Table Of ContentThe Role of Lattice Coupling in Establishing Electronic and Magnetic Properties in
Quasi-One-Dimensional Cuprates
W. S. Lee,1,∗ S. Johnston,1,2 B. Moritz,1,3,4 J. Lee,5 M. Yi,5 K. J. Zhou,6 T. Schmitt,6 L. Patthey,6
V. Strocov,6 K. Kudo,7 Y. Koike,7 J. van den Brink,2 T. P. Devereaux,1 and Z. X. Shen1
1SIMES, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
2IFW Dresden P.O. Box 27 01 16, D-01171 Dresden, Germany
3Department of Physics and Astrophysics, University of North Dakota, Grand Forks, ND 58202, USA
4Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA
5Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
3 6Paul Scherrer Institut, Swiss Light Source, CH-5232 Villigen PSI, Switzerland
1 7Department of Applied Physics, Tohoku University, Japan
0 (Dated: January 21, 2013)
2
Highresolutionresonantinelasticx-rayscatteringhasbeenperformedtorevealtheroleoflattice-
n
coupling in a family of quasi-1D insulating cuprates, Ca2+5xY2−5xCu5O10. Site-dependent low
a
energy excitations arising from progressive emissions of a 70 meV lattice vibrational mode are
J
resolvedforthefirsttime,providingadirectmeasurementofelectron-latticecouplingstrength. We
7
show that such electron-lattice coupling causes doping-dependentdistortions of theCu-O-Cu bond
1
angle, which sets the intra-chain spin exchange interactions. Our results indicate that the lattice
degrees of freedom are fully integrated into theelectronic behavior in low dimensional systems.
]
l
e PACSnumbers: ValidPACSappear here
-
r
t
s
Electron-lattice coupling is an important mechanism super-exchange interaction according to Goodenough-
.
t
a in solids that determines the groundstate properties via Kanamori-Andersontheory[13,22–24],isalsodopingde-
m renormalizingthemassofchargecarriers[1],and,insome pendent[20]. However,theimportantmechanismbehind
- cases, induces novel symmetry-broken states like super- the doping induced Cu-O-Cu angle change remains un-
d
conductivity [2] and charge density waves [3]. While re- clear. Usinghighresolutionresonantinelasticx-rayscat-
n
search on the electron-lattice interaction has a long his- tering (RIXS), we find a 70 meV phonon strongly cou-
o
tory in condensed matter physics, it continues to be an pled to the electronic state. As we will demonstrate, the
c
[ importanttopicinestablishingnewparadigmsforunder- doping dependent Cu-O-Cu angle is driven by electron-
standing the properties of strongly correlated materials lattice coupling due to the ineffectiveness of screening
1
v inwhichchargesbecomemorelocalizedandscreeningef- in 1D. Further, the phonon energy is found to soften
7 fects are weak [4]. To date the electron- lattice coupling when cooling across the antiferromagnetic phase tran-
6 in two dimensionalcorrelatedmaterials such as cuprates sition in the undoped compounds. These observations
2
[5–9] and manganites [10–12] has drawn much attention demonstrate that the lattice degrees of freedom are fully
4
in the field. In one dimensional (1D) cuprate systems, integratedinto the electronic and magnetic properties of
.
1 althoughunusualspinandchargedynamics[13–17]have low-dimensional correlated materials.
0
beenrevealed,studiesoftheroleofelectron-phononcou-
3 pling are still lacking. Such studies are important since Single crystals of Ca2+5xY2−5xCu5O10 used in the
1
: poor screening effects in 1D systems [18] should in prin- present study were grown by traveling-solvent floating-
v zone(TSFZ)methods. Sampleswiththreedifferentdop-
ciple cause strong electronic coupling to the lattice.
i
X ing levels were selected for measurements, nominally x
To address this issue, we study a family of quasi-1D = 0, 0.3, and 0.33. The RIXS measurements were per-
r
a cuprates Ca2+5xY2−5xCu5O10, in which CuO2 plaque- formed at the ADRESS beamline, Swiss Light Source,
ttes arrange in a chain-like structure by sharing their with the energy resolution set at either 50 meV or 80
edges with neighboring CuO plaquettes. This system meV. The sample surface was the (0, 1, 0) plane, coinci-
2
is important as it is the only quasi-1D cuprate that can dent with the chain plane, prepared by either polishing
be doped over a wide range of hole concentrations, pro- (x = 0) or cleaving (x = 0.3 and 0.33). The scattering
viding a unique opportunity to study doping induced anglewassetat90degreetominimizetheelasticpeakin-
phenomena [19, 20]. By increasing carrier concentra- tensity. As sketched in Fig. S1(c) in the Supplementary
tion, the spin ground state evolves from A-type antifer- Material, the scattering plane was the a-b plane with a
romagnetic order (intra-chain ferromagnetic order with grazing angle of 20 degree to the sample surface. The
inter-chain antiferromagnetic alignment), to spin glass, polarization of the incident photon is perpendicular to
followedbyspingap,andeventuallytoaspindisordered the scattering plane (σ-polarization),while the recorded
phase [20, 21]. Curiously, the structural Cu-O-Cu bond spectrum includes all the polarizations of the scattered
angle, which determines to the size and sign of the spin photons.
2
(a) (b) Initial State Intermediate State Final State
XAS UHB hν + |Ψen > |0p> core hole + |Ψ’en+ 1 > Σn αn|np> hν’ + |Ψen >Σn αn|np>
LEP
UHB
x=0 Cu
O hν’
x=0.3 hν LEP
E
x=0.33 XAS ULEHPB .......|2p> hν’
|1 >
526 528 530 532 p
Photon Energy (eV) |0p>
FIG. 1: (color online) (a) x-ray absorption spectrum near the oxygen K-edge for Ca2+5xY2−5xCu5O10 compounds of three
different doping levels. The “UHB” and “LEP” denotes the absorption peaks at 529.5 and 528 eV, respectively. The average
numberofholeperCuionisdenotedasx. (b)|Ψn>and|Ψn+1 >denotestheelectronicgroundstateandtheexcitedelectronic
e e
intermediatestatewithanadditionalelectronexcitedfromtheoxygen1scorelevel. |np >(n=0,1,2,...) denotesthenumber
of phonon quanta excited in the lattice degree of freedom with a wavefunction superposition coefficient α. For purposes of
illustration, the wavefunction is expressed as product states of the diagonalized electron and lattice Hamiltonians. Here, the
lattice vacuumstate|0p >is referenced totheinitial equilibrium phononoccupation and |np >describes excitationsfrom this
state. IntheRIXSintermediatestate,anelectron(greenball)isexcited,leavingacorehole(whiteball)intheO1slevel. The
excitedelectroncanbeclosertoeitherCuorOsitebytuningtheincidentphotonenergytomatchtheUHBorLEPresonance,
respectively. The change of the local charge density on Cu (blue shade) and O (red shade) sites induce local relaxation of the
distorted lattice, creating a distribution of |np >. In the final state, the excited electron can recombine with the core hole,
leaving the lattice in excited states. These final states have non-zero overlap with the intermediate state, yielding harmonic
phonon excitations in RIXSspectrum.
It is informative to first introduce the doping evolu- the spectrum with an energy separation corresponding
tion of the electronic wave function, revealed by the x- to the energy of the quanta of the lattice vibrations (i.e.
rayabsorptionspectrum(XAS)neartheOK-edge(1s-2p phonons) in a fashion analogous to a generalized Frank
transition). As shown in Fig. 1(a), the XAS of the un- Condon picture. The spectral weight of phonon excita-
doped compound exhibits a single dominant absorption tions in the RIXS spectrum is directly dependent on the
peak(529.5eV),whichisassociatedwiththeupperHub- electron-phonon (e-ph) coupling strength. Furthermore,
bardband(UHB). Uponhole-doping,the UHB peak de- the e-ph coupling strength at Cu and O sites can be de-
creases,indicating a reduction of the weight of the UHB termined by tuning the incident photon energy to the
component [25]. In addition, a lower energy peak (LEP) UHB andLEPresonances,respectively. This sitedepen-
emerges,whicharisesfromthespectralweighttransferto dency stems from differences in the electronic character
wavefunctioncomponentsthataredirectlyrelatedtothe of the XAS final states.
doped holes [26]. Approximately, in real space, the XAS Figure2(a)displaysRIXSspectrafortheundopedpar-
attheUHBresonanceproducesafinalstatewithonead- entcompound. Astheincidentphotonenergyistunedto
ditional valence electron near the copper site, while the neartheUHBresonance(‘e’and‘f’),thespectranearthe
XAS at the LEP resonance puts the additional valence elastic scattering peak, develops an unusual asymmet-
electron near the oxygen site, as sketched in Fig. 1(b). ric broadening, indicating the excitations of low energy
Toinvestigatetheeffectsoflatticecouplingontheelec- modes. Upon doping, as shown in Fig. 2(b), an asym-
tronic states, we use resonant inelastic x-ray scattering metric spectrumnearthe elasticpeak isalsoobservedat
(RIXS)[27,28]. Theunderlyingprincipleisillustratedin the UHB resonance, however it is now most pronounced
Fig. 1(b). IntheOK-edgeRIXSprocess,a1scoreelec- at the LEP resonance. The shift of resonance behavior
tron will first be excited into an XAS final state, either is associatedwith the doping evolutionofthe XAS spec-
the UHB or LEP resonance. This causes a local change tralweightdue to changesof the wavefunctioncharacter
in the charge density which locally distorts the lattice. [26], suggesting that the origin of the low-energy modes
Later, the electron de-excites, filling the O 1s core hole, is coupled directly with the electronic wavefunction.
leaving the lattice in an excited state. The RIXS spec- HigherresolutionRIXSspectra(Fig. 2(c))providefur-
trumrecordstheoverlapsoftheinitial,intermediate,and therinformationabouttheoriginoftheselow-energyex-
final states as a function of energy loss (the energy dif- citations. AtbothUHBandLEPresonances,weresolved
ference between the incident and emitted photons), and multiplepeaksinthespectrum,whichlieinharmonicor-
includes the possibility of producing multiple peaks in derofasingleenergyscaleof 70meV(Fig. 2d). Wenote
3
(a) (b) (c) (d)
XAS UHB x = 0 XASLEP x = 0.33
abcdefg abcdUefHgB Ux H= B0 (at ‘f’) #1 #0 Width 120
526 528 530 532 u.) #2 V) m
526 Ph5o2to8n En5e3rg0y (eV5)32 RIXPShoton Energy (eV) a. #3 me200 80Ve
RgfIXS efg ensity ( nergy ( R e s o l uEtixopn. 400
dec cd RIXS Int xL E= P0 .(3a3t ‘b’) #2 #1 #0 Peak e100 #0 #1 #2 #3 x = 0
x = 0.3
#3
b b x = 0.33
0
a a
0.5 0.0 0.5 0.0 0.4 0.2 0.0 #0 #1 #2 #3
Energy Loss (eV) Energy Loss (eV) Energy Loss (eV) Peak Number
FIG.2: (coloronline)TheRIXSspectrumfor(a)x=0and(b)x=0.33samplestakenatseveralincidentphotonenergies,as
indicated by the red bars in the XAS plots. The length of these red vertical bars reflects the relative elastic peak intensity of
the corresponding RIXS spectrum. The darker shaded areas highlight the spectra with prominent additional spectral weight
near the elastic peak. (c) High resolution data taken at UHB resonance for the x = 0 sample (upper) and at LEP resonance
forthex=0.33sample(lower). Multi-peakfeaturesareannotatedwithnumberidentifiers. TheblackcurvesaretheGaussian
functions used for the fit (red curves). Purple curves are the remaining spectrum after subtracting the fit. Background is
plottedas blackdottedlines. (d)Asummaryplot ofthefittedpeakpositions andwidths(inset)of theRIXSspectratakenat
UHB(x = 0) and LEP (x = 0.3 and 0.33) resonances. All data were taken at 30 K.
that since the spin super-exchange energy (10-14 meV) dition, our calculation explicitly demonstrates that the
[25,29]is muchsmallerthan the extractedmode energy, difference between gCu and gO can be resolved by com-
theobservedexcitationscannotbeattributedtospinex- paring the RIXS spectrum taken at the UHB and LEP
citations. Rather they are most likely due to an oxygen resonances (Fig. 3(c)). This site dependent information
bond-stretching vibrational mode, similar to those com- is unique to RIXS and confirms the concepts illustrated
monly found in2D cupratesata similar energyscale [5]. in Fig. 1b.
In addition, the mode energy extracted from the RIXS
With these insights, we can compare the electron-
spectratakenattheUHBandLEPareidentical,indicat-
lattice coupling strength via the spectral shape of the
ing that the observedphononexcitations share the same
phonon excitations. First, as shown in Fig. 3(d), we
origin. These observations demonstrate that the elec-
foundthatthe couplingstrengthisessentiallydopingin-
tronic states in the CYCO system are coupled strongly
dependent,eventhoughasignificantnumberofholesare
with this 70 meV phonon mode.
doped into the system. This demonstrates that screen-
ing remains ineffective upon doping, as expected for a
To gain further insight into harmonic progression of
onedimensionalsystem[18]. Second,thecouplingatthe
phonon excitations, we use exact diagonalization to cal-
UHB resonance is found to be stronger than at the LEP
culate RIXS for CuO clusters coupled to a subset of
2
resonance (Fig. 3(e)), which is caused by the difference
opticaloxygenvibrations. Inthismodel,weincludecou-
plingtoavibrationalmodewhoseeigenvectorissketched between gCu and gO. By fitting to our model, we esti-
in Fig. 3(a) with coupling strengths of gCu and gO on mate gCu ∼ 2gO ∼ 0.22 eV, also in agreement with our
Madelung potential analysis (Supplementary Material).
Cu and O sites, respectively. (Supplementary Material)
This mode derives its coupling from the strong electro- A doping-independent electron-lattice coupling has an
static modification it produces to the electronic states intriguingconsequence to the doping evolutionof the in-
of the edge-shared CuO2 chains (Supplementary Mate- tertwinedelectron-latticegroundstate. AsshowninFig.
rial). Our calculations (Fig. 3(a)) capture the essen- 4(a), the number of phonons intertwined in the ground
tial physics related to the observed excitations, repro- state is larger in the doped system than in the undoped
ducing the XAS spectrum, the phonon excitations, and system due to the increased carrier concentration. This
their shift fromthe UHB to LEPresonanceinthe doped implies a larger lattice distortion along the c-axis and
cluster. Importantly, we show that their spectral weight results in a larger Cu-O-Cu angle in the doped system.
is extremely sensitive to the e-ph coupling strength: the Withinourmodel,weestimatea0.16 contractionofO-O
strongerthe coupling,the greaterthe spectralweightfor distancealongc-axis,correspondingtoa3.7%increaseof
higher-harmonic phonon excitations (Fig. 3(b)). In ad- the Cu-O-Cu bond angle in the x = 0.33 doped cluster.
4
(a) Cu O a Cu O (b) (d)
3 8 c 3 6
nsity CUaHlcBulations x = 0 nsity UH Bx = 0 #1
e e
nt g = 0.20 nt x = 0.3 #2
d I gCu = 0.15 d I x = 0.33
XAS x = 0 XAS x = 0.33 e Cu e
UHB LEP z g = 0.10 z
abcdef ghi abc d e f ghUiHB mali (g C=u 2g ) mali
nits) RIX0SEne2rgy (eV4) 6 RIX0S En2ergy (e4V) 6 Nor Cu O Nor
S Intensity (Arb. U efghi efghi (ed Intensityc) CalcuULlaHEtBiPons x = 0.33 (eed Intensity) x x=UL =EH0 P.B03 3 #2 #1
RIX d d aliz gCu = 0.15, gO = 0.075 aliz
c c m m
b b or or
N N
a a g = 0.15 ,g = 0.15
Cu O
0.4 0.2 0 0.4 0.2 0 0.4 0.2 0.0 0.2 0.1 0.0
Energy Loss (eV) Energy Loss (eV) Energy Loss (eV) Energy Loss (eV)
FIG. 3: (color online) (a) The calculated RIXS intensities for the x = 0 (left) and x = 0.33 (right) hole-doped systems,
respectively, with g = 0.15 eV. The incident photon energies are indicated in the calculated XAS spectra and the elastic line
has been removed by excluding the ground state from the final state summation. The calculations were performed on Cu3O8
andCu3O6clusters(openandperiodicboundaryconditions)forthex=0andx=0.33cases,respectively. Thearrowsindicate
thedisplacementpatternofthephononeigenvectorinvolvingc-axismotionoftheOatoms.(b)Acomparisonofthenormalized
phonon excitations at the UHB resonance for the x = 0 case and different coupling strengths. (c) The normalized phonon
excitation spectrum at theLEP and UHBresonance in a doped cluster (x = 0.33). Spectra of two different values of gO were
calculated to demonstrate the site dependence of the RIXS process at the LEP and UHB resonances. (d) Experimental data
ofharmonicphononexcitations(elastic peakand backgroundsubtracted)normalized tothefirstphononpeakintensityatthe
UHB resonance for three different doping levels. (e) Experimental data of the normalized harmonic phonon excitations for x
= 0 and x = 0.33 taken at theUHB and LEP resonance, respectively.
The estimation is comparable to the reported doping in- The authors thank J. Ma´lek, S.-L. Drechsler, and M.
ducedincreaseoftheCu-O-Cuangle(∼2.5%)[20]. Since Berciu for useful discussions. This work was supported
the size and sign of the spin super-exchange coupling is by the U. S. Department of Energy, Office of Basic En-
sensitive to the Cu-O-Cu bond angle, this result shows ergy Science, Division of Materials Science and Engi-
that e-ph coupling strength is an important underlying neering under the contractno. DE-AC02-76SF00515. S.
mechanism to drive the lattice structure that hosts the J. acknowledges funding from FOM (The Netherlands).
spin dynamics of this 1D system. ThisworkwasperformedattheADRESSbeamlineofthe
Swiss Light Source using the SAXES instrument jointly
Finally, as shown in Fig. 4(b), the phonon excitations
built by Paul ScherrerInstitut, Switzerland and Politec-
exhibit a softening of up to ∼10 meV when the system
nico di Milano, Italy.
is cooledacrossthe antiferromagnetictransitiontemper-
ature TN (30 K). Importantly, inelastic neutron scatter-
ing measurements also have reported a spin excitation
hardeningofapproximately1-2meVwhencoolingtolow
temperatures[21],demonstratingacooperativeinterplay ∗ Electronic address: [email protected]
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