confirmed forone composition ( x = 0 .
15) by neutron diffraction.
An early observation of checkerboard-like modulationsin the electronic density of states for Bi Sr CaCu O δ and in Ca − x Na x CuO Cl observed by scanning tunnel-ing spectroscopy (STS) caused some researchersto raise questions about the interpretation of thespin and charge order peaks detected previously by neu-tron and x-ray diffraction. As a check, Christensen etal. used polarized neutrons to characterize the mag-netic superlattice peaks and the low-energy spin fluctu-ations in a crystal of La . Nd . Sr . CuO . Their re-sults were consistent with a unidirectional stripe modu-lation together with collinear spin order, although theycould not rule out a more complicated two-dimensionallymodulated noncollinear spin structure. It is interestingto note that more recent STS studies, especially onBi Sr CaCu O δ , have found that the electronic mod-ulations break four-fold rotational symmetry, consistentwith a locally unidirectional modulation. In fact,Parker et al. have shown that stripe-like modulationsin Bi Sr CaCu O δ are strongest for hole concentra-tions p ∼ /
8, similar to the 214 cuprates.As mentioned above, the detection
88, 89) of 2D super-conducting correlations, appearing concomitantly withspin stripe order, in La − x Ba x CuO with x = 1 / planes; however, the presenceof a Josephson coupling between the planes drives thesuperconductivity to 3D order before 2D order can bedetected. To explain the results in LBCO, it is necessaryto find a mechanism associated with the stripe order thatcan frustrate the interlayer Josephson coupling. The con-cept of the pair-density-wave (PDW) superconductor hasbeen proposed as part of one such mechanism.
90, 91)
Theidea is that the pair wave function has d -wave characterwithin each charge stripe, but, in contrast to the uniform d -wave state, the phase of the pair wave function changesphase by π from one stripe to the next, as indicated inFig. 10. When one combines this finite q superconduc-tivity with the fact that the stripe orientation rotates90 ◦ from one layer to the next in the LTT phase, it isnot hard to see that the Josephson coupling should aver-age to zero (for 3D long-range stripe order). The PDWstate was originally introduced to explain the decrease
7. Phys. Soc. Jpn.
FULL PAPERS
SDWCDW PDW
Fig. 10. (Color online) Schematic diagram of CDW, SDW, andPDW orders, indicating the relationships among the phases of themodulations. in the Josephson plasma resonance detected by c -axis in-frared reflectivity on approaching the LTT phase, andthe onset of stripe order, in La . − y Nd y Sr . CuO .In the case of La − x Ba x CuO , the PDW concept wasinitially expected to explain both the frustration of theinterlayer Josephson coupling and the onset of strong2D superconducting correlations; however, new exper-iments have led to a more complicated interpretation. Analysis of the gap structure of the PDW state in-dicates that there should be a large gap in the antin-odal electronic states, but that the nodal arc should begapless. In principle, a d -wave gap can develop on thenodal arc associated with a uniform d -wave state. Angle-resolved photoemission studies on LBCO x = 1 / d -wave-like gap at low tem-perature, with the near-nodal gap closing near 40 K, where the 2D superconducting correlations also disap-pear. A possible scenario is that PDW correlations de-velop together with the charge stripe order, and thatuniform d wave superconductivity develops on top of thisbelow 40 K.Stripe-like spin order is not unique to the 214 cuprates.Incommensurate elastic peaks have also been observed inYBa Cu O x with x = 0 .
3, 0.35, and 0.45 (correspond-ing to p = 0 . T c = 0, 10 K, and35 K, respectively) by Hinkov and coworkers.
37, 38)
Theability to resolve the split magnetic peaks was enabledby the use of detwinned crystals. (Stock et al. did notresolve incommensurability in the elastic magnetic scat-tering from an x = 0 . T c = 18 K, twinned crystal.) Infact, it was demonstrated that the spin modulation direc-tion is uniquely oriented with respect to the Cu-O chains;in particular, the spin and chain modulation directionsare parallel. Furthermore, Suchanek et al. found thatdoping YBCO x = 0 . δ is significantly smaller than p , in contrast to the behavior in 214 cuprates. The elastic magnetic peaks are only observed be-low T SDW ∼
40 K; however, the incommensurability inlow-energy magnetic excitations can be resolved up to ∼
150 K.
37, 38)
The onset of the anisotropy in the spin dynamics has been discussed in terms of the developmentof nematic electronic correlations.
The onset temper-ature is comparable to that for in-plane anisotropy ofthe Nernst effect, and also to the onset of bilayersuperconducting correlations identified by c -axis opticalconductivity. The elastic magnetic signal in YBCO disappears for x (cid:38) .
5, as a spin gap opens; nevertheless, a “1/8” effecthas been identified by Taillefer and coworkers by examin-ing transport properties in high magnetic fields. For ex-ample, they have shown that, when superconductiv-ity is suppressed by a c -axis magnetic field, the tempera-ture at which the thermopower changes sign is maximumat p = 1 / . − x Eu . Sr x CuO .Similarly, the temperature at which the Hall constantchanges sign in YBCO has a maximum at that samepoint. Boothroyd et al. have recently reported a study ofspin excitations in an insulating, stripe-ordered cobaltatesystem, La / Sr / CoO . The interesting feature here isthat the magnetic dispersion has the hour-glass shapeof the cuprates. This example clearly demonstrates thatsuch a dispersion can occur in the absence of itinerantelectrons. Neutron scattering studies of magnetic-field effects onthe incommensurate spin density wave (SDW) order fromthe stripe phase, as well as on the dynamical spin excita-tions, have been performed mostly using the LSCO sys-tem. This system exhibits the SDW order in the under-doped superconducting regime (0 . < x < .
14) whilethe system has a gap in the spin excitations in the opti-mally and slightly overdoped regime (0 . < x < . et al. whoreported a small enhancement of the incommensuratemagnetic order in LSCO with x = 0 .
12 by applicationof magnetic field of 10 T along the c -axis. More drasticenhancement by magnetic fields were observed in under-doped LSCO and stage-4, 6 La CuO y . The Ba-doped system LBCO is known to have a ro-bust stripe order and a limited superconducting phasenear 1/8 doping associated with the LTT structure. Themagnetic field effect on the stripe order was reported tobe very limited in underdoped LBCO and in LBCOwith x = 1 / Nd-doped La − x Sr x CuO also has awell-developed stripe order. In this case, a c -axis mag-netic field suppresses the subordinate order of Nd spins,but the stripe order itself is not affected by magneticfields up to 4 T. These results indicate that the mag-netic field generally enhances the SDW state at a costof the superconducting volume faction, but the degreeof enhancement depends on the volume fraction of SDWand superconducting phases in zero field. This behaviorsuggests that the “normal” state achieved by the sup-pression of superconductivity in magnetic vortex coresinvolves stripe order.
8. Phys. Soc. Jpn.
FULL PAPERS angle neutron scattering. For x = 0.145, we observe a VL re-sembling that at optimum doping but only for ! H " x = 0.12, where the largest elasticfield effect is observed. Although vortices might exist in dis-ordered structures, we find it difficult to correlate the elasticfield effect with vortex matter physics. Instead, we interpretour data in terms of competing order parameters. Recently,we reported the observation of a single d -wave gap in theangle-resolved photoelectron spectroscopy ! ARPES " spectraof the x = 0.145 sample. The most likely ZF ground state of x = 0.145 is therefore pure d -wave SC similar to that ob-served at optimum doping. Application of a magnetic fieldtunes the system into a different ground state where static ICAF coexists with SC. This ground state resembles that ofmore strongly underdoped LSCO ! x " " , where static AFand SC orders compete even in ZF. For x ! H = 15 T is close to that the 1/8 groundstate ! see Fig. 3 " . Therefore we argue that the effect of theapplied field is to drive the system toward the 1/8 groundstate. IV. CONCLUSIONS
To summarize our combined ! SR and neutron-diffractionexperiments, we present in Fig. 4 a schematic ! H - x phasediagram, in which the ordered Cu moment is depicted by afalse color scheme. The 1/8 state and the pure d -wave SCground state are pictured as the dark red and the blue regions,respectively. Colors in between represent a state where AFand SC coexist. With the application of a magnetic field, onecan tune the pure SC state into the mixed state of AF and SC.At the specific doping x = 0.12, we found that the field drivesthe system toward the 1/8 state. The different ground statesare therefore very close in energy. Our results clearly supportthe notion of competing SC and static AF order parameters.The systematics of our data shows that the existence of AF isintrinsic and not due to defects or chemical inhomogeneities.Any suppression of superconductivity either by a change inchemistry or by an external perturbation goes along with aconcurrent and systematic enhancement of static magnetism. ACKNOWLEDGMENTS
This work was supported by the Swiss National ScienceFoundation ! through NCCR, MaNEP, and Grants Nos.200020-105151 and PBEZP2-122855 " and the Ministry ofEducation and Science of Japan. A major part of this workwas performed at the Swiss spallation source SINQ and theSwiss Muon Source, Paul Scherrer Institut, Villigen, Switzer-land. * [email protected] C. Niedermayer, C. Bernhard, T. Blasius, A. Golnik, A. Mood-enbaugh, and J. I. Budnick, Phys. Rev. Lett. , 3843 ! " . A. R. Moodenbaugh, Y. Xu, M. Suenaga, T. J. Folkerts, and R.N. Shelton, Phys. Rev. B , 4596 ! " . J. Tranquada, B. Sternlieb, J. Axe, Y. Nakamura, and S. Uchida,Nature ! London " , 561 ! " . J. M. Tranquada, J. D. Axe, N. Ichikawa, Y. Nakamura, S.Uchida, and B. Nachumi, Phys. Rev. B , 7489 ! " . N. B. Christensen, H. M. Rønnow, J. Mesot, R. A. Ewings, N.Momono, M. Oda, M. Ido, M. Enderle, D. F. McMorrow, and A.T. Boothroyd, Phys. Rev. Lett. , 197003 ! " . J. D. Axe, A. H. Moudden, D. Hohlwein, D. E. Cox, K. M.Mohanty, A. R. Moodenbaugh, and Y. Xu, Phys. Rev. Lett. ,FIG. 4. ! Color " Schematic doping-field phase diagram forLa − x Sr x CuO . The ordered moment is given in false colors withred ! blue " as the maximum ! minimum " . Magnetic Field (T) O r d e r e d m o m e n t( µ l o / µ l o ( / )) x =0.145, T=2 K x =0.105, T=2 K x =0.12, T=2 KLa . Nd . Sr . CuO , T=15 K FIG. 3. H dependences of the response at Q IC for LSCO x =0.105, x =0.12, x =0.145, and LNSCO. The solid lines are fits to ! = $ I ! H " $ ! H / H c " ln ! H c / H " ! Ref. 33 " . Here the ZF moments es-timated by ! SR are used and the gray colors indicate the errorrelated to the determination of the ZF order moment. The x =0.145 data are presented in arbitrary units.CHANG et al. PHYSICAL REVIEW B , 104525 ! " Fig. 11. (Color online) Phase diagram indicating relative mag-nitude of ordered magnetic moment as a function of magnetic fieldand hole doping in LSCO. Reprinted with permission from Chang et al. c (cid:13) The magnetic field effect on dynamical spin fluctua-tions was first reported by Lake et al.
They found thatapplication of a 7.5-T magnetic field on the spin-gapped,optimally-doped LSCO induces an additional spin fluc-tuation spectrum below the gap energy. Further detailedmeasurements have shown the redistribution of the spec-tral weight from above to below the gap energy.
25, 134, 135)
The study of magnetic field effects can provide a testof the theoretical prediction of a quantum phase tran-sition between the superconducting phase and one in-volving the coexistence of SDW and superconducting or-ders.
Khaykovich et al. performed a detailedstudy of LSCO samples with x between 0.14 and 0.15,evenutally finding that a finite magnetic field inducesSDW order in the x = 0 .
144 sample, which is pure su-perconducting phase, with a small spin gap, in zero field.This is direct evidence of the quantum phase transition,and the composition x = 0 .
144 is in vicinity of the quan-tum critical point. Later, Chang et al. have observedthe magnetic-field-induced SDW order for x = 0 . ∼ ∼ Combinedwith the results of muon spin rotation ( µ SR) studies,they have summarized the situation with the schematicdoping-field phase diagram shown in Fig. 11.Recently, in a study of LBCO with x = 0 . Weak charge order is generally more difficult to detectthan spin order, which might explain why this effect wasnot detected before. Given the strong connection betweencharge and stripe order, there is a good possibility thatthe field-induced SDW results also have an associatedcharge order.The impact of a magnetic field on magnetic correla-tions has also been studied in YBCO. Measurements ondetwinned crystals of x = 0 .
35 and 0.45 showed an en-hancement of the elastic incommensurate magnetic sig-nal,
38, 138) with a greater relative increase for x = 0 . et al. on YBCO x = 0 .
33 and 0.35 (twinned) crystalsfound no field enhancement of the elastic magnetic inten-sity; however, a field was found to enhance the inelasticmagnetic response for energies (cid:46)
5. Impurity effects and related studies
Impurities in cuprates modify the carrier mobility andthe spin correlations. Therefore, impurity substitutionprovides invaluable information on the interplay betweensuperconductivity and magnetism in cuprates. In partic-ular, contrasting effects of nonmagnetic Zn and magneticNi impurity have been extensively studied. From µ SRstudies by Nachumi et al. , a “swiss cheese” modelwas proposed for Zn-doped LSCO and YBCO: a Znimpurity locally destroys superconductivity and inducesstatic spin correlation. Furthermore, scanning-tunneling-spectroscopy studies on Zn-doped and Ni-doped Bi2212 have revealed that superconductivity is locallydestroyed around a Zn atom, in contrast to weak degra-dation around a Ni atom. As for the effect of impuri-ties on magnetism, quasielastic magnetic peaks were firstobserved by Hirota et al. in 1.2% Zn-doped LSCO( x = 0 . T c = 19 K). Subsequent neutron scatter-ing studies by Kimura et al. revealed that dilute Zndoping into optimally doped LSCO induces excitationswithin the spin gap, much like the magnetic-field-inducedin-gap excitations. Based on the “swiss-cheese”model, it is likely that the in-gap excitations are pro-duced locally by the Zn. With increasing Zn concentra-tion, the in-gap state is enhanced, and the spin corre-lations become more static as superconductivity is sup-pressed.The contrasting Zn and Ni impurity effects on spincorrelations have been studied in optimally-doped LSCOby Kofu et al. using neutron scattering. Figure 12(top) shows peak profiles of the incommensurate elasticpeak for La . Sr . Cu − y A y O with A = Zn: y = 0 . T c = 16 . A = Ni: y = 0 .
029 ( T c = 11 . y = 0 . y = 0 . ω = 0 owing to coarse energy resolution. Thus, diluteNi impurities do not induce static spin order, whereas asmaller concentration of Zn impurities does. In addition,Kofu et al. found that dilute Ni doping does not in-duce the in-gap state, but, instead, reduces the spin-gapenergy. The reduction of the gap energy seems to corre-spond to the reduction of T c by Ni. Such scaling behaviorstrongly suggests the renormalization of the characteris-tic energy of the spin excitations. A similar discussionwas made by Tokunaga et al. based on NMR results.Matsuura et al. have performed extended neutronscattering studies on Zn- and Ni-doped LSCO to higherenergies. Figure 13 shows the contrasting effect of thetwo types of impurities on the spin excitation spectra.Zn doping does not drastically change the peak profile,
9. Phys. Soc. Jpn.
FULL PAPERS width ! T c is almost constant as a function of the Zn concen-tration, while ! T c broadens with increasing Ni. It seems thatthe effects on the spin-gap state are associated with thechange of the electronic state of the superconductivity.
4. Inhomogeneous picture
For impurity-doped systems, spatially inhomogeneouspictures have been proposed ; impurities make the non-superconducting island with radius " in the superconducting sea and induce local moments in the island. Our results re-vealed that the magnetic excitations in Zn-doped LSCO con-sist of two components: the spin-gap state and in-gap state.Combining these results, we thus consider that the supercon-ducting sea gives the spin-gap state and the coherence be-tween the local moments inside the nonsuperconducting is-land results in the in-gap state. In our speculation, thecoherence of local moments is connected across the super-conducting sea, which we call an interisland correlation. Wediscuss in detail this correlation in Sec. IV B.In Ni-doped LSCO, we observed no evidence for the in-gap state. SR studies and uniform susceptibility measure-ments suggest that Ni also induces local moments in a non-superconducting island similar to Zn.
However inthese studies, the estimated value of radius " induced by Niis smaller than the case of Zn doping. In the case of Nidoping, therefore, it is considered that the interisland corre-lation extends not enough to be detected by neutron scatter-ing due to small " . lower temperature appear at a lower tem-perature Thus, we conclude that the in-gap state is invisibleand that we only observed the spin state of superconductingsea in the case of Ni doping.We schematically show our concept in Fig. 13 from aviewpoint of the inhomogeneous picture. Zn induces nonsu-perconducting islands and hardly affects the superconductingsea, so that the spin-gap state and ! T c are almost unchanged.On the contrary, Ni primarily influences the sea. In otherword, Ni affects the electronic and magnetic states of thesuperconductivity, leading to the modified spin-gap state andthe broadening of ! T c . B. Zn doping effects: The in-gap state
A primary effect by Zn on the spin excitations is the ap-pearance of an in-gap state. The most obvious evidence forthe in-gap state is the upturn in the temperature dependenceof $ ! ! Q % , & " at & =3 meV. Previously Kimura et al. reportedthe upturn behavior in Zn: y =0.008. In the present study,we also confirmed the upturn behavior in Zn: y =0.011. InYBa ! Cu − y Zn y " O ! y =0.02 " , similar results have beenreported by Sidis et al. Their inelastic neutron scatteringmeasurements showed that magnetic signals emerge around & $ ! at & =10 meV is almost temperature independent below T c . Theirresults indicate the coexistence of the in-gap state with thespin-gap state at low temperature, signifying that the appear-ance of in-gap state is a universal phenomenon in Zn-dopedhigh- T c cuprates. Note that the in-gap state appears at thesame Q position as that of the normal and high-energy statesfor both LSCO and YBCO. Therefore, Zn locally slows spinfluctuations without modifying the AF wave vector. In otherwords, Zn seems to act as a pinning center of AF spin fluc-tuations.As for Zn: y =0.017, the in-plane static spin correlationlength " ab !
80 Å " is much longer than R Zn-Zn !
29 Å " FIG. 12. The incommensurate elastic peak intensities as a func-tion of temperature for La Sr Cu − y Zn y O ! Zn: y =0.017 " andLa Sr Cu − y Ni y O ! Ni: y =0.029 " . The top figures show q pro-files along ! a " the k direction ! trajectory C in Fig. 2 " for the Zn-doped sample and ! b " the h direction ! trajectory D in Fig. 2 " for theNi-doped sample at 1.5 and 40 K. Solid lines represent the result offits by a Gaussian function. ! c " Temperature dependence of intensityat the peak position Q = ! − " for the Zn-doped sample.Solid and dashed lines are guides to the eye and estimated back-grounds. ! d " Temperature dependence of peak ! solid circles " andbackground ! open circles " intensities for the Ni-doped sample. Peakintensity corresponds to the average of intensity at Q = ! − " , ! − " , and ! − " , and backgroundintensity corresponds to the average of intensity at Q = ! − " and ! − " . Solid and dashed lines are guidesto the eye of peak and background.Zn AND Ni DOPING EFFECTS ON THE LOW-ENERGY … PHYSICAL REVIEW B , 064502 ! " Fig. 12. (Top panels) The incommensurate elastic peak profilefor La . Sr . Cu − y A y O with A = Zn: y = 0 .
017 ( T c = 16 . A = Ni: y = 0 .
029 ( T c = 11 . which remains incommensurate up to at least 21 meV,while for Ni doping a broad commensurate peak appearsby 15 meV. The former effect is attributed to the lo-cal pinning effect of Zn, while latter is consistent witha reduction of the characteristic energy by Ni doping.Therefore, Matsuura et al. predicted a reduction ofthe crossover energy E cross , at which a commensuratepeak starts to appear. They also proposed that Ni dopingrenormalizes the upper branch of the hour-glass disper-sion, with the energy scale of the branch directly relatedto T c .What is the origin of the different impacts on high- T c superconductivity and spin dynamics between Zn and Niimpurities? Is it simply associated with the non-magneticnature of Zn ( S = 0) and the magnetic nature ofNi ( S = 1)? One possibility is that each Ni dopantmight tend to localize a hole near it. To test thisidea, polarized X-ray-absorption-fine-structure (XAFS)measurements were performed at the Ni K -edge on sin-gle crystals La − x Sr x Cu − y Ni y O . The measure-ments revealed two distinct types of Ni-dopant site, withsignatures given by shifts in the edge energy and in ω ω ω Fig. 13. (a)-(c) Profiles of constant-energy scan along the[100] ortho direction around the AF zone center ( h = 1 .
0) at T = 11 K for La . Sr . Cu − y A y O with A = Ni: y = 0 . A = Zn: y = 0 .
017 (solid circles).
The rightaxes for rhw Zn data are shifted for ease of comparison. The dottedlines indicate background. R Ni − O(1) , where R Ni − O(1) is the interatomic distance be-tween Ni and in-plane oxygen O(1) (Fig. 14). A statewith a higher valence than Ni was observed for x eff ( ≡ x − y ) ≥
0, while a state consistent with Ni was foundfor x eff <
0. The higher-valence state is most likely de-scribed by Ni L with S eff = 1 / L represents a ligandhole), rather than Ni , as proposed previously. In otherwords, a hole is strongly bound around Ni on neighbor-ing oxygen orbitals, thus forming a Zhang-Rice doubletstate; this picture is supported by theory. It is alsoconsistent with recent experimental work by Tanabe etal. based on specific heat and µ SR measurements.They claimed that a Ni dopant changes its characterfrom a strong hole absorber, in the underdoped region,to a Kondo scatterer in the overdoped, metallic region.Therefore, the impact of a hole-trapped Ni impurity onthe Cu-spin network must be small in magnitude and ex-tended in space, resulting in the renormalization of theenergy scale for magnetic fluctuations.
This is apossible reason for the smaller effect of hole-trapped Nion high- T c superconductivity, as compared to nonmag-netic Zn.
10. Phys. Soc. Jpn.
FULL PAPERS La x Sr x Cu y Ni y O K -edge , E // CuO plane, T = 290 K -100 -10 0 10 20 x eff (= x - y ) R N i - O ( ) ( Å ) Ni-O(1)in La NiO Cu-O(1)in La CuO Fig. 14. (Color online) The bond length R Ni − O(1) inLa − x Sr x Cu − y Ni y O as a function of x eff determined by Ni K -edge XAFS measurements. The hole and Ni concentrationsare expressed as (100 x − y ). The upper and lower arrowscorrespond to the Ni-O(1) distance in La NiO and the Cu-O(1)distance in La CuO , respectively. At ambient pressure, the lattice distortion associatedwith the CDW order has so far been observed only inthe LTT phase. (We note that CDW order was observedin the pressure-induced HTT phase of LBCO by X-ray diffraction measurement. ) In particular, there hasbeen no diffraction evidence reported for CDW order inthe LTO phase, though we have seen that thereis evidence for SDW order. Thus, the degree to whichCDW and SDW order appear together is in question. Toshed more light on this issue, the impurity effect on bothspin and charge orders has been investigated in Fe-dopedLSCO (Fe-LSCO), where the average LTO crys-tal structure is not affected by the small concentrationof Fe dopants.Peak profiles for SDW order inLa . Sr . Cu . Fe . O are shown in Fig. 15(a). Fourincommensurate (IC) peaks are located at (0 . , . ± δ, . ± δ, . ,
0) positions with δ = 0 . ± . . Sr . Cu . Fe . O system. Indeed, the SDWorder in Fe-free LSCO was difficult to detect under theidentical experimental setups. The onset temperature forthe appearance of SDW peaks ( T m ) of ∼
50 K is slightlyhigher than T m ∼
40 K in LSCO. The enhancement ofpeak intensity and the ordering temperature suggest thestabilization of SDW order by Fe-doping.Even more importantly, an IC peak from CDW or-der was detected in the Fe-doped LSCO sample, asshown in Fig. 15(b). At low temperature, a clear en-hancement of intensity was observed at (0 , ± (cid:15),
0) with (cid:15) = 0 . ± . ≈ δ . Since the well-defined CDWorder has not been detected in the Fe-free LSCO, theobservation of CDW order in the present system indi-cates the inducement (or strong enhancement) of CDWorder by Fe-doping. Surprisingly, the onset temperaturefor the appearance of CDW order is close to that in theLBCO system, in which the well-stabilized CDW order isrealized at low temperature. Furthermore, the volume- C oun t s / m i n k (r.l.u.) (b) CDW
400 600 800 1000 0.3 0.4 0.5 0.6 0.7 C oun t s / m i n (a) SDW (0 k k La Sr Cu Fe O Fig. 15.
Incommensurate peaks from (a) SDW and (b) CDWorders in the LTO phase of La . Sr . Cu . Fe . O measuredat low-temperature (closed circles) and high- temperature (opencircles). corrected intensity in the present Fe-doped LSCO is halfof that in LBCO. Therefore, the Fe doping has stabilizedbulk CDW order, not just local patches. Indeed, the co-herence length for the lattice distortion evaluated fromthe width of the CDW peak, 60 ˚A, exceeds the meandistance between nearest-neighbor Fe ions ( ∼
38 ˚A).
Thus, bulk stripe order, which is identical to that ob-served in the LTT phase, indeed exists in the presentsystem with LTO structure, and the static stripe ordercan be realized by impurity substitution as is expectedfrom the the stripe-pinning picture.
The Fe-doping in the underdoped region stabilizesstripe order, as presented above. In contrast, Fe-dopingeffects in the overdoped regime have suggest a differentbehavior. Hiraka et al. substituted Cu sites with Fespins in overdoped Bi . Pb . Sr . CuO z , a systemfor which both neutron scattering and µ SR experimentshave never detected any sign of magnetic correlations.The Fe substitution resulted in short-ranged incommen-surate static spin correlations. Interestingly, the observedincommensurability of δ = 0 .
21 is far beyond the upperlimit of δ ∼ .
13 observed so far for LSCO and YBCO.Instead, δ is close to the hole concentration p ∼ . δ in various compounds. Wakimoto et al. concluded from the magnetic field dependences
11. Phys. Soc. Jpn.
FULL PAPERS (Bi,Pb)2201+Fe,
As-grown δ (r . l . u . ) hole doping, p δ = p LSCOYBCO (Bi,Pb)2201+Fe N e t , I K - I K (1/2, k , 0) tet (k cts/~15 min) δ Fig. 16. (Color online) Comparison of δ of the parallel spinmodulation between Fe-doped (Bi,Pb)2201, pristine LSCO, andYBCO. The inset shows magnetic, incommensurate elasticpeaks from Bi . Pb . Sr . Cu . Fe . O z (as-grown, over-doped sample). Dynamical data are plotted for LSCO ( ω = 3 − ω (cid:28) (resonance energy)). The solid line is aguide for LSCO and YBCO data. The dashed line shows the linearrelation δ = x . of resistivity and spin correlations in the Fe-doped Bisystem that RKKY coupling between the Fe-spins viaconduction electrons is the most plausible origin of theincommensurate spin correlation, which is rather differ-ent from the underdoped region. Substitution of Cu siteswith Fe spins for overdoped LSCO induces a similar in-commensurate static spin correlation. In this case, the δ is also larger than 0.12 and monotonically increases withincrease of carrier concentration up to near the upperboundary of superconductivity. ARPES experimentson the same system predict a similar doping dependenceof the δ in the overdoped region based on Fermi-surfacenesting.These results strongly suggest a change in the degree ofelectronic correlation between the underdoped and over-doped regions. Concerning the orbital character of car-riers in cuprates, comprehensive studies have concludedthat the doped holes predominantly enter into the oxy-gen 2 p orbital at least up to optimal doping. Asa result, the unusual physical properties of underdopedcuprates have been analyzed mainly by ascribing a sin-gle orbital character to the doped holes. However, in theoverdoped cuprates the orbital character is not fully un-derstood, even though distinct doping dependencies of x-ray absorption and optical reflectivity spectra between the underdoped and overdoped regions suggesta change in the oxygen 2 p orbital character with over-doping.In a recent study on single crystals of LSCO covering abroad range of doping, high-resolution Compton scatter- ing measurements confirmed the change of orbital statewith overdoping. The holes in the underdoped regimeare found to primarily populate the O 2 p x /p y orbitals.In sharp contrast, holes mostly enter Cu- e g orbitals inthe overdoped system. These studies in the overdopedregion reveal how the standard Zhang-Rice picture ofdoped holes in this strongly correlated cuprate systemevolves into a more conventional mean-field descriptionof electronic states as correlations weaken with doping.
6. Electron doping
In electron-doped ( n -type) high- T c cuprates there re-main more unsolved issues than in hole-doped ( p -type)cuprates. Here, we briefly review doping dependenceof low-energy magnetic excitations of n -type cupratesand compare the results with those for p -type cuprates.Low-energy magnetic excitations exhibit commensuratepeaks centered at Q AF for both antiferromagnetic andsuperconducting phases, in contrast to the incommensu-rate ones for the p -type superconducting cuprates. Carrier doping or annealing under reduced atmospherebroadens the peak width of the commensurate magneticsignal.Wilson et al. performed inelastic neutron scatter-ing experiments on Pr − x LaCe x CuO δ (PLCCO) with x = 0 .
12 and several different oxygen concentrations atvarious temperatures ( T ) with energies up to ∼ T -insensitive magnetic excitation spectrum near the opti-mally doped SC phase.An alternative approach was taken by Motoyama etal. in a study of Nd − x Ce x CuO (NCCO) where theyperformed neutron total scattering measurements. Fromthe thermal evolution of instantaneous spin-spin corre-lation length, they extracted the effective spin stiffness.The spin stiffness is well-defined in the AF phase, de-creasing with increasing x , and eventually reaching zeroat the AF-SC boundary. Within the SC phase, the spincorrelation length is temperature independent, with amagnitude comparable to the superconducting coherencelength.Fujita et al. performed comprehensive neutron in-elastic scattering experiments on PLCCO over a widedoping region, extending close to the upper critical con-centration for superconductivity, to elucidate the natureof low-energy spin fluctuations in the SC phase. Lookingat how the effective dispersion, the excitations appear toform a filled cone with its tip at Q AF and (cid:126) ω = 0. Fromconstant energy scans, one can extract the half-width-at-half-maximum as a function of momentum, κ , which isplotted in Figure 17 for a series of samples. For each con-centration, κ increases linearly with ω up to ∼
12 meV.The inverse of the slope, ρ s = ω/κ , defines the low energyspin stiffness, which decreases linearly with increasing x within the entire SC region, as shown by the green cir-cles in Fig. 18. Extrapolation indicates that ρ s goes tozero near the SC/non-SC phase boundary ( x c ∼ . x c ∼ .
21 is
12. Phys. Soc. Jpn.
FULL PAPERS x =0.15 x =0.18 x =0.09 (cid:116) (meV) (cid:103) - ) Pr x LaCe x CuO (cid:98) , T =8K x =0.07 x =0.11 hk (cid:116) scan-direction x =0.13 Fig. 17. (Color online) ω -dependence of resolution correctedpeak-width (half width at half maximum) κ of commensurate peakfor Pr − x LaCe x CuO with x = 0 .
07, 0.09, 0.11, 0.15 and 0.18, fromRef. well below the percolation limit, ∼ . in thetwo-dimensional square-lattice spin system. Therefore,the observed degradation is not explained by the sim-ple model of randomly-diluted quantum spins.Such contrasting doping dependences of spin stiffnessdefined either by the thermal evolution of the instanta-neous (energy-integrated) spin correlation length or bythe energy dependence of the low-energy spin dispersionwidth strongly suggests the contrasting nature of spinfluctuations between the AF and SC phases, which ispossibly attributed to the existence of a quantum criti-cal point (QCP) at the phase boundary in the electron-doped cuprates. Furthermore, Fujita et al. found alinear relation between T c and the characteristic energyΓ, at which the q -integrated intensity around Q AF showsa maximum, consistent with the doping dependence ofthe low-energy spin stiffness mentioned above.In the case of n -type PLCCO, the overall spectralweight does not change much with doping concentra-tion, even in the overdoped region (see the inset of Fig.18). This suggests that even in the SC phase localizedspin character remains in the low energy region. Thisis one possible reason why a simple band model cannotreproduce the commensurate nature of the spin fluctua-tions in the n -type cuprate. The continuous degrada-tion of the effective magnetic interactions and the peak-broadening upon doping reflects a more homogeneouselectronic state in the electron-doped cuprates than inthe hole-doped ones. Such contrasting behavior can beunderstood if we consider the difference in the orbitalcharacter of doped carriers in the n -type and the p -typecuprate. In the case of n -type, the doped electrons gointo the Cu 3 d -orbitals and continuously degrade thespin correlations as the excess electron concentration in-creases. On the other hand, in the case of p -type, dopedholes first enter into O 2 p -orbitals. Upon overdoping,however, the holes start entering also into Cu 3 d -orbitalsyielding two types of locations for holes, that may cause x AFM (cid:116) / (cid:103)
800 400 0 Pr x LaCe x CuO (cid:98) , T =8K non-SC
200 150 100 50 0 (cid:47)(cid:108) s _ N CC O ( m e V ) AFM+SC SC -3 (cid:114) ( (cid:116) ) d (cid:116) ( µ B / f . u . ) (cid:116) = m e V (cid:116) = m e V Fig. 18. (Color online) Doping dependence of the low energyspin fluctuations: (a) the spin stiffness, ω/κ , and (b) the partialspectral weight obtained by integrating χ (cid:48)(cid:48) ( ω ) from 2 meV to 11meV, as a function of x . Dashed lines are guides to the eye. FromRef. the inhomogeneous phase separation.
79, 84, 186, 187)
The resonance like enhancement of magnetic signal inthe low-energy spin excitation has been independentlystudied by two groups. For PLCCO with T c = 24 K, Wil-son et al. found a resonance-like peak at Q AF withthe energy E r ∼
11 meV ∼ . k B T c , and they claimedthe similar relation between E r and T c for both p -typeand n -type cuprates. On the other hand, for NCCO with T c = 25 K, Yu et al. revealed two distinct magneticenergy scales in the superconducting state: 6.4 meV and4.5 meV, both of which are much smaller than the reso-nance energy for PLCCO. According to their interpreta-tion, the former energy is the maximum superconduct-ing gap, but the origin of the latter has remained unex-plained. They also discussed that the latter energy is con-sistent with a resonance and with the recently establisheduniversal ratio of resonance energy to superconductinggap in unconventional superconductors. However, Zhao et al. independently performed a neutron inelasticscattering experiment on NCCO with T c = 25 K andfound a resonance-like enhancement of magnetic signal at ∼ T c in the NCCO system. Very recently, Zhao et al. have combined neutronscattering and scanning tunneling spectroscopy (STS)measurements on a pair of PLCCO samples. They foundevidence both for a resonance peak and in-gap excita-tions. The STS results indicate that the spin resonance(in-gap signal) is correlated (anti-correlated) with themagnitude of the superconducting gap, which varies on
13. Phys. Soc. Jpn.
FULL PAPERS La Ba CuO (cid:114) ( (cid:116) ) ( µ B / e V / f . u . ) (cid:116) (meV)
100 150 Pr LaCe
CuO Fig. 19.
Energy dependence of local susceptibility χ (cid:48)(cid:48) ( ω ) for Pr . LaCe . CuO , from Ref. Results forLa . Ba . CuO is referred by a dashed line. the scale of nanometers. As shown in §
3, neutron-scattering experiments haverevealed a remarkable similarity of the overall magneticexcitation spectrum in the hole-doped cuprates. In theelectron-doped superconducting cuprates however, onlytwo independent neutron scattering experiments have ex-plored the overall spin excitation spectrum. The exper-iment on PLCCO with x = 0 .
12 sample ( T c = 21 K)by Wilson et al. found that the effect of electron-doping is to cause a wave-vector broadening in the low-energy ( E <
80 meV) commensurate spin fluctuationsat Q AF and to suppress the intensity of spin-wave-likeexcitations at high energies ( E >
100 meV). The ob-tained magnetic dispersion is anomalous. If they fit itby a two dimensional spin wave dispersion, the near-est neighbor interaction J is obtained to be ∼
162 meVwhich is much larger than that of non-doped Pr CuO ( J ∼
121 meV).
Furthermore, the local spin suscep-tibility χ (cid:48)(cid:48) ( ω ) is anomalously smaller than those of non-doped La CuO and hole-doped La . Ba . CuO .An independent high-energy inelastic neutron scatter-ing experiment was performed by Fujita et al. using alarge number of single crystal of optimally doped PLCCO( x = 0 . T c = 25 . Q AF in a wide energy rangeup to ∼
180 meV, except for a gap at (cid:126) ω ∼
60 meV, asshown in Fig. 19. As the energy transfer (cid:126) ω increases,the commensurate peak broadens and weaken in inten-sity, consistent with the results of Wilson et al. How-ever, the observed high-energy excitations, at least upto 180 meV, are difficult to understand by the conven-tional spin-wave approximation because the expected up-per bound energy from the value of J evaluated in thelow-energy region is only ∼
120 meV. Therefore, the au-thors predict a different nature for the high-energy spinexcitations from that of the low energy excitations inthe electron-doped cuprate. In fact, in the high-energyregion between 100 and 180 meV, the q width shows lit- tle variation with (cid:126) ω and is comparable to the value at ∼
60 meV; the overall q -dependence of the spin exci-tations is approximately pencil-shaped, as illustrated inFig. 20. The spin excitations extending up to the high-energy region remind us of similar spectra observed inthe nearly antiferromagnetic metals Cr . V . andMn . Fe . Si.
The persistence of the high-energy spin fluctuationsaround Q AF is consistent with a result from Fermi liquidtheory which shows that the spin fluctuations in thenarrow range of momentum space around Q AF weakensthe pairing interaction, so that T c becomes lower com-pared to the case of the hole-doped system. Combinedwith the fact that commensurate low-energy spin fluctu-ations can not be reproduced by a band model, this simi-larity suggests that the itinerant nature of electrons is thepossible origin of high-energy spin excitations. The dualstructure of the spin excitations would reflect a crossoverin the nature between the itinerancy and the localizationof electrons, namely, the high-energy part of the excita-tions is a response of quasiparticles, while the low-energy h (r.l.u.) (cid:116) ( m e V ) (cid:103) (r . l . u . ) (cid:116) (meV)
100 150 P r LaCe
CuO , T =6K (b)(a) La Ba CuO Fig. 20. (a) Energy dependence of the resolution corrected peakwidth κ for Pr . LaCe . CuO , from Ref., and (b) the overallshape of spin excitation spectrum In the lower figure, the horizon-tal(vertical) length of the rectangle represents a fitted result offull-width at half-width with assuming a single Gaussian function(sliced energy range for the analysis).14. Phys. Soc. Jpn. FULL PAPERS part involves localized spins. This energy-dependent fea-ture from the two spin degrees of freedom is differentfrom what has been discussed in the hole-doped systemas introduced in §
3. (In the hole-doped superconductingsystem, it has been discussed that high-energy disper-sive magnon-like modes are a sort of remnant excitationof the AF phase, while the low-energy spin dynamics, in-cluding the resonance feature, might originate from theresponse of quasiparticles. Indeed, phenomenological the-ory, which treats both itinerant fermions and local spinshave well reproduced the overall spin susceptibility inYBCO. ) Therefore, even though both systems showevidence of dual character in the excitation spectrum andthe energy for the separation is comparable, the differ-ences in the dispersion of spin excitations between the n - and p -type systems suggest the different origins of thedual nature.
7. Other topics
Varma has proposed that valence fluctuationsbetween a Cu atom and its O neighbors should leadto complicated patterns of current loops. These cur-rent loops should generate magnetic moments that breaktime-reversal symmetry and four-fold rotational symme-try, but that preserve translational symmetry. Becauseof the translation symmetry, magnetic scattering fromordered loop currents should occur only at reciprocal lat-tice vectors. The form factor is Q dependent and falls offrapidly with Q because of the spatially extended natureof the magnetization density.Motivated by Varma’s predictions, Bourges andcoworkers have performed a series of polarizedneutron diffraction experiments to test for unusual mag-netic order. These are very challenging experiments, ason must detect a small magnetic signal on top of a sub-stantial diffraction intensity from the chemical order. Ini-tial measurements on several good quality, underdopedYBCO crystals revealed a small enhancement of the spin-flip cross section relative to the non-spin-flip cross sectionat temperatures comparable to the pseudogap regime( T mag ∼
200 K for YBCO x ∼ . Based on the orig-inal current loop model, one would expect the magneticmoments to point along the c axis; however, the experi-ment found that the effective moment direction was ap-proximately 45 ◦ away from c . A collaborative experimentwith Mook on a large YBCO x = 0 . q width as the nuclear scattering,including along the c axis, implying long-range order.A recent study on YBCO x = 0 .
45 and 2% Zn-doped x = 0 .
37, 117) found a reduced magnitude of the spin-flipsignal at Bragg wave vectors. For the x = 0 .
45 crystal,the onset temperature was also reduced.A study of LSCO x = 0 .
085 identified a spin-flip signalat the tetragonal (100) reflection; however, in contrast toYBCO, the signal was independent of Q z (indicating 2Dcharacter) and had a correlations length of ∼
10 ˚ A within the CuO planes. The onset temperature was 120 K.Greven’s group has studied unique crystals ofHgBa CuO δ . Li et al. identified a spin-flip signal,similar to that in YBCO, for three underdoped com-positions. More recently, intriguing inelastic responseshave been reported. After first reporting an antiferro-magnetic resonance at 56 meV in a sample with T c =96 K (measured with unpolarized neutrons), polar-ized neutron scattering has been used to identify aweakly dispersing branch that connects with the reso-nance and has roughly constant intensity across the Bril-louin zone. He and Varma argue that this branchis a collective mode of the loop-current state. While thisnew feature is interesting, it is important to note thatstudies on other cuprates have found no evidence for sucha weakly dispersing magnetic mode. In particular, a re-cent polarized-beam inelastic study of YBCO x = 0 . Neutron-scattering studies of high- T c superconductorsreveal a close correlation between local antiferromag-netism and the superconductivity. For instance, the hour-glass-shaped dispersion commonly observed in the super-conducting phase of LSCO, YBCO and Bi2212 systemssuggests the existence of a universal nature to the spincorrelations in hole-doped cuprates.
28, 29, 46)
However, itwould only take one counter example to disprove thetrend. We have hence started a systematic study of thespin excitations in the single-layer Bi x Sr − x CuO δ (Bi2201) system, in which the carrier concentration canbe controlled by substituting Bi ions onto the Sr site.Figure 21 shows the inelastic neutron-scattering pro-file measured at (cid:126) ω = 4 and 6 meV on Bi . Sr . CuO δ ,which is a lightly-doped sample. In each measure-ment, the scan was made along along the [1 , − , Q AF . A well-defined single peak was observedat T = 40 K (closed-circled), and a similar result wasobtained from a scan along the [1 , , Q . InFig. 21(a), the inelastic spectrum measured at T = 10 Kand (cid:126) ω = 6 meV is shown by open squares. The peakintensity at 10 K is weaker than that at 40K, showingclearly the thermal evolution of the signal. This resultsuggests that the signal originates from an intrinsic ex-citation, such as a magnon or phonon. The comparisonbetween the spectrum measured around Q = (0 . , . . , .
5) is shown in Fig. 21(b) for (cid:126) ω = 4 meV.The smaller intensity for larger Q is consistent with theexpected fall off of the magnetic form factor at larger | Q | , and therefore, suggests that the observed intensityis magnetic in origin. Thus, the existence of spin exci-tations in the Bi2201 system has been demonstrated forthe first time.The present success in observing spin excitations pro-vides motivation to extend the study of spin correlations
15. Phys. Soc. Jpn.
FULL PAPERS (a) (cid:116) =6 meV (1- k , k (cid:116) =4 meV T =40 K C oun t/ . m i n . C oun t/ . m i n . k (r.l.u) Bi Sr CuO (cid:98) T =40 K T =10 K (1- k , k , 0)(2- k , k , 0) Fig. 21.
Spin excitation spectra for Bi . Sr . CuO δ for(a) (cid:126) ω = 4 meV and (b) 6 meV. Filled-circles and open-squaresare the data measured around (0 . , . ,
0) at T = 40 K and10 K, respectively. Open-triangles are the data measured around(1 . , . ,
0) at T = 40 K. in the B2201 system. Since both LSCO and B2201 aresingle-layered systems, a comparative study should yieldvaluable information about universal features of the spincorrelations.
8. Summary and remaining issues
One of the striking features of the cuprates is that,while dynamic AF correlations tend to coexist with su-perconductivity, AF and SC orders generally do not co-exist. In hole-doped systems, a small density of mobilecharge carriers is sufficient to destroy long-range AF or-der. Remnant excitations of the AF state appear to sur-vive at higher energies, but the correlations are reorga-nized at energies below E cross . At the same time, thereis a strong damping of magnetic excitations at energiesgreater than that of the electronic pseudogap. Further-more, the magnetic spectral weight decreases monotoni-cally with doping, disappearing in the overdoped regimetogether with the superconductivity.All of these effects suggest that the doped holes andthe superexchange-coupled spins organize themselves ina cooperative way to enhance both carrier mobility andlocally AF correlations. Charge and spin stripe order iscertainly one motif that exhibits such cooperative self-organization. In 214 cuprates, stripe order can be in-duced by suitable lattice anisotropy or by local pertur-bations, such as magnetic vortices or impurities. Thereare indications of related nematic behavior in YBCO. Anunresolved question is: are stripes a common feature ofthe hole-doped cuprates? Certainly stripe order is notcommon among the cuprates. Dynamical stripes mightbe more common, but are there any unique signaturesof fluctuating stripes? Stripe order is only observed atmodest temperatures, on the scale of T c , so it cannotexplain the electronic pseudogap; nevertheless, could the onset of the pseudogap reflect the self-organizing processof carriers and spins? Neutron scattering studies of thethermal evolution of spin correlations through T ∗ mighthelp to resolve this issue, although such measurementswill be challenging.There has been a long-term debate over the natureof the magnetic excitations, and the relative importanceof particle-hole excitations vs. the flipping of local mo-ments. The trend of magnetic spectral weight vs. dop-ing suggests that superexchange-coupled moments likelyplay a dominant role over much of the phase diagram.Particle-hole excitations must contribute at some level,but what level is that? Is there some feature that changeswith doping in a fashion that would provide circumstan-tial support for the role of particle-hole excitations? Theenergy E cross grows with doping, at least in the under-doped regime, which certainly demonstrates that the car-riers and the magnetic properties are interacting, but isthere a unique signature for particle-hole excitations?Our conclusion that AF and SC orders cannot coex-ist is challenged by NMR experiments on cuprate fam-ilies with three, four, or more CuO layers stacked to-gether. The NMR measurements have been interpretedas providing evidence for the coexistence of SC and AForders. Now, these are complicated systems with in-equivalent layers, and it can be challenging to determinewith a local whether antiferromagnetic correlations arelong-range commensurate or spatially modulated. Futureneutron scattering experiments could resolve this issues,if suitable crystals can be grown.In the electron-doped cuprates, mobile charge carriersseem to be compatible with commensurate antiferromag-netic order, although superconductivity is not. Overall,the magnetic spectral weight appears to weaken morerapidly than in the hole-doped cuprates. Recently, We-ber et al. claimed that parents of the n -type cupratesare not Mott insulators but Slater insulators, in whichthe insulating character is a consequence of the AF or-der. Such a system should become a metal the magneticorder is lost; however, since the cuprates are quasi-two-dimensional magnets with a large J , one needs to probethe system at high temperatures, T ∼ J , to test the the-ory. One would like to compare magnetic neutron scat-tering with transport and optical conductivity measure-ments. Such a neutron scattering experiment is currentlydifficult to perform, but it is one of the challenging exper-iments to try in combination with new techniques suchas high-energy polarized neutron spectroscopy. Testingthe nature of the parent material is also relevant to un-derstanding the unusual “non-doped” superconductivityreported in thin films of compounds such as Nd CuO and Pr CuO .
9. Acknowledgments
We would like to thank K. Hirota, H. Kimura, M. Kofu,S. Iikubo, M. Enoki, C. Frost, S.-H. Lee, Y. Endoh, andR. J. Birgeneau for the fruitful discussions. The workat JRR-3 and SPring-8 was partially performed underthe Common-Use Facility Program of JAEA and joint-research program of ISSP, the University of Tokyo. MF issupported by Grant-in-Aid for Encouragement of Scien-
16. Phys. Soc. Jpn.
FULL PAPERS tific Research B (23340093). MM and HH was supportedby Grant-in-Aid for Encouragement of Young ScientistsB (22740230) and Scientific Research B (2234089), re-spectively. JMT and GYX are supported at Brookhavenby the Office of Basic Energy Sciences, Division of Ma-terials Science and Engineering, U.S. Department of En-ergy (DOE), under Contract No. DE-AC02-98CH10886.
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