High-resolution angular resolved photoemission data reveal well-defined quasiparticle bands of unusually low weight, emerging in line with the metallic phase of 

Ca

3

Ru

2

O

7

 below 

∼

30

 

 

K

. At the bulk structural phase transition temperature of 48 K, we find clear evidence for an electronic instability, gapping large parts of the underlying Fermi surface that appears to be nested. Metallic pockets are found to survive in the small, non-nested sections, constituting a low-temperature Fermi surface with 2 orders of magnitude smaller volume than in all other metallic ruthenates. The Fermi velocities and volumes of these pockets are in agreement with the results of complementary quantum oscillation measurements on the same crystal batches

Baumberger, F

Damascelli, A

Hossain, MA

Hussain, Z

Ingle, NJC

Kikugawa, N

Lu, DH

Mackenzie, AP

Meevasana, W

Perry, RS

Rost, A

Shen, KM

Shen, ZX

English

UCL Discovery

PRL 96, 107601 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending17 MARCH 2006Nested Fermi Surface and Electronic Instability in Ca3Ru2O7F. Baumberger,1 N. J. C. Ingle,1,2 N. Kikugawa,3 M. A. Hossain,2 W. Meevasana,1 R. S. Perry,4 K. M. Shen,1,2 D. H. Lu,1A. Damascelli,2 A. Rost,3 A. P. Mackenzie,3 Z. Hussain,5 and Z.-X. Shen11Departments of Applied Physics and Physics, and Stanford Synchrotron Radiation Laboratory, Stanford University,Stanford, California 94305, USA2Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada3School of Physics and Astronomy, Scottish Universities Physics Alliance, University of St. Andrews,St. Andrews, Fife KY16 9SS, Scotland4Department of Physics, Kyoto University, Kyoto 606-8501, Japan5Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA(Received 15 July 2005; published 17 March 2006)0031-9007=High-resolution angular resolved photoemission data reveal well-defined quasiparticle bands ofunusually low weight, emerging in line with the metallic phase of Ca3Ru2O7 below 30 K. At thebulk structural phase transition temperature of 48 K, we find clear evidence for an electronic instability,gapping large parts of the underlying Fermi surface that appears to be nested. Metallic pockets are foundto survive in the small, non-nested sections, constituting a low-temperature Fermi surface with 2 orders ofmagnitude smaller volume than in all other metallic ruthenates. The Fermi velocities and volumes of thesepockets are in agreement with the results of complementary quantum oscillation measurements on thesame crystal batches.DOI: 10.1103/PhysRevLett.96.107601 PACS numbers: 71.18.+y, 71.45.Lr, 79.60.iThe characterization and description of novel phasesfound in transition metal oxides (TMOs) has stimulatedprogress in condensed matter physics over the last decades[1]. The itinerant electron system of the perovskite ruthe-nium oxides provides a prime opportunity to study suchcomplex ground states and phase transitions or competitionin TMOs starting from a quasiparticle (QP) band structurepicture [2]. Ruthenates can be grown with extremely highpurity, which has allowed detailed studies of the Fermisurface (FS) topology through the detection of quantumoscillations (QOs) [3,4], and Sr2RuO4 has served as abenchmark system for the potential of angular resolvedphotoemission (ARPES) to derive quantitative informationon band dispersion and QP scattering rates [5,6]. Althoughthese studies yielded fully consistent results, it should benoted that ARPES probes a larger energy scale and canreveal information that is complimentary to low-temperature transport and thermodynamic measurements.While all Sr-based ruthenates of the Ruddlesden-Popperseries Sr;Can1RunO3n1 are metallic at low tempera-ture, the situation becomes more ambiguous upon substi-tution of Sr with the isovalent but smaller Ca ion. Thiscauses structural distortions leading to a rotation and tiltingof the RuO6 octahedra, which in turn reduces hoppingmatrix elements and thus emphasizes correlation effects[7,8]. The subject of this study, Ca3Ru2O7, has been re-ported to be ‘‘semimetallic,’’ with two phase transitions, aNéel transition at 56 K and a structural phase transition at48 K [9], where the in-plane resistivity increases by about30%. At lower temperatures the resistivity is metallic, butvery large [10–12].In this Letter, we report the growth of crystals with anorder of magnitude lower residual resistivity than previ-06=96(10)=107601(4)$23.00 10760ously achieved, and high-resolution ARPES and QO mea-surements on them. We find an extremely small QP residueZ (fraction of spectral weight in the coherent quasiparticleexcitation), extended parallel Fermi surface sections, and amomentum dependent gap, opening at the bulk phasetransition temperature. Comparison of Fermi volumesand velocities from the two techniques establishes theground state of Ca3Ru2O7 as a low carrier density metal.Together, the data indicate that the unusual ground stateresults from a Peierls-like electronic instability, gappingaway large parts of the Fermi surface.Photoemission experiments were performed with aScienta SES 2002 spectrometer, using He I  radiation(21.22 eV) from a microwave driven monochromatizeddischarge lamp (Gammadata VUV5000). The differentialpumping of the He leakage from the plasma chamber hasbeen optimized to provide a partial pressure in the mea-surement chamber near the sensitivity limit of UHV iongauges, without restricting the large solid angle of 10collected by the refocusing toroidal monochromator.Energy and angular resolutions were set to 7:5 meV=0:15 for all measurements. Single crystals of Ca3Ru2O7with lowest residual in-plane resistivity of 40  cm weregrown by a floating zone method [12], oriented by Lauediffraction and cleaved in situ at a pressure below 5	1011 torr along the ab plane. Samples cleaved at 10 and60 K yielded consistent results and the low-energy spectrashowed minimal changes over the time span of a typicalexperimental run of 24 h. Magnetoresistance and the Halleffect were studied between 50 mK and 1 K in a dilutionrefrigerator/15 T magnet.Full details of our QO and magnetotransport measure-ments will be published elsewhere, but to form a basis for1-1 © 2006 The American Physical SocietyPRL 96, 107601 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending17 MARCH 2006comparison with the ARPES results we summarize themhere. The Fermi surface consists of tiny, quasi-two-dimensional pockets of electrons and holes, typical areas0.3% of that of the Brillouin zone (BZ). The measuredquasiparticle effective masses correspond to Fermi veloc-ities of approximately 5	 104 m=s. The masses account,within experimental error, for the small electronic specificheat of 2:8 mJ=mol K2, which we measured on the samecrystals, so we are confident that the QOs are probing theentire Fermi surface.In Fig. 1, we compare the ARPES spectra of Ca3Ru2O7and Sr3Ru2O7 over a large energy range. The isoelectronicnature upon substitution of Sr with Ca is clearly reflected inthe spectra which show similar energies and dispersivebehavior of the main valence band peaks. Despite this grosssimilarity of the lower valence states, there is a strikingdifference in the spectral function near the Fermi levelEF. While Sr3Ru2O7 shows intense quasiparticle peaksand multiple bands crossing the Fermi level, the spectralweight in Ca3Ru2O7 is dramatically suppressed below150 meV and only a weak tail extends towards EF[Fig. 1(c)]. For the rest of the Letter, we will focus onthis tail, which reflects the lowest lying excitations respon-sible for the transport and thermodynamic properties. Thehigh resolution and stability of our spectrometer has al-lowed us for the first time to observe well-defined quasi-particle bands, emerging on this faint tail below atemperature of  30 K, in line with the onset of coherentmetallic transport in the ab plane [10,12]. These statesexhibit an extremely low QP residue Z, over an order ofmagnitude lower than in Sr3Ru2O7, indicative of stronglyenhanced interactions, but remain sharply defined in en-ΓΓΓFIG. 1 (color online). (a),(b) Valence band spectra ofSr3Ru2O7 and Ca3Ru2O7 taken with equal momentum stepsalong M (h  21:2 eV, T  10 K). In (c) and (d), spectraof the two compounds have been normalized to the total spectralweight of the valence band (integrated from 0 to 7 eV) and arecompared on two different energy scales. A fit of the low-energyweight assuming a FL-like QP on a rising incoherent part,indicates a self-energy I  5 meV at E EF  15 meV.10760ergy. From fits to empirical spectral functions [seeFig. 1(d)], we estimate an intrinsic lifetime broadeningI  5 meV at binding energies around 15–20 meV, com-parable to the value found for the intense quasiparticlepeaks in the moderately correlated Fermi liquid compoundSr2RuO4 [5]. For a Fermi liquid with momentum indepen-dent self-energy, the QP spectral weight depends only onthe mass enhancement and therefore on the scattering rate.The observation of sharp QPs at energies >15 meV withsmall Z thus points to strongly momentum and possiblyorbital dependent interactions [13].The momentum distribution of the spectral weight nearEF is shown in Figs. 2(a) and 2(b). These maps are oftencasually identified with the Fermi surface. However, thepresent case requires a more careful interpretation.Integrating the spectral weight over a typical energy rangeof EF  12 meV results in two dominant structures, assummarized in Fig. 2(c): a ‘‘large square’’ contour withrounded corners, connecting the M points of the reducedorthorhombic BZ, and a smaller, more intense squarecomposed of four broad triangular features. The identifi-cation of these contours as Fermi surface sheets wouldconflict with the QO data, which indicate extremely smallFIG. 2 (color). (a),(b) Momentum distribution of the lowestlying spectral weight in Ca3Ru2O7 at T  9 K. The two differentenergy windows correspond to effective resolutions of 25 and10 meV, respectively. Red lines in (b) indicate momentum spacelocations of the dispersion plots in Fig. 3. (c) Schematic of thedominant features in the low-energy excitations. The smallFermi arc near theM point is backfolded by the proposed nestingvector to connect to a closed Fermi surface contour (see text).(d) Selected spectra, extracted from the data set of (a) and (b)demonstrating different gap sizes for various points in the BZ.Metallic states are found only in the vicinity of the M points.1-2FIG. 3 (color). (a),(b) Dispersion of QP states along M dis-played as false color plot or stack of equally spaced EDCs,respectively. A metallic band is found near the M point. Whitedots indicate the peak positions found from Lorentzian fits toMDCs. (c)–(e) are taken along the momentum space linesindicated in Fig. 2(b) and show in detail how the bands bendback and a gap opens as the nested part of the underlying FS isapproached. White dots mark the peak positions in EDCs.PRL 96, 107601 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending17 MARCH 2006carrier pockets with an average volume of only 0.3% of theBZ. It is important to elucidate the origin of the apparentinconsistency, because large FS sheets are expected fromband structure calculations [14] and were observed in theisovalent Sr3Ru2O7 in density functional calculations [15],ARPES [16,17], and de Haas–van Alphen data [4].In Fig. 2(b), the spectral weight is integrated over anarrower energy range of 3 meV. Clearly, this sup-presses the intense inner square contour, indicating thatthe constituting states are gapped and do not contribute tothe Fermi surface. Extracting energy distribution curves(EDCs) at selected momentum points from the same dataset confirms this finding. The spectra at points 1–3 and 4–6, marked in Fig. 2(a), show weakly dispersing, faint QPpeaks and a clear leading edge that is gapped by 5–9 meV[Fig. 2(d)]. Next, we focus on the large square contour.Two sets of spectra, crossing it (7–9, 10–12) show tailsextending up to EF but a distinct leading edge with mid-points (LEM) clearly below the Fermi level. Metallic stateswith a LEM at the chemical potential are found only in therounded edges of the large square, near the M points.Summarizing the data of Fig. 2, we find a peak in thezero-frequency momentum distribution (bright spot in theFermi surface map), coexisting with a leading edge gap.This behavior is characteristic for systems where an elec-tronic instability such as a charge density wave or theformation of Cooper pairs opens a gap in the single particleexcitation spectrum. Assuming a particle-hole symmetricbut gapped band, the remnant intensity in the photoemis-sion Fermi surface map can be identified with the under-lying band structure before the instability gapped awaymost of the FS [18]. The diamond shape seen in Fig. 2(b)suggests that the FS of Ca3Ru2O7 is composed of quasi-1Ddxz;yz orbitals, as detailed in Ref. [12]. Strikingly, thedetected underlying FS contour exhibits extended parallelsections and is almost perfectly nested with the vector=a;=b corresponding to a real space periodicity oftwo Ru-Ru nearest neighbor distances. Based on this find-ing, we postulate the formation of a commensurate densitywave below 48 K. This idea is fully consistent with thetemperature dependence of the gap, the QO data, and thelow electronic specific heat as will be shown later.The postulate of a density wave in Ca3Ru2O7, introduc-ing the new periodicity of =a;=b, is further supportedby the details of the quasiparticle dispersion, shown inFig. 3. The dispersion of the metallic states in the roundedcorners of the underlying FS is traced in Fig. 3(a) by whitedots, obtained from Lorentzian fits of the momen-tum distribution curves (MDCs). The group velocity of0:26 eV A for this band is in good agreement with theestimate of 5	 104 m=s (0:33 eV A) from the QOs. Theevolution of the dispersion upon approaching the nestedsections of the underlying FS is shown in Figs. 3(c)–3(e).Moving away from the high symmetry line by as little as0:09=b [Fig. 3(d)], the QP band starts to bend back and a10760gap of a few meV opens. This raises the intriguing ques-tion of how the Fermi level crossing around 0:88=a,seen in Fig. 3(a), connects to a closed FS contour. Fold-ing the rounded corner of the large square by the newlyimposed periodicity corresponding to the nesting vector of(=a;=b), we would expect a roughly square electronpocket centered at M with slightly concave edges, assketched in Fig. 2(c). The volume of such a pocket canbe estimated as 0:12=a2  0:36%ABZ, assuming a sim-ple square shape, in good agreement with the average FS-sheet volume deduced from the QOs. The apparent absenceof the folded bands in the FS map and dispersion plots doesnot disprove this model, since the intensity of folded bandsin ARPES is proportional to the coupling responsible forthe folding [18]. Taking the energy gap (5 meV) as ameasure of this coupling, and comparing it to typical bandgap sizes (0:5 eV), we expect a suppression of the foldedbands to intensities clearly below a level detectable byARPES. Additional metallic states are found near M0, butthe band topology is less clear, in part because of thesmaller BZ-dimension along b, which moves the zoneboundary closer to the edge of the large square contour.In Fig. 4, we show the temperature and momentumdependence of the gap. The direct comparison of spectrataken above and below the 48 K phase transition tempera-ture along the high symmetry line M [Fig. 4(a)] clearlydemonstrates a significant momentum dependence in thelow-temperature phase and confirms that the states in thecorners of the low-energy square contour remain metallic:the highlighted spectra at point 1 show identical leadingedge midpoints, which coincide within the experimentalerror with the Fermi level. The evolution of the low-energyspectral weight with temperature is shown in Fig. 4(b) for1-3ππFIG. 4 (color). Temperature and momentum dependence of thegap. (a) shows spectra taken at 9 and 52 K along the red linedepicted in the BZ inset. (b) Temperature series of spectra atpoint 3. (c) Evolution of the leading edge gap with temperaturefor momentum space points 1–3 with kx; ky  0:88a ; 0,0:69 a ; 0:34b, and 0:5a ; 0:5b, respectively.PRL 96, 107601 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending17 MARCH 2006point 3 marked in the BZ inset. The spectral line shapedoes not change significantly at the Néel transition tem-perature of 56 K, and only a minor redistribution of weightoccurs at 48 K. This is consistent with the weak perturba-tion, expected from a symmetry breaking ordering withlow phase transition temperature and small gap. Morepronounced changes of the spectral function are observedbelow 35 K, where sharply defined, faint QP peaks emerge.Notably this coincides with the onset of metallic transport,roughly 10 K below the structural phase transition tem-perature [12], rather than with the transition temperatureitself.Leading edge gaps LE were obtained from empiricalfits to the data and are shown in Fig. 4(c). The opening ofthe gap is observed at 48.3 K, in perfect agreement with thebulk structural phase transition temperature of 48 K [19].No hysteresis was observed within the experimental errorsof 2 K. The gap opens to a full size of LE 10–12 meV at low temperature. It is thus of the same orderof magnitude as the mean-field value for the Peierls gap of2  3:5kT (14.6 meV at 48 K), but significantly smallerthan the value of 0:1 eV, reported previously from ananalysis of Raman data from flux grown crystals [20].The nested Fermi surface and the above described tem-perature dependence of the gap suggest that the unusualground state of Ca3Ru2O7 does not result from an orbitalselective Mott transition, as it has been proposed forCa2xSrxRuO4 [7], but originates from the interactionwith spin, orbital or lattice degrees of freedom and bearssome resemblance to a Peierls transition. Although muchof the data reported in this Letter are consistent with weakcoupling theory, we found several spectroscopic signatureswhich point beyond a nesting driven Peierls instability. The10760very small Z and the coexistence of heavy, non-nestedbands which become similarly gapped at 48 K with adispersive nested band suggest a more complex picturewhere strong and possibly orbital dependent interactionsare present. Whether the observed electronic instability isthe consequence or the driving force of the simultaneousstructural and magnetic phase transition remains ambigu-ous, as does the nature of the symmetry breaking ordering,which we propose from the observed nesting vector of(=a;=b) and the gapping of all nested states. It is hopedthat the present work stimulates neutron or x-ray diffrac-tion studies which can give direct evidence for ordering oflattice, spin, or orbital degrees of freedom. The latter hasbeen proposed independently from recent Raman scatter-ing, magnetization and transport measurements [21,22].We thank G. Wigger and J. Denlinger for helpful dis-cussions. This work has been supported by ONR GrantNo. N00014-01-1-0048. Additional support from SSRL isprovided by the DOE’s office of Basic Energy Science,Division of Material Science with Contract No. DE-FG03-OIER45929-A001.1-4[1] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.70, 1039 (1998).[2] A. P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75,657 (2003).[3] A. P. Mackenzie et al., Phys. Rev. Lett. 76, 3786 (1996).[4] R. A. Borzi et al., Phys. Rev. Lett. 92, 216403 (2004).[5] N. J. C. Ingle et al., Phys. Rev. B 72, 205114 (2005).[6] A. Damascelli et al., Phys. Rev. Lett. 85, 5194 (2000).[7] V. I. Anisimov et al., Eur. Phys. J. B 25, 191 (2002).[8] S. Nakatsuji and Y. Maeno, Phys. Rev. Lett. 84, 2666(2000).[9] Y. Yoshida et al., Phys. Rev. B 72, 054412 (2005).[10] Y. Yoshida et al., Phys. Rev. B 69, 220411(R) (2004).[11] E. Ohmichi et al., Phys. Rev. B 70, 104414 (2004).[12] N. Kikugawa et al. (unpublished).[13] Data taken at various photon energies between 16 and41 eV showed a similarly low weight of the coherent QP.[14] D. J. Singh and S. Auluck, Phys. Rev. Lett. 96, 097203(2006).[15] D. J. Singh and I. I. Mazin, Phys. Rev. B 63, 165101(2001).[16] A. V. Puchkov et al., Phys. Rev. Lett. 81, 2747 (1998).[17] A. V. Puchkov, Z. X. Shen, and G. Cao, Phys. Rev. B58, 6671 (1998).[18] J. Voit et al., Science 290, 501 (2000).[19] The given temperatures may contain an absolute error ofabout 2 K at temperatures around 48 K, due to theunknown gradient within sample and sample holder.[20] H. L. Liu et al., Phys. Rev. B 60, R6980 (1999).[21] J. F. Karpus et al., Phys. Rev. Lett. 93, 167205 (2004).[22] G. Cao et al., New J. Phys. 6, 159 (2004).

Nested Fermi surface and electronic instability in Ca3Ru2O7

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Nested Fermi surface and electronic instability in Ca3Ru2O7

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