Lattice dynamics and the electron-phonon interaction in Ca$_2$RuO$_4$

0.23 MB·English

by  H. Rho

Lattice dynamics and the electron-phonon interaction in Ca RuO
2 4
H. Rho,1,2 S. L. Cooper,2 S. Nakatsuji,3 H. Fukazawa,3 and Y. Maeno,3,4
1Department of Physics, Chonbuk National University, Jeonju 561-756, Korea
2Department of Physics and Frederick Seitz Materials Research Laboratory,
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
3Department of Physics, Kyoto University, Kyoto 606-8502, Japan
4International Innovation Center, Kyoto University, Kyoto 606-8501, Japan
5
(Dated: February 2, 2008)
0
0 We present a Raman scattering study of Ca2RuO4, in which we investigate the temperature-
2 dependence of the lattice dynamics and the electron-phonon interaction below the metal-insulator
n transition temperature (TMI). Raman spectra obtained in a backscattering geometry with light
a polarized in the ab-plane reveal 9B1g phonon modes (140, 215, 265, 269, 292, 388, 459, 534, and
J 683 cm−1) and 9Ag phonon modes (126, 192, 204, 251, 304, 322, 356, 395, and 607 cm−1) for the
6 orthorhombiccrystalstructure(Pbca−D125h). WithincreasingtemperaturetowardTMI,theobserved
phonon modes shift to lower energies and exhibit reduced spectral weights, reflecting structural
2
changes associated with the elongation of the RuO6 octahedra. Interestingly, the phonons exhibit
] significantincreasesinlinewidthsandasymmetriesfor T>TN. Theseresultsindicatethatthereis
l anincreaseintheeffectivenumberofelectronsandtheelectron-phononinteractionstrengthsasthe
e
- temperatureisraisedthroughTN,suggestingthepresenceoforbitalfluctuationsinthetemperature
r regime TN < T < TMI.
t
s
. PACSnumbers: 75.30.-m,75.50.Ee,78.30.-j,71.30.+h
t
a
m
I. INTRODUCTION the two-magnon (2M) energy and linewidth, and an in-
-
d creaseofthe electron-phononinteractionstrength.10 Ra-
n man scattering measurements further suggest that the
co hibLiitkestrmonagnycoortrheelartiotrnasnsaimtioonn-gmseptainl,ocxhidaregse,thoartbiteaxl-, etixvcehlyanignesecnosuitpivliengtocopnresstsaunrte9JainndCSar2−cxoSnrtxenRtu.1O04 is rela-
[
and lattice degrees of freedom, Ca2−xSrxRuO4 ex-

1 hibits many exotic phenomena throughoutits richphase
Other complex oxides are known to exhibit signifi-
v diagram.1,2,3,4,5,6,7,8,9,10,11 For instance, not only do
cant changes in phonon dynamics near important phase
0 the ruthenates exhibit orbital ordering,5,6,7,8, but also
2 orbital-dependent superconductivity, heavy-mass Fermi transitions. For example, La0.7Ca0.3MnO3 displays a
6 significant shift of the transverse optical phonon en-
liquid behavior, and metal-insulator transitions.1,2,4
1 ergy near the MI transition, giving rise to an increased
0 The single-layer ruthenate material Sr RuO is a su- electron-phononinteractionrelatedtochangesinthelat-
2 4
5 perconductorbelowT =1.5K,possiblywithanuncon- tice parameters.18 Raman studies of LaMnO reveal an
0 c 3
ventional p-wave pairing state.12 Substitution of Ca for effectofthespin-latticeinteractionnearthetransitionto
/
at Sr significantly distorts the lattice structure and lowers AF order.19 InLa2−xSrxCuO4, anincreaseofSr concen-
m thecrystalsymmetryfromcubictoorthorhombic,giving tration causes the appearance of an asymmetric phonon
rise to remarkable changes in magnetic, electronic, and lineshape and a dramatic decrease of the phonon inten-
-
d structuralproperties.2,4,13 ThegroundstateofCa2RuO4 sityassociatedwiththe apicaloxygenvibration,indicat-
n is antiferromagnetic (AF) insulating.14,15 With increas- ing that the electron-phonon interaction is also impor-
o ing temperature,Ca RuO becomes paramagnetic(PM) tant in this material.20 Inelastic neutron scattering and
2 4
c insulating at T = 113 K and then PM metallic at T x-rayscatteringstudieshavesuggestedthepresenceofor-
: N MI
v = 357 K.2,15,16 The metal-insulator (MI) transition is bital fluctuations in LaTiO .21 As described in Ref. 21,
3
i first-order, as evidenced by the observation of thermal an electronic continuum and anomalous phonon behav-
X
hysteresis. Further,thetransitionisdrivenbyanelonga- ior with a Fano profile observed in the Raman response
ar tion of the RuO6 octahedra with increasing temperature of RTiO3 (R=rare earth)22 may also indicate the pres-
through T , and therefore the insulating and metal- ence of orbital fluctuations in the insulating region of
MI
lic states are characterized by short (S-Pbca) and long this system. Therefore, it is of great interest to study
(L-Pbca) c-axis lattice parameters, respectively.13,17 As how spin, charge, orbital, and lattice correlations evolve
a function of Sr-substitution, x, the AF ground state in Ca RuO through different phase transitions, partic-
2 4
of Ca2−xSrxRuO4 persists for x < 0.2. Sr substitution ularly as a means of comparing the exotic properties
changesbothT andT , andsignificantly affectsmag- of this system to those of complex oxides such as the
N MI
netic, electronic, orbital, and structural correlations in cuprates, manganites, and titanates. In this paper, we
thismaterial. Forinstance,Ramanscatteringresultsob- use the unique strengths of Raman scattering to explore
tained on Ca2−xSrxRuO4 have shown that Sr substitu- lattice dynamics and the electron-phonon interaction in
tioncausesa dramatic increasein the renormalizationof Ca RuO asafunctionoftemperaturebetween10Kand
2 4
2
TABLE I: Site symmetries and IR’s of the atoms in Ca2RuO4 with space group Pbca−D125h. Mode classifications are: ΓRaman
= 9 (Ag + B1g + B2g + B3g), Γinfrared = 11 (B1u + B2u + B3u), Γsilent = 12 Au, and Γacoustic = B1u + B2u + B3u. The
correspondingpolarization tensorelementsforeach oftheRaman-activefactor groupspecies are: Ag →αxx,αyy,αzz;B1g →
αxy,αyx; B2g → αxz, αzx;and B3g → αyz, αzy.
Atom Sitesymmetry IR’s
Ru Ci 3 (Au +B1u + B2u + B3u)
Ca C1 3 (Ag + B1g + B2g + B3g + Au +B1u + B2u + B3u)
O(1) C1 3 (Ag + B1g + B2g + B3g + Au +B1u + B2u + B3u)
O(2) C1 3 (Ag + B1g + B2g + B3g + Au +B1u + B2u + B3u)
300 K.
*
II. EXPERIMENT 140 215265269 388
292 459 534 683
byAasflinogaltei-ncgry-zsotanlesmametphloedo,f2,C16a,223RuwOas4,mwohuicnhtewdaisngsirdoewna units) 126 395 B1g
251
continuous He-flow cryostat. The 647.1-nm excitation b. 322 607
wavelength from a Kr-ion laser was used in a backscat- (ar 192204 304 356 260265270275
teringgeometrywiththepropagationvector(k)oriented w)
along the c axis of the sample, k k c-axis. Scattered c( Ag
m
light from the sample was dispersed using a triple-stage *
I
spectrometer,andthen recordedusing a liquid-nitrogen-
cooled charge-coupled device (CCD) detector. Various B +A
1g g
polarization configurations of the incident and scattered
light were employed in order to identify the scattering 0 200 400 600 800
symmetriesoftheRamanspectraobtainedforCa2RuO4: EnergyShift(cm-1)
(E , E ) = (x, y), B symmetry; (E , E ) = (x, x), A
i s 1g i s g
symmetry; and (E , E ) = (x′, x′), B + A symme-
i s 1g g
try, where E and E are the incident and the scattered
i s
polarization directions, respectively, B and A are ir-
1g g
reducible representations (IR’s) of the space group D2h, FIG. 1: Polarized Raman spectra at T = 10 K with B1g,
′
andxk[1,0,0],yk[0,1,0],andx k[1,1,0]. AlltheRaman Ag, and B1g + Ag scattering symmetries from top to bot-
spectra were corrected,first, by removing the CCD dark tom, respectively. The inset shows a high-resolution Raman
current response, and second, by normalizing the spec- spectrum, indicating two resolved 265 and 269 cm−1 phonon
trometer response using a calibrated white light source. modes.
Finally, the corrected spectra were divided by the Bose
thermal factor, giving rise to the spectral responses dis-
played in this paper. These responses are proportional
phonons are Raman-active, orthorhombic Ca RuO ex-
2 4
to the imaginary part of the Raman susceptibility.
hibits numerous phononlines. This reflects the fact that
substitution of Ca for Sr strongly distorts the RuO oc-
6
tahedra, causing a rotation of the octahedra around the
III. RESULTS AND DISCUSSION
c axis, and a tilt of the octahedra around an axis on the
RuO plane.13,17 As shown in Fig.1, polarized Raman
2
Ca RuO hasanorthorhombiccrystalstructure(space spectra in a backscatteringgeometry (with the propaga-
2 4
group Pbca−D15) with four formula units per unit cell. tionvectorkkc-axis)revealallofthephononmodescor-
2h
A factor-groupanalysis, summarized in Table I, yields a responding to each of scattering symmetries: 9B sym-
1g
total of 81 Γ-point phonons, of which 36 [9 (A + B metrymodesin(E ,E )=(x,y),9A symmetrymodes
g 1g i s g
+ B + B )] are Raman-active modes involving Ca, in (E , E ) = (x, x), and 9B + 9A symmetry modes
2g 3g i s 1g g
in-planeoxygen[O(1)],andapicaloxygen[O(2)]ions,33 in(E ,E )=(x′,x′)polarizationconfigurations,respec-
i s
[11(B +B +B )]areinfrared-activemodes,and12 tively. Note in the inset of Fig. 1 that the B phonon
1u 2u 3u 1g
(12 A ) are silent modes. The Ru ions are located at a peak energies assigned at 265 and 269 cm−1 are clearly
u
center of inversion symmetry and, thus, do not partici- resolvedinahigh-resolutionRamanspectrum. Morespe-
pate in anyRaman-active phononmodes. Unlike tetrag- cific assignmentsof the observedopticalphonons to par-
onalSr RuO ,inwhich2A and2E symmetryoptical ticularatomicnormalmodeswillrequirelatticedynamic
2 4 1g g
3
220
140
CaRuO:B (a) 210
2 4 1g 135
-1m) 200 -1m)
units) 1505KK w(c 112350 (a) B1g140cm-1 (b) B1g215cm-1 190 w(c
b. 80K 390 180
ar 460
w)( 130K 385
455
c( 180K -1m) 380 -1m)
Im 230K w(c 375 B1g388cm-1 B1g459cm-1 444550 w(c
300K (c) (d)
370 440
0 200 400 600 800 125 605
EnergyShift(cm-1) -1m) 120 600 -1m)
c c
( (
Ca2RuO4:Ag (b) w 115 Ag126cm-1 Ag607cm-1 595 w
(e) (f)
590
10K 110
s) 0.0 0.5 1.0 1.5 2.0 2.50.0 0.5 1.0 1.5 2.0 2.5
unit 55K T/TN T/TN
b. 80K
ar
( 130K
cw() 180K mFIoGd.es3a:t (Tae)m1p4e0r,at(ubr)e-2d1e5p,en(dc)en3t88f,re(qdu)en4c5y9 cshmif−t1s, oafndB1ogf
Im 230K Ag modes at (e) 126 and (f) 607 cm−1.
295K
T . Unlike the cuprates, the 2M scattering intensity in
N
0 200 400 600 800 Ca RuO diminishes rapidly above T , indicating that
2 4 N
EnergyShift(cm-1) local AF order disappears for T > TN. More details of
the 2M characteristics in Ca2−xSrxRuO4 have been de-
scribed elsewhere, including the effects of pressure9 and
Sr substitution.10
FIG. 2: (a) B1g and (b) Ag Raman spectra with increasing With increasing temperature toward T , the out-of-
temperature from 10 K to room temperature. MI
plane Ru-O(2) bond length is nearly unchanged for T
< T , but gradually elongates as temperature is raised
N
above T .13,17 In order to elucidate the temperature-
N
calculations. dependence of the lattice parameters and the electron-
Figure1alsoshowsaRaman-activemodeat102cm−1 phonon interaction below T , both B and A sym-
MI 1g g
(denoted with an asterisk) that is observed only in the metry Raman spectra from Ca RuO were studied as a
2 4
B scattering geometry. This mode is likely associ- function of increasing temperature from 10 to 300 K, as
1g
ated with a 2M scattering response, although we can- summarized in Figs. 2(a) and 2(b). There are several
not completely rule out the possibility that it is a one- key features observed in the Raman spectra as a func-
magnon excitation. The 2M scattering response, which tion of increasing temperature, including (i) a softening
involves a photon-induced flipping of spins on nearest- of all the B and the A optical phonon energies, (ii)
1g g
neighborRusites,providesusefulinformationconcerning a decrease of phonon spectral weights, and (iii) a sig-
the AF correlations.9,10,24,25 Using the fact that the 2M nificant broadening and increased asymmetry of phonon
energyforanS=1AFinsulatorisgivenbyh¯ω=6.7J,25 lineshapes across T .
N
where J is the in-plane exchange coupling constant be- The systematic shifts of phonon peaks to lower ener-
tween nearest-neighbor Ru-4d4 sites, we can estimate J gies with increasing temperature through T primarily
N
= 15.2 cm−1 in Ca RuO . With increasing tempera- reflect an elongation of the RuO octahedra along the
2 4 6
ture toward T , as shown in Fig. 2(a), the 2M response c axis. Figures 3(a) to 3(f) summarize the phonon en-
N
weakensinintensity,broadensinlinewidth, andshifts to ergy changes with increasing temperature for some rep-
lower energy, reflecting the reduction of the AF corre- resentative B (140, 215, 388, and 459 cm−1) and A
1g g
lations in Ca RuO as the temperature is increased to (126and607cm−1)opticalphononmodes. Thephonon-
2 4
4
energyshiftsarenegligibleforT<T ,indicatinglittleor
N
no change in the lattice parameters in this temperature
regime. Incontrast,remarkablephonon-energyshiftsare
observed for T > T . Most of phonon modes display (a)
N 0.00
downward shifts of ∼ 15 cm−1 as temperature is raised
from 10 to 300 K. Interestingly, the B phonon at 215
1g
cm−1 shows a much more dramatic energy shift of ∼ 30 K) -0.02
cm−1. These Raman results are consistent with neutron 0
1
scattering measurements, which show that there is little w(
/ B 140cm-1
change in the lattice parameters for T < TN, but that DG -0.04 B11gg215cm-1
there is a significantchange in the lattice parametersfor B 388cm-1
1g
TN < T ∼ TMI.13,17 All the other B1g and Ag optical BA1g142569ccmm--11
phononsdecreaseinenergywithincreasingtemperature. -0.06 Agg607cm-1
Note that all the B phonon modes exhibit a dramatic
1g
decreaseinintensityastemperatureisraisedtowardT 0.0 0.5 1.0 1.5 2.0 2.5
MI
(∼ 357 K ∼ 3.2TN), possibly reflecting increased damp- T/T
N
ing of the modes by thermally activated carriers.
1
One notes in Figs. 2(a) and 2(b) that the B1g and (b)
the A phonon lineshapes at low temperatures for T <
g
T arequitesymmetricandnarrow. Incontrast,within-
N
creasingtemperaturethroughTN,thephononlinewidths 0.1
broadensignificantly andthe lineshapes become increas-
q|
ingly asymmetric. The latter reveals a Fano effect, |
/
caused by the interaction between the discrete phonon 1 B 140cm-1
1g
state and a broad electronic continuum of states.26 0.01 BB1g231858ccmm--11
Similar behavior has been observed in Raman spectra B1g459cm-1
1g
of numerous other strongly correlated materials such A 126cm-1
g
as Ca2−xSrxRuO4,10 La1−xCaxMnO3,27 Ca3Ru2O7,28 Ag607cm-1
Sr RuO ,29 and RTiO (R = rare earth).22
2 4 3 0.0 0.5 1.0 1.5 2.0 2.5
To study the temperature-dependence of the
T/T
electron-phonon interaction in Ca RuO in detail, N
2 4
the temperature-dependence of the phonon linewidths
and asymmetries of the B and A phonon modes were
1g g
FIG. 4: (a) Phonon linewidth changes divided by the corre-
extracted by fitting these modes to a Fano lineshape,
spondingphononenergy at T =10 K,[Γ(T) −Γ(RT)]/ω(10
I(ω) = I (q + ǫ)2/(1 + ǫ2), where ǫ = (ω − ω )/Γ,
0 0 K)=∆Γ/ω(10K),asafunctionoftemperaturenormalizedto
ω is the phonon energy, Γ is the effective phonon
0 TN. (b)Magnitudesofinverseoftheasymmetryparameters,
linewidth, and q is the asymmetry parameter. In this 1/|q|, as a function of temperaturenormalized to TN.
way, one obtains information on the electron-phonon
interaction. The inverse of the asymmetry parameter,
1/|q|, is proportional to the electron-phonon coupling above T , which influences the substantial phonon en-
N
strength V and the imaginary part of the electronic ergy renormalizations observed above T , can be ex-
N
susceptibility ρ according to 1/q ∼ Vρ.10,26,27 More- plored by plotting as a function of temperature the
over, the electron-phonon coupling contribution to the phonon linewidth changes divided by the correspond-
phonon linewidth can be estimated from the fractional ing phonon energy at T = 10 K, ∆Γ/ω(10K). These
change in the phonon damping rate below TMI, [Γ(T) plots are displayed in Fig.4(a). Interestingly, in con-
− Γ(RT)]/ω0 = ∆Γ/ω0 ∝ N(0)ω0λ, where N(0) is the trast to the negligible change in phonon linewidths ob-
electronic density of states at the Fermi surface, ω0 is served below TN, there is significant broadening in the
the phonon energy, and λ is the dimensionless electron- phonon linewidths above T . For example, the phonon
N
phonon coupling parameter.30,31,32 The parameter λ is linewidths at 300 K are significantly broader than those
related to the BCS parameter N(0)Vph, where Vph is at 10 K, ∆Γ/ω0 ∼ 5.3 %, which is even larger than the
the pairing potential arising from the electron-phonon fractionalbroadeningobservedinthecorrelationgapma-
interaction.31,32,33 Therefore, by carefully monitoring terial FeSi, ∆Γ/ω ∼ 3.5 %.30 We attribute the system-
0
the phonon linewidths, as well as the inverse asymmetry aticbroadeningofthephononlinewidths withincreasing
parameters, as a function of temperature, one can temperatureaboveT toanincreaseoftheeffectivenum-
N
obtain useful information regarding the evolution of ber of electrons in the system for T > T . Indeed, Jung
N
the electronic density of states and the electron-phonon etal. recentlyreportedthatthe effectivenumberofelec-
coupling strengths in Ca2RuO4. tronssystematicallyincreases,andtheopticalgapcloses,
The role of the electronic contribution to the system with increasing temperature above T in Ca RuO .7
N 2 4
5
The evolution of the electron-phonon interaction in whichare associatedwith increasedelectrontransfer be-
Ca RuO can be carefully illustrated by plotting the tween the d and d orbitals,are responsible for the
2 4 xy yz/zx
inverse of the asymmetry parameter, 1/|q|, for differ- behavior observed in this temperature regime. Indeed,
ent modes as a function of temperature, as shown in a recent O 1s x-ray absorption spectroscopy study of
Fig.4(b). Note thatthe magnitudes ofthe inverseasym- Ca2−xSrxRuO4 (x=0.0and0.09)hassuggestedthator-
metry parameters, 1/|q|, which are obtained from the bitalfluctuationsgraduallyincreaseuponheatingevenin
representative B and the A phonon modes, are neg- the insulatingregionwellbelowT .34 Note thatthe in-
1g g MI
ligible at low temperatures, but increase significantly verseasymmetry parametersandthe spectrallinewidths
as temperature is raised through T . Even when the for the phonon mode near 300 cm−1 in the insulating
N
temperature is much lower than the MI transition tem- RTiO (R =Gd, Sm,Nd,Pr,Ce,La)exhibitthe largest
3
perature, there is no additional increase of the inverse values in LaTiO ,22 suggesting that orbital fluctuations
3
asymmetry parametersfor T/T > ∼ 1.2. These results are important in LaTiO , as pointed out by Keimer et
N 3
stronglysuggestthatthelargestincreaseintheelectron- al.21
phonon coupling strength occurs near T , rather than
N
near T . By contrast, between x = 0.45 and 0.76 in
MI
La1−xCaxMnO3, the 1/|q| value decreases linearly with IV. CONCLUSIONS
increasingxintheferromagneticlow-temperaturemetal-
lic region (x ≤ 0.52), and vanishes in the AF region (for
x>0.52).27 Notealsothatthe magnitudesofthe inverse Insummary,temperature-dependentRamanspectraof
asymmetry parameters, 1/|q|, in the PM insulating re- Ca RuO allow us to explore the lattice dynamics near
2 4
gion of Ca RuO for T < T < T are comparable to the MI transition temperature of this system. With in-
2 4 N MI
those in the metallic region of Sr RuO (Ref. 29) and creasing temperature through the N´eel temperature, the
2 4
La1−xCaxMnO3.27 B1g andthe Ag phononmodesexhibitasubstantialshift
ItisinterestingtonotethatpreviousRamanresultson to lower energies. Moreover, the phonons significantly
Ca2−xSrxRuO4 have revealed that substitution of Sr for broaden and exhibit increasingly asymmetric lineshapes
Ca increases the electron-phonon coupling strength, as uponheatinginthevicinityofT . Theseresultsdemon-
N
evidenced by an increase of both the inverse asymmetry strate that both the electron-phonon coupling strength
parameters and the phonon linewidths with Sr substi- and the effective number of electrons increase as tem-
tution at T = 10 K.10 Moreover, for the Sr-substituted perature is raised through T , suggesting that orbital
N
samples(x=0.06and0.09),achargegapobservedat10 fluctuations are present in the PM insulating region in
K was found to close well below the MI transition tem- the temperature regime T < T < T .
N MI
perature, suggesting that the intermediate temperature
regime between T and T consists of a coexistence of
N MI
insulating S-Pbca and metallic L-Pbca phases.10 In con-
Acknowledgments
trast, inthis study, the broadeningof phononlinewidths
andtheincreaseofthe1/|q|valuesuponheatingthrough
T (≪ T ) in Ca RuO are probably not attributable Work in Korea was supported by Korea Research
N MI 2 4
to the coexistence of metallic and insulating phases in FoundationGrant(KRF-2004-005-C00003). WorkinIlli-
thistemperatureregimeforseveralreasons,includingthe nois was supported by the National Science Foundation
highstoichiometryofthe sample,andthe absenceofany under Grant No. DMR02-44502and by the Department
residual low frequency conductivity in Ca RuO in the of Energy through the Materials Research Laboratory
2 4
temperature regime T < T < T .6,7 under Grant No. DEFG02-91ER45439. The work at
N MI
In Ca RuO , the observed increase in both the KyotoUniv. was supportedin partby Grants-in-Aidfor
2 4
electron-phonon coupling strength and the number of Scientific Research from JSPS and for the 21st Century
effective carriers with increasing temperature near T COE “Center for Diversity and Universality in Physics”
N
strongly suggests that enhanced orbital fluctuations, from MEXT of Japan.
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