A resonant inelastic x-ray scattering study of the spin and charge excitations in the overdoped superconductor La1.77Sr0.23CuO4

0.82 MB·

by  C. Monney

A resonant inelastic x-ray scattering study of the spin and charge excitations in the
overdoped superconductor La Sr CuO
1.77 0.23 4
C. Monney,1,2 T. Schmitt,1 C. E. Matt,1,3 J. Mesot,1,4,3
V. N. Strocov,1 O. J. Lipscombe,5 S. M. Hayden,5 and J. Chang1,4,2
1Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
2Physik-Institut, Universita¨t Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland
3Laboratory for Solid State Physics, ETH Zu¨rich, CH-8093 Zu¨rich, Switzerland
6 4Institute for Condensed Matter Physics, E´cole Polytechnique Fed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
1 5H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom
0
2 We present a resonant inelastic x-ray scattering (RIXS) study of spin and charge excitations in
n overdopedLa1.77Sr0.23CuO4alongtwohigh-symmetrydirections. Thelineshapeoftheseexcitations
is analyzed and they are shown to be highly overdamped. Their spectral weight and damping are
a
J foundtobestronglymomentumdependent. Qualitativeagreementbetweentheseobservationsand
acalculatedRPAsusceptibilityisobtainedforthisoverdopedcompound,implyingthatasignificant
4
contribution to the RIXS signal stems from a continuum of charge excitations. Furthermore, this
1
suggests that the spin-excitations in the overdoped regime can be captured qualitatively by an
] itinerant picture. Our calculations also predict a new low-energy spin excitation branch to exist
n alongthenodaldirectionnearthezonecenter. Withtheenergyresolutionofthepresentexperiment,
o thisbranchisnotresolvablebutweshowthatnextgeneration ofhigh-resolutionspectrometerswill
c beable to test this prediction.
-
r
p
u I. INTRODUCTION (LSCO) x = 0.23. The line shape of these excitations
s isanalyzedusingtheresponsefunctionofadampedhar-
.
t monic oscillator. In this fashion, their dispersion and
a Conventional superconductivity emerges as a result
m momentum dependence of spectral weight and damping,
of electron-phonon interaction1. Information about the
γ, are extracted. We find that the spectral weight and
- phonon excitation spectrum (dispersions and lifetime ef-
d dampingγ aredisplayingasignificantmomentumdepen-
fects2) are therefore of great importance. Similarly, for
n dence. The line shape is sharpest around the zone cen-
o magnetic superconductors3, there is a strong interest in ter, whereas the spectral weight increases upon moving
c understandingandexperimentallyreveallingthespinex- towards the zone boundary. As reported for Bi-based
[ citationspectrum. Mappingoutthedetailedevolutionof cuprates15,26, we also find a strong nodal / antinodal
thespinexcitationspectrumacrossthehigh-temperature
1 anisotropy of spectral weight. These observations are
v superconducting cuprate phase diagram, from the Mott capturedbysusceptibilitycalculationsbasedonthe elec-
8 insulator to the Fermi-liquid ground state, is hence im- tronic band structure. The model calculation further-
5 portant. Spin excitations have traditionally been stud-
morepredicts a low-energyspinexcitationbranch,along
5 ied by inelastic neutron scattering (INS)4,5. Studies of
the (π,π)-direction, which turns out to be particularly
3 high-energy spin excitations6 have, however, been chal-
0 pronounced and dispersive in LSCO with x = 0.23 in
. lenged by weak neutron cross sections. Over the last comparison to other doped cuprates15,27. Future RIXS
1 decade,resonantinelasticx-rayscattering(RIXS)hasde-
experimentswithimprovedenergyresolutionshouldtest
0 veloped rapidly7 and energy resolution now allows stud-
this prediction.
6 ies of spin excitations8–10. RIXS is therefore an at-
1
tractive complementary technique to neutron scatter-
:
v ing. This has, in particular, lead to progress in un- II. METHOD
i
X derstanding correlated low-dimensional 3d and 5d elec-
tronsystems11,12. The spinexcitationspectraofinsulat-
r High-resolution RIXS experiments were carried out
a ing one- and two-dimensional cuprates have, for exam-
at the ADvanced RESonant Spectroscopy (ADRESS)
ple, been studied by soft x-ray RIXS using the copper
beamline28,29 at the Swiss Light Source (SLS) on high
L -edge12–18. In recent years, spin excitations of doped
3 quality single crystallineLSCO x=0.23samples25,30–32,
cuprate and pnictide superconductors have also been in-
grown by the traveling floating zone method33. For
vestigated9,10,12,19. These studies suggest that the high
the tetragonal crystal structure (a = b ≈ 3.8 ˚A and
energy (ω >100 meV) spin excitation dispersion under-
c ≈ 13.2 ˚A), we index the reciprocal space by q =
goes little change with doping12,19,20. This is in strong ha∗ +kb∗ +ℓc∗ where a∗ and b∗ point along the Cu-
contrastto the low-energypartof the spectrum (studied O bonds. Samples were aligned ex-situ, using the x-ray
by INS), that has a strong dependence on impurities21,
Laue technique, in order to access the scattering planes
magnetic field22,23 and doping24,25. (h,0,ℓ) or (h,h,ℓ). Cleaving was performed in-situ un-
We present a systematic RIXS study of the spin and der ultra high vacuum conditions (< 5 × 10−10 mbar)
charge excitations found in overdoped La2−xSrxCuO4 using a standard top-post technique and the sample was
2
meVthathasbeeninterpretedasaspinexcitationinthe
parent compound9,10 and (3) so-called dd-excitations at
about 1700 meV. The dd-excitations are in agreement
with what has previously been reported on LSCO34 and
explained by crystal field calculations35,36. Following
common practice, all spectral intensities are renormal-
ized to total integrated intensity of these dd-excitations,
Idd 20,27,37.
Asexpected,significantelasticscatteringisfoundnear
the specular condition [q =(0,0)] – see Fig. 2a. The in-
creasedelasticscatteringnear the grazingincidence con-
dition q ≈ (0.4,0) was previously interpreted as a result
of a phonon branch10. Herein, we make no attempt to
disentangle contributions from phonons and elastic scat-
tering. We also stress that contrary to what was re-
ported10 in underdoped LSCO x = 0.08, only one low-
energyexcitationbranchis resolvedinour RIXS spectra
ofoverdopedLSCO.Hence,thereisnoevidenceforphase
separation in our compound.
AsystematiccompilationofRIXSspectratakenalong
the (h,0) and (h,h) directions are shown in Fig. 2. For
simplicity only the elastic scattering and low-energy ex-
citations are shown. In Fig. 1c, the spectral weight
originating from these excitations is displayed using a
FIG. 1: (a) RIXS spectrum, recorded on overdoped LSCO false color scale and after subtracting the elastic com-
x = 0.23 using σ−polarized light, displays elastic scatter- ponent. Without any detailed analysis, following ob-
ing, a low-energy excitation and a dd-excitation. The in-
servations can be made. (1) Although weaker, their
set shows thescattering geometry andreciprocal space(h,k)
spectral weight remains finite in the region near the
schematically. (b) Overdamped response function showing
howχ′′ →0forω→0. (c)InterpolatedRIXSintensity,with zone center q = (0,0), see Fig. 1c. (2) The spec-
tral weight is weaker and the excitations broader and
elastic scattering subtracted, versus momentum q = (h,0),
less dispersive along the (h,h) direction. A similar di-
(h,h) and photon energy loss ω. Red ticks indicate the grid
of spectra used for theinterpolation. chotomy between “nodal” (h,h) and “antinodal” (h,0)
directions has been reported also for optimally and un-
derdoped Bi2Sr2CaCu2O8+δ15,26 (Bi2212). The less dis-
kept at a temperature of 20 K for all measurements. At persive nodal excitation has also been reported for over-
theCuL -edge(∼930eV),theinstrumentalenergyand doped LSCO (x=0.25)38.
3
momentum half-width-at-half-maximum (HWHM) reso-
lutions are 65 meV and 0.01 ˚A−1, respectively. The in-
coming light was σ−polarized for all measurements. For IV. ANALYSIS
eachspectrum,theelasticlinewasobtainedbymeasuring
non-resonant elastic scattering from polycrystalline car- A. Data modelling
boncontainingtapeplacedjustnexttothesample14. Re-
ciprocal space positions of the form (h,0,ℓ) and (h,h,ℓ) To model the spectral weight from elastic and low-
were sampled by changing the grazing incident angle θ, energy scattering, we use the formula I (ω) = G(ω)+
I
definedinFig.1. Thelayeredcupratesareknowntohave nBχ′′(ω) where nB = (1−exp(~ω/kBTd)d)−1 accounts of
weak magnetic coupling along the c-axis leading to little
the Bose factor. G(ω) is a Gaussian function (to fit the
dispersionalongℓ. We thereforedescribe positions using
elastic line) on top of a background modeled by a cubic
atwo-dimensionalnotation(h,k)toquantifymomentum ′′
polynomial. The response function χ (ω) is that of a
transfer q.
damped hamonic oscillator:
γω
′′ ′′
χ (ω)=χ
III. RESULTS 0[ω2−ω02]2+ω2γ2
′′
χ γ/2 γ/2
= 0 − ,
A typical RIXS spectrum recorded with σ−polarized 2ω (cid:20)(ω−ω )2+(γ/2)2 (ω+ω )2+(γ/2)2(cid:21)
1 1 1
light at (h,k) = (0.38,0) is shown in Fig. 1a. As previ-
ouslyreportedonthe cuprates10,12,27,the spectrumcon- where the damping coefficient γ/2 = ω2−ω2. Con-
0 1
sists of three features: (1) elastic and quasi-elastic scat- sideringfora momentonly magneticexpcitations,this re-
teringatω ≈0,(2)alow-energyexcitationataround300 sponsefunctionspanstwoconceptuallydifferentregimes.
3
0.5
(a) M (b) (c) (d) (e)
0.4 ω
0
U.)
b. 0.3 a b c d e
Ar
y ( Γ X
nsit 0.2
e
nt
I
0.1
0
0.4
(f) M (g) (h) (i) (j)
0.35
j
i
h
0.3
U.) g
b. 0.25 f
y (Ar 0.2 Γ X
sit
n 0.15
e
nt
I 0.1
0.05
0
0 400 800 0 400 800 0 400 800 0 400 800 0 400 800
ω (meV) ω (meV) ω (meV) ω (meV) ω (meV)
FIG. 2: RIXS spectra recorded on LSCO x=0.23, at T =20 K,in grazing incidence geometry using σ−polarized light tuned
to the Cu L3-edge (930 eV) line. Top panels, (a)-(e), are spectra measured with momenta along q=(h,0) as indicated in the
inset of (a). Bottom panels, (f)-(j), displays spectra taken along q =(h,h) as indicated in the inset of (f)-(g). Blue and gray
shaded areas are modelled contributions from elastic and low-energy excitations on top of a cubic background (dashed line).
Solid black line is thesum of these contributions. See text for furtherexplanation.
′′
In the limit γ ≪ω (γ →0), χ ∼δ(ω−ω )−δ(ω+ω ) damping γ/2softens upon movingfromthe zone bound-
0 0 0
describes coherent propagating magnon excitations with ary towards the zone center (Fig. 3b). A similar angular
ω = ω as a pole. The overdamped limit (γ ≈ ω ), in dependence has previously been reported in optimally
0 1 0
contrast, is characterized by χ′′ ∝ ω for ω → 0 – see dopedBa0.6K0.4Fe2As219 (reproducedin Fig.3a). Addi-
Fig. 1b. Furthermore, for ω > ω , neither of these two tionnally, ω disperses upward from the zone center and
0 1 0
energy scales reflect the pole of a coherent excitation. saturates near the zone boundary along both (h,0) and
′′
However,asχ isbroadlypeakedatω ,thisenergyscale (h,h)directions. Asimilardispersionofω isfoundalong
1 1
is often refered to as the paramagnon excitation energy (h,0). As γ/2 ≈ ω , along the nodal (h,h)-direction, it
0
scale12,19,37. is difficult to extract ω reliably. Finally, we observe in
1
′′
Fig.5thattheintegratedintensityχ ·γofthelow-energy
Fits to spectra taken at different momenta q along 0
excitation is weakly anisotropic, as it is larger along the
q = (h,0) and (h,h) are shown in Fig. 2. Solid lines in-
(h,0) direction than the (h,h) direction (for a given ab-
dicate the elastic (blue) and low-energy excitation (red)
solute value of the momentum |q|).
′′
contributions. In this fashion γ, ω , ω and χ were ex-
0 1 0
tractedforLSCO x=0.23alongthe twohigh-symmetry
directions – see Fig. 3, 4 and 5. From this analysis, it is
B. RPA susceptibility calculations
found that γ/2 and ω are comparable for all measured
0
spectra. Interpreting the low-energy excitation along
(h,0) as a spin excitation, as will be confirmed below, ToanalyzetheRIXSintensitiesandneutronscattering
implies that it is overdamped. Along (h,h), the nature spectra, itinerant approaches have been applied15,40–44.
of this excitation is less clear and has probably a mixed These approaches are expected to be especially relevant
spin and charge character, which makes the interpreta- for very overdoped cuprates, where the system enters
tion of its parameters more delicate. We note that the a state with some of the characteristics of a Fermi liq-
4
M X Γ M
X Γ M 400
a b c
120
Ba K Fe As a V) 300
0.6 0.4 2 2 e
V) 10800 ω= (m1200
me ω 0100
2 ( 60 INS La2CuO4 RIXS
γ / 40 0 500
d e
20 HWHM 400
M V) 300
0 e
m
400 La1.77Sr0.23CuO4 b ω (0200
100 La1.77Sr0.23CuO4 RIXS
Γ X
V) 300 500 0
me f INS La Sr CuO g RhIX iSn (h,h) (r.l.u.) h
2 ( 200 400 1.77 0.23 4
γ./ V) 300
e
100 m
ω (1200
0 100
−0.5 −0.25 0 0.25 0.5
HWHM
h in (h,0) (r.l.u.) h in (h,h) (r.l.u.) 0
−0.5 −0.25 0 0.4 0.2 0 0.25 0.5
k in (0.5,k) (r.l.u.) h in (h,0) (r.l.u.) h in (h,h) (r.l.u.)
FIG. 3: Damping γ/2 (see text) of the low-energy excita-
tions measured by RIXS in LSCO x = 0.23 (this work) and FIG.4: Comparisonofthespinexcitationdispersionsω0 and
Ba0.6K0.4Fe2As219 along the high-symmetry directions ΓX ω1 (see text) extracted on La2CuO4 (LCO) with the low-
and ΓM. Error bars in bottom panels are set by the applied energyexcitationdispersionsonLa1.77Sr0.23CuO4 alonghigh
energy resolution (65 meV - HWHM) that is also indicated symmetry directions as indicated. Data obtained from INS
by a horizontal dash line. andRIXSaredisplayedbysquareandcircularpointsrespec-
tively. For LCO good agreement between INS [(cid:3) - Ref. 39]
and RIXS [◦ - Ref. 10] is found along the ΓX-direction. No
uid32,45,46. We have therefore calculated the RPA spin overlap between RIXS (• - this work) and INS ((cid:3) - Ref. 25)
susceptibility χs(q,ω) for overdoped LSCO, to analyse has been reached for overdoped compositions of LSCO. The
insetindicatesthehigh-symmetrydirectionsanddisplaysthe
the low-energy excitations in the paramagnetic state.
calculatedstaticLindhardsusceptibility(forω→0)(seetext
The RPAsusceptibility describesthe collectivemagnetic
for further explanation).
excitations of the itinerant electrons. Similar to Guarise
et al. (Ref.15),weobtainherethetransversepartofthe
spin susceptibility as
4
χ (q,ω)
χs(q,ω)= 0 ,
1−Uχ (q,ω)
0 U.)3
b.
twiohner4e2 aχn0d(qU,ωi)s trheperleosceanltsCothuelomLibndinhtaerrdacrteiospn.onAses ifnupnuct- sity (Ar
ttioonχ407, owfetuhseeetlehcetrsoinngicled-bisapnedrstiiognhto-bbtianidniendgfproamramAeRtrPizEaS- ed Inten2
at
measurements on this sample30. The renormalized band gr
width4t=490meVwasusedandU ischosentobe1.2t, Inte1
so that the susceptibility is not diverging, meaning that
the system is far enough from a density-waveinstability.
0
In fact, the RPA susceptibility, χs, induces moder- −0.5 −0.4 −0.3 −0.2 −0.1 00 0.1 0.2 0.3
h in (h,0) h in (h,h)
atemodificationsoftheparticle-holecontinuumobtained
from the Lindhard response function χ . Along (π,0),
0
the dispersion in the particle-hole continuum is renor- FIG. 5: Integrated intensity χ′0′·γ of the low-energy excita-
malizedtolowerenergies(smallerbandwidth)andstarts tions measured by RIXS in LSCO x = 0.23 along the high-
to develop a second branch, leading to a second min- symmetry directions ΓX and ΓM. The dash lines are a guide
imum (softening) at around (0.15,0). In this sense, it to theeyes.
can be interpreted as a spin excitation. Along (π,π),
5
FIG.6: (a)CalculatedRPAsusceptibilityalongthenodal(h,h)andantinodaldirectionq=(h,0). (b)TheRPAsusceptibility
convoluted by instrument resolution to make a direct comparison to Fig. 1c. (c-e) A zoom of the low-energy nodal RPA
susceptibility. In (d,e) a Gaussian convolution with FWHM = 60 and 130 meV has been applied. This demonstrates that a
spectrometer with a 60 meV energy resolution at theCu L3−edgeis sufficient to test the RPAprediction of low-energy nodal
spin-excitations.
the main changes occur aroundthe M-point, where low- Moreover, the calculation also produced stronger damp-
energy spin excitations near (π,π) are reproduced con- ing as the excitations disperse towards the zone bound-
sistently with previous susceptibility calculations43 (see ary. Second, the susceptibility calculation captures the
Fig. 4,inset). Interestingly,aweaklydispersingbranchis intensity anisotropybetween (0,0)→(π,0)and (0,0)→
found inthe range(0,0)→(0.2,0.2),seeFig. 6a,c. As it (π,π). Such a clear anisotropy in the intensity distri-
getsstrongerwithincreasingU,weinterpreteitasaspin bution (see Fig. 5) had not been observed previously
excitation branch. Notice, however, that after convolu- in other RIXS studies on doped cuprates15,26,38. The
tionoftheappliedinstrumentalresolution(σ =55meV) susceptibility calculation furthermore makes a number
these detailedfeaturesarebeing smearedoutcompletely of predictions, that can be tested by improving the in-
(Fig. 6b,e). strumental resolution. Most notable is the low-energy
excitation branch along (0,0) → (π,π). Such a low-
energy dispersion appeared already in the RPA calcu-
lated of other doped cuprates15,26, but was not recog-
V. DISCUSSION
nizedassuch,mainlybecauseitwasnotasdistinctasin
thepresentcase. Weattributeitscleardispersivecharac-
The calculated RPA susceptibility contains contribu- terheretothespecificLSCOelectronicstructurethathas
tionsfrombothexcitedparticle-holecontinuumandspin avanHovesingularityintheantinodalregion30. Improv-
excitations15,44. RIXS should be sensitive to both these ingthe resolutionto haveaGaussianstandarddeviation
components. The convoluted RPA calculation repro- σ ∼ 25 meV (FWHM ∼ 60 meV) would be sufficient to
duces the most salient observations. First, along the resolve this predicted low-energy branch, see Fig. 6d.
(π,0)direction,the spectralweightdistributionis repro-
duced quite successfully, compare Fig. 1c with Fig. 6b. In comparison to the case of undoped cuprates10,12,
6
thisanalysisshowsthatthemeasuredexcitationsinover- (h,h) are strongly damped and the damping is display-
doped LSCO are in generalbroaderand their width (see ingasignificantmomentumdependence–largermomen-
Fig. 3b) has a stronger momentum dependence. This tum yields largerdamping. Spectralweightalsohas mo-
most likely comes from the efficient damping of spin ex- mentum dependence. Along the antinodal region more
citations by the electron-holecontinuum, as wellas from spectral weight is found near the zone boundaries and
the contributionofelectron-holeexcitationsto the RIXS more spectral weight is found in the antinodal direction
signal44. thanthenodaldirection. RPAsusceptibilitycalculations
We conclude the discussion by comparing RIXS and starting from the experimental observed band structure
INS studies of LSCO10,38. For the undoped compound, captures these trends. This suggests that the measured
La CuO , INS39 and RIXS10 experiments overlap along RIXSsignaloriginatesfromamixtureofspinexcitations
2 4
the ΓX direction and excellent agreement of the mea- and a continuum of charge excitations. Furthermore,
sured magnon dispersion is found (see Fig. 4). Neutron based on these calculations,we predict a low-energy dis-
scattering experiments on doped cuprates are typically persivespinexcitationbranch,alongthe(π,π)-direction,
restricted – due to weak cross sections – to a much nar- whichis particularlyintense and distinct from other fea-
rower range around the (0.5,0,5)-point (indexed M)25,48 tures in the case of La1.77Sr0.23CuO4. The emerging
where the so-called hour-glass spin excitation dispersion ultra-high-resolution spectrometers will be able to test
is revealed49–51. The RIXS technique on the other hand this prediction.
haskinematicconstrainslimitingstudiestoaregioncen-
tered around the Γ-point. For doped cuprates, it is thus
difficulttoobtainadirectoverlapofRIXSandINSspec- VII. ACKNOWLEGDEMENTS:
tra. Within the present RPA calculation the Γ- and M-
points are not equivalent. Caution should therefore be C.M., C.E.M.andJ.C.acknowledgesupportby the
taken when comparing neutron scattering data near the Swiss National Science Foundation under grant number
M−point with RIXS data recorded around the Γ-point. PZ00P2 154867, 200021−137783, PZ00P2 142434, and
BSSGI0 155873. C. M. also thanks the Alexander von
HumboldtFoundationandMaNEPforfinancialsupport.
VI. CONCLUSIONS S. M. H. acknowledges support by the United Kingdom
Engineering and Physical Science Research Council un-
In summary, we presented a Cu L −edge RIXS study der grant number EP/J015423/1. This work was per-
3
of the low-energy spin and charge excitations in over- formedat the ADRESS beamline ofthe SLS at the Paul
doped La1.77Sr0.23CuO4. Two high-symmetry directions Scherrer Institut, Villigen PSI, Switzerland. We thank
(h,0)and(h,h)wereinvestigated. Spinexcitationsalong the ADRESS beamline staff for technical support.
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