Electron Correlation Driven Heavy-Fermion Formation in LiV2O4
P. E. Jönsson, K. Takenaka, S. Niitaka, T. Sasagawa, S. Sugai, H. Takagi
aa r X i v : . [ c ond - m a t . s t r- e l ] J un Electron Correlation Driven Heavy-Fermion Formation in LiV O P. E. J¨onsson,
1, 2, ∗ K. Takenaka,
1, 2
S. Niitaka,
1, 2
T. Sasagawa,
S. Sugai, and H. Takagi
1, 2, 3 RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan CREST, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan Department of Advanced Materials Science, University of Tokyo,5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan (Dated: November 6, 2018)Optical reflectivity measurements were performed on a single crystal of the d -electron heavy-fermion (HF) metal LiV O . The results evidence the highly incoherent character of the chargedynamics for all temperatures above T ∗ ≈
20 K. The spectral weight of the optical conductivity isredistributed over extremely broad energy scales ( ∼ f -electron Kondo lattice HFsystems, characteristic of a metallic system close to a correlation driven insulating state. Our resultsthus reveal that strong electronic correlation effects dominate the low-energy charge dynamics andheavy quasiparticle formation in LiV O . We propose the geometrical frustration, which limitsthe extension of charge and spin ordering, as an additional key ingredient of the low-temperatureheavy-fermion formation in this system. PACS numbers: 78.30.Er,71.27.+a,75.20.Hr
Electrons in solids, by coupling with spins and lattices,form dressed particles called quasiparticles (QP). Themass of such QPs can in some cases be extremely heavy,100-1000 times the bare electron mass. The systems withextremely heavy QPs are called heavy fermions (HF) andhas been attracting considerable interest since they dis-play a variety of novel phenomena including exotic su-perconductivity [1]. Recently, a few d -electron systemshave been found to exhibit physical properties charac-teristic of HF systems, e.g Y(Sc)Mn [2], Na . CoO [3]and LiV O [4, 5, 6, 7]. Conventional HF metals are f -electron systems containing rare-earth or actinide ions,in which the low temperature heavy QP formation canbe understood based on the Kondo-coupling between lo-calized f -electron moments and itinerant electrons. Inthe case of d -electron metals, it is not obvious to iden-tify the same Kondo coupled itinerant and localized elec-trons. A common point for the d -electron HF metals isinstead that the magnetic ions occupy sites on geomet-rically frustrated lattices. It has been discussed that theHF behaviour of d -electron systems might imply a newroute to the formation of heavy quasiparticles.Among the d -electron HF metals the spinel LiV O ,has the largest quasiparticle specific heat coefficient γ =420 mJ/mol.K [4]. It exhibits a short-range antiferro-magnetic order below 80 K [8], and no other kind of long-range magnetic order at any measured temperature. Ata characteristic temperature, T ∗ ≈
20 K, the heat capac-ity over temperature
C/T shows a steep increase and theelectrical resistivity ρ a sharp drop, suggesting that co-herence is formed [6]. This, in addition to a Fermi liquidground state [6] and a peak in the density-of-states (DOS)located ∼ E F ) [7], confirmthe low- T HF properties. Band structure calculationson LiV O indicate that mainly vanadium 3 d t g bands crosses the Fermi level [9, 10]. These V(3 d ) t g bands arewell separated from the filled O(2 p ) bands and the emptyV(3 d ) e g bands. The triply degenerate t g orbitals aresplitted into doubly degenerate E g and nondegenerate A g orbitals due to the trigonal crystal field. As a resultof this trigonal splitting and d - d Coulomb interaction, ithas been proposed that the A g orbitals can be consid-ered as localized and the E g orbitals as itinerant per-mitting to map the electronic structure of LiV O into aKondo-lattice picture [10]. It requires, however, a subtlecancellation of ferromagnetic coupling through double ex-change with antiferromagnetic coupling through Kondo-like exchange. Other scenarios have been proposed inwhich the geometrical frustration is an important ingre-dient for the HF formation [11, 12]. Still, the origin ofthe HF formation in LiV O is a matter of controversy,which can only be resolved by new detailed experiments.In particular, a method probing the electronic structureover wide energy scales, such as optical spectroscopy,may reveal valuable information about the mechanismsresponsible for the low energy HF formation.In this Letter, we report the first detailed investigationof the optical properties of single crystals of LiV O . Theincoherent charge dynamics at T > T ∗ and the transfer ofspectral weight over broad energy scales ( ∼ O , in contrast to conventional f -electron HFmetals, is a correlated metal in proximity to a correlationdriven insulating state. We outline a scenario in whichstrong correlation effects are controlling the formation ofheavy QP states, while the key role of the geometricalfrustration is to limit the extension of charge and spinorderings.Single crystals of LiV O were grown by the fluxmethod described in Ref. [13]. Near-normal incident re-flectivity spectra were measured on the as-grown shinysurface of crystals with octahedral shape and { } faceswith edges of at most 1 mm. We confirmed that the re-flectivity at room temperature was the same as that of asmall cleaved surface. The reflectivity was measured us-ing a Fourier-type interferometer for the photon energyrange of ~ ω =0.01–1.0 eV and grating spectrometers forthe energy range 0.5–6 eV. The crystal size was sufficientfor optical measurements using microscopes designed forthe infrared (IR) and visible-ultraviolet spectrometers.As a reference mirror we used an evaporated Au film ona glass plate with the same shape and size as the sam-ple for the far-to-near IR regions, in order to cancel outdiffraction effects. The experimental error of the reflec-tivity, determined by the reproducibility, was less than1%. The dc resistivity ρ was measured using a four-probetechnique. R e f l e c t i v i t y −1 LiV O FIG. 1: (color online). Optical reflectivity spectra measuredon the as-grown surface of LiV O crystals at temperaturesof 6, 100, 200 and 295 K (solid lines, from top to bottom) andon the polished surface (using lapping films with diamondpowder of diameter 1 µ m) at 295 K (dashed line). The insetshows the low-energy part of the as-grown surface spectrawith an optical phonon peak at ∼
420 cm − (0.05 eV). Thedotted lines are the extrapolations using the Hagen-Rubensformula. The reflectivity spectra measured on the as-grown sur-face at different temperatures are shown in Fig. 1. Areflectivity edge, observed around 1.5 eV, reflects themetallic character of this system, which produces the far-infrared (FIR) spectral weight in the optical conductiv-ity due to charge carriers. In ordinary metals, the edgeis steep and the reflectivity below the edge is alreadyclose to 1. However, in LiV O the reflectivity shows agradual increase below the edge and the reflectivity inthe mid-infrared (MIR) and near-infrared (NIR) regionsare rather suppressed, suggesting the incoherent natureof the charge carriers. With decreasing temperature thereflectivity edge becomes sharper, and the reflectivity inthe FIR to MIR region higher, indicating that coherenceis gained at lower temperatures. No significant changewas observed in the reflectivity spectra from 50 K downto the lowest measured temperature of 6 K in the con- sidered frequency range.The room temperature reflectivity for a polished sur-face is also shown in Fig. 1. The reflectivity of thepolished surface is significantly reduced in the mid-to-near IR region and rather enhanced in the visible-to-ultraviolet region. If the scattering of the incident light isincreased simply due to residual surface roughness, thereflectivity measured on the polished surface would besuppressed over all energy regions. We therefore con-sider that the observed variation of the reflectivity re-flects changes in the electronic states. The charge exci-tations are sensitive to static imperfections and/or struc-tural strain. The suppressed IR reflectivity indicates thetendency of the charge carriers to localize while the en-hanced visible-to-ultraviolet reflectivity suggests an inti-mate relation between the charge carrier dynamics andthe higher-lying interband transitions. This sensitivityof the reflectivity to surface treatment, similar to that ofsome manganites in a metallic phase [14], suggests theimportance of electronic correlations in LiV O [15].Group theory predicts that four F u phonons are IR ac-tive in a cubic spinel. For insulating cubic spinels, the twolower-energy modes have much smaller spectral weightcompared with the two higher-energy modes [16, 17].In the high electrical resistivity metal or semiconduct-ing MgTi O , only the two higher-energy phonons areobserved at 420 cm − and 600 cm − [18]. The 420 cm − mode having the largest spectral weight in the metallic(semiconducting) phase. The absence of the two lower-energy modes is ascribed to the screening by free carri-ers. Only one phonon is observed at 420 cm − in metallicLiV O (inset of Fig. 1). Taking into account the screen-ing effect, the other phonon modes are likely buried inthe noise level of the reflectivity spectrum.The optical conductivity σ ( ω ) was determined fromthe reflectivity data by Kramers-Kronig transformation.To do this, we assumed the Hagen-Rubens formula in thelow-energy region and used a constant reflectivity above6 eV followed by a well-known function of ω − in thevacuum-ultraviolet region. The optical conductivity inthe low-energy region is shown in Fig. 2, and the con-nection with the dc conductivity σ dc (= ρ − ) in the rightinset.The evolution of σ ( ω ) as a function of temperatureclearly demonstrates a crossover from coherent to inco-herent charge dynamics. At T = 6 K (below T ∗ ≈
20 K),by extrapolating the measured σ ( ω ) to σ dc , a clear Drudecontribution is identified at low energies, consistent withthe formation of coherent quasiparticles. The Drude con-tribution shows a very slow decay with ω , which is typicalfor strongly correlated transition-metal oxides. A sharpcoherence peak in the DOS, located ∼ E F ,was observed recently by high-resolution photoemissionspectroscopy at temperatures below T ∗ [7]. The DOSof f -electron HF systems exhibits a similar low- T DOSpeak, known as the Kondo resonance, yielding an narrowDrude peak in σ ( ω ) [1]. In addition, a pseudogap anda broad MIR peak, originating from optical inter-bandtransitions between renormalized hybridization bands,appears for many f -electron HF systems [19, 20]. Whilethe low temperature narrow Drude peak is observed in σ ( ω ) of LiV O , the broad MIR peak and pseudogapcannot clearly be identified. ω [eV] σ ( ω ) [ Ω − c m − ] LiV O σ ( ω ) h ω x 10 x 10 ρ [ m Ω . c m ] FIG. 2: (color online). Real part of σ ( ω ) of LiV O at T =6,100, 200 and 295 K (from top to bottom). The peaks near0.05 eV are due to optical phonons. The left inset shows thetemperature dependence of the resistivity ( ρ = σ − ). Theright inset the connection between σ ( ω ) (solid lines) and σ dc (markers), the dotted lines are only guides for the eye. Above T ∗ ≈
20 K, the Drude contribution is not welldefined anymore, instead, a finite energy peak shows upin σ ( ω ). This is most clearly seen in the spectrum at295 K, where a broad peak centered around 0.1 eV isobserved. The presence of such finite energy peak is lessclear at lower temperatures. However, the fact that σ dc above T ∗ ≈
20 K is much lower than naively anticipatedfrom low energy σ ( ω ) clearly indicates the presence of alow energy peak. The resistivity, shown in the left insetof Fig. 2, exhibits almost T -linear dependence above T ∗ ,followed by a rapid decrease below T ∗ with decreasingtemperature. Although the temperature dependence of ρ is seemingly metallic above T ∗ , the large magnitude ofthe resistivity in this temperature range yields k F l . T ∗ .With increasing temperature to above T ∗ , the FIR con-ductivity does not only become incoherent but also loosesits spectral weight. The missing spectral weight is trans-ferred over an extremely broad energy region as shownin Fig. 3. The effective carrier density defined as N eff = 2 m Vπe Z ω σ ( ω ′ ) dω ′ (1) (with m being the bare electron mass and V the unit-cellvolume) indicates that the f -sum rule is finally fulfilledabove ∼ W of the conduc-tion band. This is a feature characteristic of correlatedmetallic systems close to a Mott insulating or charge or-dered state [21], but in sharp contrast to f -electron HFsystems in the Kondo-lattice regime[1, 22]. In HF met-als, spectral weight redistribution is confined to energies ~ ω < W [23]. Typically this energy scale is very lowof the order of 10-100 meV [1, 22]. The possibility ofKondo lattice formation resulting from the band struc-ture and d − d Coulomb correlations has been proposedfor LiV O [10]. In that model, the mechanism for theheavy QP formation is similar as for f -electron systems,i.e. hybridization between the “localized” A g band andthe “itinerant” E g band. While such a model may explainthe resonance peak in the DOS, it is not obvious that itcan account for the redistribution of spectral weight overthe energy range of 5 eV in Fig. 3. ω [eV] N e ff /f. u . (b)0 2 4 600.06 ∆ N e ff σ ( ω ) [ Ω − c m − ] LiV O (a)6K295K FIG. 3: (color online). (a) Real part of σ ( ω ) on a semiloga-rithmic scale. (b) Integrated spectral weight N eff per formulaunit. Inset: ∆ N eff ( ω ) = m Vπe R ω [ σ K ( ω ′ ) − σ K ( ω ′ )] dω ′ . The incoherent transport in LiV O is similar to thatof a wide range of correlated bad metals, including vana-dates [24], manganites [25], cobaltates [26], cuprates [27],ruthenates [28], and organic conductors [29]. In corre-lated metals, the coherence temperature is suppresseddown to room temperature or lower and the charge dy-namics is incoherent at higher temperatures. In the in-coherent regime, σ ( ω ) is characterized by a finite-energypeak, instead of a conventional zero-energy (Drude) peak.The metallic T -dependence of the dc resistivity does notreflect the broadening of a Drude peak as in ordinarymetals, but the collapse of the Drude peak into a finiteenergy peak and the reduction of the FIR spectral weightwith increasing temperature. These features typical ofcorrelated bad metals, as well as the transfer of spectralweight over a large energy scale (shown in Fig. 3) demon-strate that strong electronic correlations dominate thecharge dynamics and the recovery of the quantum coher-ence at low temperatures in LiV O .LiV O is a mixed valent spinel with equal ratio of V and V , and it is very likely located in the close vicinityof a charge ordered state. In general, the QP mass isenhanced when approaching a correlation driven metal-insulator transition from the metallic side [30]. In mostcases, however, spin and/or charge ordering occurs beforeany gigantic enhancement of the mass is realized, givingrise to only a moderately enhanced mass. In LiV O however, the long range spin-orbital-charge order is pre-vented by the geometrical frustration and hence the massenhancement may proceed further. Accordingly, theoret-ical studies of simple models for strongly correlated elec-tron systems suggest a considerable suppression of thetemperature scale of electronic coherence by magneticfrustration [31] and a Kondo-like resonance in the metal-lic phase close to a Mott or charge-ordered transition[32].In summary, we have investigated the temperaturedependent optical properties of LiV O using well-characterized single crystals. A strongly incoherentcharge dynamics is found for all temperatures above T ∗ ≈
20 K, in agreement with the “bad-metal” behav-ior observed in resistivity measurements. The transferof spectral weight occurs over an extremely wide energyrange when the quantum coherence of the electrons is re-covered, as observed in correlated metals close to a cor-relation driven insulating state. This clearly indicatesthat strong correlation effects are controlling the forma-tion of quasiparticle states at low energies in LiV O . Wepropose the geometrical frustration, which limits the ex-tension of charge and spin ordering, as an additional keyingredient of the low-temperature HF formation. Thisgeneral scenario might be extended to other geometricalfrustrated d -electron metals with heavy quasiparticles.We are grateful to K. Okazaki for his help in the IRmeasurements and to J. Matsuno for valuable discus-sions. This work was supported by Grant-in-Aids forCreative Scientific Research from the Ministry of Educa-tion, Culture, Sports, Science and Technology of Japan. ∗ Current address: Department of Physics, Uppsala Uni-versity, Box 530, SE-751 21 Uppsala, Sweden[1] L. Degiorgi, Rev. Mod. Phys. , 687 (1999). [2] M. Shiga, K. Fujisawa, and H. Wada, J. Phys. Soc. Jpn. , 1329 (1993).[3] K. Miyoshi, E. Morikuni, K. Fujiwara, J. Takeuchi, andT. Hamasaki, Phys. Rev. B , 132412 (2004).[4] S. Kondo et al. , Phys. Rev. Lett. , 3729 (1997).[5] A. Krimmel, A. Loidl, M. Klemm, S. Horn, and H.Schober, Phys. Rev. Lett. , 2919 (1999).[6] C. Urano, M. Nohara, S. Kondo, F. Sakai, H. Takagi, T.Shiraki, and T. Okubo, Phys. Rev. Lett. , 1052 (2000).[7] A. Shimoyamada et al. , Phys. Rev. Lett. , 026403(2006).[8] S.-H. Lee, Y. Qiu, C. Broholm, Y. Ueda, and J. J. Rush,Phys. Rev. Lett , 5554 (2001).[9] J. Matsuno, A. Fujimori, and L. F. Mattheiss, Phys. Rev.B , 1607 (1999).[10] V. I. Anisimov, M. A. Korotin, M. Z¨olfl, T. Pruschke,K. LeHur, and T. M. Rice, Phys. Rev. Lett , 364(1999).[11] P. Fulde, A. N. Yaresko, A. A. Zvyagin, and Y. Grin,Europhys. Lett. , 779 (2001).[12] J. Hopkinson and P. Coleman, Phys. Rev. Lett. ,267201 (2002).[13] Y. Matsushita, H. Ueda, and Y. Ueda, Nature Materials , 845 (2005).[14] K. Takenaka, K. Iida, Y. Sawaki, S. Sugai, Y. Moritomo,and A. Nakamura, J. Phys. Soc. Jpn. , 1828 (1999).[15] A. J. Millis, Solid State Commun. , 3 (2003).[16] H. D. Lutz, B. M¨uller, and H. J. Steiner, J. Solid StateChem. , 54 (1991).[17] A. B. Sushkov, O. Tchernyshyov, W. Ratcliff , S. W.Cheong, and H. D. Drew, Phys. Rev. Lett. , 137202(2005).[18] Z. V. Popovic, G. De Marzi, M. J. Konstantinovi´c, A.Cantarero, Z. Dohcevic-Mitrovic, M. Isobe, and Y. Ueda,Phys. Rev. B , 224302 (2003).[19] S. V. Dordevic, D. N Basov, N. R. Dilley, E. D. Bauer,and M. B. Maple, Phys. Rev. Lett., , 684 (2001).[20] L. Degiorgi, F. B. B. Anders, and G. Gr¨uner, Eur. Phys.J. B , 167 (2001).[21] O. Gunnarsson, M. Calandra, and J. E. Han, Rev. Mod.Phys. , 1085 (2003); M. Imada, A. Fujimori, and Y.Tokura, Rev. Mod. Phys. , 1039 (1998).[22] D. E. Logan and N. S. Vidhyadhiraja, J. Phys.:Condens.Matter , 2935 (2005); N. S. Vidhyadhiraja and D. E.Logan, J. Phys.:Condens. Matter , 2959 (2005).[23] N. E. Hussey, K. Takenaka, and H. Takagi, Phil. Mag. , 2847 (2004).[24] M. J. Rozenberg, G. Kotliar, H. Kajueter, G. A. Thomas,D. H. Rapkine, J. M. Honig, and P. Metcalf, Phys. Rev.Lett. , 105 (1995).[25] K. Takenaka, Y. Sawaki, and S. Sugai, Phys. Rev. B ,13011 (1999); K. Takenaka, R. Shiozaki, and S. Sugai,Phys. Rev. B , 184436 (2002).[26] N. L. Wang, P. Zheng, D. Wu, Y. C. Ma, T. Xiang, R.Y. Jin, and D. Mandrus, Phys. Rev. Lett. , 237007(2004).[27] K. Takenaka, J. Nohara, R. Shiozaki, and S. Sugai, Phys.Rev. B , 134501 (2003); D. N. Basov and T. Timusk,Rev. Mod. Phys. , 721 (2005).[28] Y. S. Lee, Jaejun Yu, J. S. Lee, T. W. Noh, T.-H.Gimm, Han-Yong Choi, and C. B. Eom, Phys. Rev. B , 041104(R) (2002).[29] K. Takenaka, M. Tamura, N. Tajima, H. Takagi, J. No-hara, and S. Sugai, Phys. Rev. Lett. , 227801 (2005). [30] Y. Tokura, Y. Taguchi, Y. Okada, Y. Fujishima, T.Arima, K. Kumagai, and Y. Iye, Phys. Rev. Lett. ,2126 (1993).[31] O. Parcollet and A. Georges, Phys. Rev. B , 5341(1999); J. Merino and R. H. McKenzie, Phys. Rev. B , 7996 (2000).[32] T. Ohashi, N. Kawakami, and H. Tsunetsugu, Phys. Rev.Lett. , 066401 (2006); H. Kusunose, S. Yotsuhashi, andK. Miyake, Phys. Rev. B,62