Symmetry breaking and unconventional charge ordering in single crystal Na 2.7 Ru 4 O 9
Arvind Yogi, C. I. Sathish, Hasung Sim, Matthew J. Coak, Y. Noda, Je-Geun Park
SSymmetry breaking and unconventional charge ordering in single crystal Na . Ru O Arvind Yogi,
1, 2, ∗ C. I. Sathish,
1, 2
Hasung Sim,
1, 2
Matthew J. Coak,
1, 2
Y. Noda,
3, 4 and Je-Geun Park
1, 2, † Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea J-PARC center, Institute of Materials Structure Science,High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan Institute of Multidisciplinary Research for Advanced Materials,Tohoku University, Sendai 980-8577, Japan (Dated: April 9, 2018)The interplay of charge, spin, and lattice degrees of freedom in matter leads to various forms ofordered states through phase transitions. An important subclass of these phenomena of complexmaterials is charge ordering (CO), mainly driven by mixed-valence states. We discovered by combin-ing the results of electrical resistivity ( ρ ), specific heat, susceptibility χ ( T ), and single crystal x-raydiffraction (SC-XRD) that Na . Ru O with the monoclinic tunnel type lattice (space group C m )exhibits an unconventional CO at room temperature while retaining metallicity. The temperature-dependent SC-XRD results show successive phase transitions with super-lattice reflections at q =(0, , 0) and q =(0, , ) below T C2 (365 K) and only at q =(0, , 0) between T C2 and T C1 (630 K).We interpreted these as an evidence for the formation of an unconventional CO. It reveals a strongfirst-order phase transition in the electrical resistivity at T C2 (cooling) = 345 K and T C2 (heating)= 365 K. We argue that the origin of the phase transition is due to the localized 4 d Ru-electrons.The results of our finding reveal an unique example of Ru /Ru mixed valance heavy d ions. PACS numbers: 75.50.Ee, 75.40.Cx, 75.10.Jm, 75.30.Et
I. INTRODUCTION
Symmetries are important in condensed matter sys-tems with strong ramifications on physical properties.Phase transitions are usually accompanied by a brokensymmetry [1], which then leads to the appearance ofsome ordered phases [2]. In solids, the conduction elec-trons experience competing interactions with each otherand elementary excitations. Ru-based materials have re-cently emerged as a fertile ground for emergent phenom-ena driven by a modest spin-orbit coupling (SOC) typicalof 4 d electronic states [3–10]. The 4 d electrons of Ru arealso known to exhibit both localized and itinerant char-acters. A subtle balance between localization and itiner-ancy commonly gives rise to a rich variety of electronicand magnetic properties [11].The heavy d ions based systems have been widelyinvestigated, particularly because of interplay betweenSOC with intermediate strength ( (cid:39) U . This competition appears to leadto numerous unusual properties with several interestingexamples: unconventional superconductivity [12], metal-insulator transitions [13–15], orbital ordering [5], non-Fermi liquid behaviour [16, 17], high-temperature ferro-magnetism [18], low-temperature p -wave spin-triplet su-perconductivity [19], electron nematic behavior [20, 21],quantum criticality [9, 22], and itinerant ferro and meta-magnetism [23, 24]. Further, the tunnel-type structuressuch as Rutile, Ramsdellite and Hollandite can accommo- ∗ [email protected] † [email protected] date valencies from +2 to +5 [25, 26] and mixed valen-cies lead to several interesting phenomena such as charge,spin, and orbital ordering [27–29]. In this context,Na . Ru O (large tunnel type structure) is a promisingmaterial for investigating the interplay between Coulombinteractions and the modest SOC of the mixed valanceheavy d ions.Among the competing phases, charge ordering is directevidence of the Coulomb interaction. When the Coulombinteraction is the dominant energy scale, systems tendto be more localized. In this localized state, one oftenfinds an insulating phase with a certain charge ordering(CO). However, this CO becomes unstable as one raisesthe itinerancy by increasing bandwidth ( W ) or reducingthe relative effects of Coulomb U . This relative ratio of W and U gives rise to two routes to the metal-insulatortransition (MIT): one is a band-width controlled MITand the other is Mott-Hubbard MIT. It is generally be-lieved that regardless of the two mechanism of MIT theCO disappears when the system becomes metallic withexamples found in 3 d transition metal oxides. However, itis not entirely clear how this picture should change withthe introduction of spin-orbit coupling. In this sense,it is very important to accumulate enough experimentaldata before reaching at least some kind of phenomelog-ical understanding of CO and related MIT for 4 d or 5 d transition metal oxides (TMO), where the spin-orbit in-teraction is stronger.Na . Ru O crystallizes in a monoclinic crystal struc-ture with a large tunnel running parallel to the crystallo-graphic b -axis. The structure consists of corner and edgesharing RuO octahedra arranged in one-dimensionalzigzag chains, which are formed by single, double and a r X i v : . [ c ond - m a t . s t r- e l ] A p r triple edge shared chains, respectively. These zigzag-chains are linked together parallel to the c -axis by theircorners. In this report, we present physical properties ina wide temperature range (1.9 K ≤ T ≤
450 K) usingsingle crystals. We studied the structural, electronic andmagnetic properties of the mixed valence Ru /Ru compound Na . Ru O and report CO behaviour with-out the loss of metallicity. II. METHODS
Polycrystalline Na . Ru O samples were synthesizedby solid state reaction of preheated RuO (99 . CO (99 . ◦ C for 72 h with several intermediategrindings and pelletizations. Subsequently, high-qualitysingle crystals of Na . Ru O were grown from this poly-crystalline powder via a modified self-flux vapor trans-port reaction under flowing Ar-gas (ultra-pure 99 . × × ) were obtained from the final products.The phase purity and temperature-dependent (300 to450 K) powder XRD were performed by using a BrukerD8 Discover diffractometer with a Cu-K α source withno impurity peaks observed. An elemental analysis wassubsequently done confirming the stoichiometry of thesamples: we used a COXI EM-30 scanning electron mi-croscope equipped with a Bruker QUANTAX 70 energydispersive x-ray system. The temperature-dependent sin-gle crystal XRD (SC-XRD) was performed from 300 to695 K by using a single crystal diffractometer (XtaLABP200, Rigaku). The crystal structure was refined us-ing both powder and single crystal XRD data with the Fullprof [30] software suite.Electrical resistivity ( ρ ) measurements were carried outusing a home-made system equipped with a furnace (300to 450 K) and a pulsed-tube cryostat (down to 3 K, Ox-ford). The electrical resistance was measured in the four-point geometry on a static sample holder, where the con-tacts to the sample were made using silver paint and 25 µ m gold wire. Current ( I ) was applied perpendicular tothe single crystal length, which is the crystallographic b -axis. Magnetic susceptibility χ ( T ) measurements weretaken using a MPMS-SQUID magnetometer (QuantumDesign). Heat capacity C p ( T ) measurements were madeusing the commercial Physical Property MeasurementSystem (PPMS, Quantum Design). III. RESULTSA. Electrical resistivity, Heat-capacity andMagnetization
Electrical resistivity is shown for single crystalNa . Ru O in Fig. 1 (a) in the temperature range of T C 2 ( c o o l ) T C2 (heat) s i n g l e - c r y s t a l
H = 0 T ( a ) r ( mW- cm) T C 2 T C 2 p o l y - c r y s t a l
H = 0 . 5 T ( c ) T ( K ) c (10-4cm3/mol-Ru) s i n g l e - c r y s t a l H = 0 T ( b ) Cp (J/mol K)
FIG. 1. (Color online). The first order phase transition isobserved at T C2 (cooling) = 345 K and T C2 (heating) = 365K, with a clear hysteresis in resistivity ( ρ ) upon warming andcooling (a), which is also evident in specific heat (C p ) (b) andin magnetic susceptibility χ ( T ) of Na . Ru O (c). ≤ T ≤
450 K for both heating and cooling cy-cles. Metallic conductivity (d ρ /d T >
0) is observed inthe entire temperature range with a room temperatureresistivity of 187.25 µ Ω-cm. The electrical resistivity re-veals a clear hysteresis, indicative of a first-order phasetransition with two transitions at T C2 (cooling) = 345K and T C2 (heating) = 365 K: which is corroboratedwell by magnetization and heat-capacity results (Fig. 1).However, no significant difference could be observed forthe resistivity up to 9 T as compared with the zero fieldresistivity. In order to shed light on the scattering mech-anism involved and to have a quantitative understandingof the measured results, the electrical resistivity data ofNa . Ru O was analyzed theoretically by using a Bloch-Gr¨ u neisen-Mott model [31]. Using this model, we canshow that the temperature dependence of the resistivitycan be explained by the electron-phonon and inter-bandelectron mediated scattering mechanisms [see supplemen-tary information (SI-1) and Fig. S1].Heat capacity for Na . Ru O was measured in the (b)
300 330 360 390 420 4500510152025
300 400 500 600 700020406080100120
Intermediate-Phase
P2/m
Pseudo
P2/m
HT-PhaseLT-Phase ( ) I n t en s i t y ( a . u . ) T (K) T C2 T C1 C2/m ( ) I n t en s i t y ( a . u . ) T (K) T C2 -8) T e m pe r a t u r e ( K ) Int ( / / ) (0 1/2 0) ( / / ) (c)(a) (0, k, l)
300 K
FIG. 2. (Color online) (a) Reciprocal lattice map of the SC-XRD data for Na . Ru O measured at 300 K below the firstorder transition temperature T C2 . It shows the fundamental (0 , k, l ) reflections (white intense spots) and the satellite weakreflections corresponding to super-lattice peaks at q =(0, , 0) and q =(0, , ) in the b ∗ - c ∗ plane, marked by red and whitearrows, respectively. (b) The line cut for various temperatures below and above the first order transition as extracted from thereciprocal image analysis exhibits two super-lattice peaks at q =(0, , 0) and q =(0, , ). (c) The super-lattice peaks at q =(0, , ) is shown as a function of temperature, which disappears above the first order transition ( > T C2 ) ≈
370 K. Above T C2 , only the q =(0, , 0) super-lattice peak was observed, which also disappear above T C1 as shown in the inset. temperature range 1.9 K ≤ T ≤
400 K and displayed inFig. 1 (b). The specific heat shows two strong kinks withan inflection point at T C2 (cooling) = 345 K and T C2 (heating) = 365 K as shown by dashed lines in Fig. 1(b). The sharp feature of the peak, different from theusual lambda-like shape, confirms a first-order transitionin Na . Ru O . The absence of a clear sign of magneticordering in the susceptibility shown in Fig. 1 (c) indicatesthat a structural transition is most likely responsible forthe observed hysteresis in the resistivity. The low tem-perature heat capacity data can be analyzed in terms of C P = γT + βT , (1)where γ is the electronic specific-heat coefficient and β isthe phonon contribution to the total specific-heat [32].The evidence for a metal-like electronic contributionto the low-temperature heat capacity was observed.The electronic contribution to the specific heat ( γ ) forNa . Ru O was determined to be 26.91 mJ/mol K , in-dicating an enhanced contribution of conduction elec-trons in excellent agreement with the transport mea-surements. Moreover, the estimated value of γ forNa . Ru O is much larger than the free electron valueof γ and comparable with the values for other ruthen-ates: e.g. Ru superconductor Sr RuO ( γ = 40 mJ/molK Ru) and non-Fermi-liquid compound La Ru O ( γ = 25 mJ/ mol K Ru) [17, 19]. This large value of γ indicates that the conduction electrons, most likely fromRu 4 d bands, are strongly correlated.Bulk magnetic susceptibility ( χ ) for Na . Ru O wasmeasured as a function of temperature in the tempera-ture range 1.9 K ≤ T ≤
400 K under an applied field0.5 T using a poly-crystalline sample as shown in Fig. 1(c). Magnetization as a function of applied field ( H ) wasmeasured at 2 and 400 K, exhibits linear variation with-out any hysteresis with a maximum applied field of 7 T. For practical reasons, we measured magnetization usinga large mass of crushed powder sample. The magneticsusceptibility (1.9 K ≤ T ≤
400 K) of the compound istemperature independent from room temperature to 150K, indicative of Pauli-paramagnetic behaviour, which isfollowed by a Curie-like increase at lower temperature.Notably, the susceptibility curve above room tempera-ture demonstrates a broad hump at the first order phasetransition as seen in Fig. 1 (c). This is probably due toshort range correlations present at such high tempera-tures.We must note that bulk properties of Na . Ru O aresignificantly different from Na Ru O − δ , which showslarge anisotropy in both resistivity and magnetic suscep-tibility ( χ ). The metallic as well as magnetic behaviour ofNa Ru O − δ was attributed to the presence of localizedas well as itinerant Ru electrons [33]. B. X-ray diffraction measurements
In order to understand the origin of the phase transi-tion observed in the electrical resistivity and heat ca-pacity data, we performed multiple diffraction experi-ments on single crystal and poly-crystalline Na . Ru O in the temperature range between 300 and 695 K. In-terestingly enough the temperature-dependent SC-XRDresults show successive phase transitions. For example, asingle super-lattice peak appears at q =(0, , 0) in theintermediate-phase ( T C1 ≡
630 K), whereas two super-lattice peaks emerge at q =(0, , 0) and q =(0, , )below T C2 in the LT-phase as shown in Fig. 2 (a and b).We note that these super-lattice peaks were not reportedin the previous study [32] on powder samples, most prob-ably due to weak reflections.In addition, the super-lattice peak at q =(0, , ) dis-
450 K a) b)
300 K c)
695 K
T < T C2
365 K
T > T C1
630 K T C2 > T > T C1 b*a* FIG. 3. (Color online) Schematic diagrams of reciprocalunit-cell at the LT-phase at 300 K (a) and at the intermediate-phase at 450 K (b) including super-lattice peaks at q =(0, ,0) and q =(0, , ) as observed in SC-XRD measurements.The SC-XRD data with schematic diagrams above T C1 atthe final HT-phase at 695 K (c), where no superstructurereflections were observed (prototype ≡ C m ). The unit-cellof the LT-phase (300 K) and the intermediate-phase (450 K)becomes ( a × b × c ) and ( a × b × c ), respectivelyas compared to the prototype HT-phase C m unit-cell ( a × b × c ). appears on heating as shown in Fig. 2 (b and c). The linecut from the temperature-dependent reciprocal imageanalysis for the peak q =(0, , ) shows a clear suppres-sion of intensity above T C2 (Fig. 2 (c)). This behavior issimilar to that observed in Na deficient Na − x Ru O [34],where Na + -NMR spectra results show motional averag-ing of the Na + sites at 390 K (above the first order phasetransition). According to Ref. [34], this motional aver-aging of the Na + sites was discussed in the context ofthe ionic motion in the material. And above 360 K theordered state begins to melt rapidly, consistent with ourtransport results. This suggests a large variation in thecharge separation patterns in a mixed valance system be-low and above the melting of the ordered state (see Sec-tion: Crystal-structure analysis).The super-lattice spots indicate that the observedmodulations in Na . Ru O are commensurate ( q =(0, , 0) and q =(0, , )) super-structure type with trans- lation and rotational symmetry breaking. Interestingly,this symmetry breaking induces large ionic displacements(Na ions) in the lattice, which can be explained by a mon-oclinic structure with the subgroup of C m . This C m unit-cell doubles the cell ( a × b × c ) with q =(0, ,0) below 630 K and with further cooling makes the cell 18times larger ( a × b × c ) with another q =(0, , )from the prototype HT-phase. The schematic diagramsof the reciprocal unit-cell are shown in Fig. 3 at roomtemperature ( q =(0, , 0) and q =(0, , )), at 450 K( q =(0, , 0)) and above the T C1 at 695 K with recip-rocal lattice maps, respectively. The mirror and two-foldsymmetry were not observed in the SC-XRD data in theLT-phase (300 K). Therefore we can conclude that theobserved Laue symmetry should be P q =(0, , 0) ap-pears at T C1 and suddenly increases again below T C2 asshown in the inset of Fig. 2 (c). The observed behavior ofthis super-lattice peak reflects the large displacements ofNa ions below T C2 (see Section: Displacement pattern).However, it is generally believed that such weak addi-tional satellite reflections are due to the presence of var-ious type of charge density wave (CDW) or CO states intunnel type structures such as Hollandite A x M O [26]. C. Crystal-structure analysis
The crystal structure of Na . Ru O has been inves-tigated at intermediate temperature (450 K) and room-temperature (300 K) SC-XRD as shown in Fig. 4 (a andb) and further confirmed by powder-XRD measurementsFig. 4 (c and d). We observed a single super-lattice peakwith q =(0, , 0) for the intermediate-phase (450 K) andtwo super-lattice peaks with q =(0, , 0) and q =(0, , ) for the LT-phase (300 K) in the SC-XRD data(Fig. 3). These super-lattice peaks can be indexed byusing the monoclinic space group C m of the prototypeHT-phase. Under the group-subgroup relation, P m isassigned to the intermediate q =(0, , 0) phase. The q =(0, , ) super-lattice reflection leads to a significantincrease of the unit cell volume and lowers the symmetrydrastically at room temperature. To explain the q =(0, , 0) super-lattice peak for the intermediate-phase at 450K, P m symmetry was used to refine the SC-XRD dataunder the group-subgroup relation by taking atomic po-sitions from the earlier report on powder samples [32] atroom room temperature with C m space group (corre-sponding to prototype HT-phase, >
630 K). The struc-ture of the room temperature phase with q =(0, , 0)and q =(0, , ) is more complicated. From the ob-served Laue symmetry, we conclude that the space groupshould be P
1, but there are too many fitting parame-ters. Thus, we ignored the q =(0, , ) super-latticereflections and made an averaged structure analysis withthe same unit-cell size and the same space group P m of the intermediate-phase as an approximant structure. ( d ) Y o b s Y c a l c Y o b s - Y c a l c B r a g g p e a k p o s i t i o n s P R u O q ( d e g r e e ) Intensity (arb. units) ( c )
Y o b s Y c a l c Y o b s - Y c a l c B r a g g p e a k p o s i t i o n s P R u O Intensity (arb. units) q ( d e g r e e ) F 2 c a l( F u n d a m e n t a l) F 2 c a l( s u p e r la t t ic e ) ( a )4 5 0 KP
F 2 o b s
F2cal
N a
R u O ( b )3 0 0 KP F 2 o b s
F 2 c a l( F u n d a m e n t a l) F 2 c a l( s u p e r la t t ic e )
F2cal
N a
R u O FIG. 4. (Color online). The left panel shows plots for F -obs and F -cal for single crystal experiments at (a) 450 and(b) 300 K, respectively. Red markers represent fundamentalreflections, while blue markers represent super-lattice reflec-tions. Note that the vertical and horizontal axis are givenin a logarithmic scale. The right panel shows Le-Bail refinedx-ray powder diffraction patterns at (c) 450 and (d) 300 K,respectively. The obtained R-factors ( R F ) for the intermediate andLT-phases are 11.41 and 16.01, respectively (see Fig. 4 (aand b)). The refined lattice parameters for the prototypeHT-phase at 695 K, the intermediate-phase at 450 K andthe LT-phase at 300 K (room temperature) are shown inTable I.The crystal structure of Na . Ru O for the intermedi-ate and low (room) temperature phases is shown in Fig. 5.The structural parameters obtained from SC-XRD refine-ment are shown in Table S1 and S2 (see SI-2) and wereused as the starting point of powder HR-XRD structuralrefinements to double check our structural model. AllBragg reflections were well indexed by assuming the mon-oclinic space group P m and the HR-XRD refinementshows an excellent fit as shown in Fig. 4 (c and d). Notethat super-lattice reflections found by single-crystal ex-periments are too weak to be seen in the powder reflectionprofiles shown in Fig. 4 (c and d).To explain the crystal structure of Na . Ru O by con-sidering the observed superstructures, we begin from theintermediate-phase where a single super-lattice peak ( q )appears (bottom panel of Fig. 5) and then two super-lattice peaks ( q and q ) emerge in the room (low) tem-perature phase, which triples the cell-parameters b and c of the unit-cell (top panel of Fig. 5). The different a c × c (q & q ) Ru Ru a c c unit-cellignoring (q ) FIG. 5. (Color online) The projection of crystal structureof Na . Ru O at the intermediate-phase (450 K) (bottompanel) and at the LT-phase (300 K) (top panel) in the crystal-lographic ac -plane. Unit cell at 300 K is simply tripled fromthe analyzed cell on drawing. BVS calculation at 450 and300 K shows the segregation of Ru-valence as Ru (green) /Ru (light brown) RuO octahedral. types of RuO octahedra of the corner sharing chainsare comprised of single, double or triple edge-sharedchains of RuO octahedra. It then has irregular zigzagchains of RuO octahedra along the crystallographic c -axis as well as large channel or cavities in the crystallo-graphic ac -plane, in which multiple Na + atoms can re-side (Fig. 5). Interestingly, along the crystallographic b -axis Na . Ru O forms a tunnel type structure, whichis different from other prototype tunnel structures suchas Rutile, Ramsdellite or Hollandite-type [25, 26] (seeSection: Tunnel structure).Furthermore, the associated bond valence sum (BVS)calculation was performed using the Fullprof softwaresuite [30], which reveals Ru (green RuO octahedron)and Ru (light brown RuO octahedron) coexisting indifferent valence states at both 300 and 450 K (Fig. 5).The electronic properties mainly depend on the charge,and charge separation is a common feature of charge or-dering phenomena. At first sight, the emergence of thesuper-lattice peaks can be interpreted as the evidenceof CO, such as in case of tunnel based structures likeHollandite-type [26] or in Na based compound Na x CoO has Co /Co CO state [35]. This features, therefore,indicates that Na . Ru O has unconventional CO with-out the loss of metallicity at room temperature. Abovethe first order phase transition at T C2 , it also shows the Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru Ru c a Na + RuO triple double Na1 Na2 Na3 ++ + + + + Na1 Na2 Na3 doublesingletriple Ru (b)(a) c a single Ru Ru FIG. 6. (Color online) Charge model based on the tunnelstructure for Na . Ru O (a) below the first order transition( ≤ T C2 ) at room temperature and (b) above the first ordertransition ( > T C2 ) at 450 K. CO state but below the first order phase transition at T C2 CO pattern drastically changed as shown in lowerpanel of Fig. 5.
IV. DISCUSSION AND SUMMARYA. Tunnel structure
The crystal structure of Na . Ru O is composed ofirregular zigzag chains forming tunnels along the b -axis.The Na ions are located inside these tunnels at threedifferent crystallographic sites. However, a large num-ber of Na + cations inside the tunnel experience strongmutual electrostatic repulsion and that increases as afunction of temperature as explained through the chargemodel in Fig. 6 (a) and (b). Na + ions gain high mo-bility at high temperature that leads to Na + being dis-ordered due to their weak bonding with ions forminga rigid framework [36]. The shift in the Na + NMR-spectra and the disappearance of one Na-site were ob-served for Na − x Ru O [34]. Therefore, in Na deficientNa . Ru O , at or above the T C2 , one of the Na + atommoves and shares one of the Na atoms site in the tunnelas shown in Fig. 6 (b). The large displacements observedin the SC-XRD data along the b -axis favors ionic motionswithin the tunnels.As Na . Ru O has tunnel geometry along the crystal-lographic b -axis with a large cross-section area, a largernumber of alkali metal atoms can be accommodated thanin Rutile, Ramsdellite and Hollandite as shown in Fig. 7.This feature makes it attractive in terms of sodiumbatteries [37] and ion motion related applications [38–41]. Interestingly, formation of the tunnel structure inNa . Ru O is purely of edge-sharing MO octahedrachains (single (1 × × × /Ru and three cations Na + can re-side in those tunnels/channels as shown in Fig. 7 (d). B. Phase-transition
The possible prototype HT-phase ( a × b × c ) wouldbe C /m which is similar to the one reported by Maeno etal. [19] as shown in Fig. 3 (c). A transition from this HTprototype phase C /m ( ≥
630 K) to an intermediate-phase occurs (630 K ≤ T ≤
365 K). This intermediatephase transition leads to a doubling ( a × b × c ) ofthe unit-cell from the prototype structure (see Table I,Fig. 3 (b) and Fig. 5). Below the intermediate-phase, afirst-order phase transition occurs as confirmed from theresistivity (Fig. 1 (a)). Below 365 K new super-latticepeaks appear in the SC-XRD data, which makes the unit-cell 18 times ( a × b × c ) larger than the prototypephase unit-cell (Table I, Fig. 3 (b) and Fig. 5) [32].These symmetry lowering structural-phase transitionsenlarge the unit-cell drastically. Further, from the re-sistivity behaviour it is clear that Fermi surface of theNa . Ru O is comprised two types of electrons, 1) itin-erant electrons (high spin state of Ru /Ru ) responsi-ble for the metallic behaviour and 2) localized electrons(possibly ultra-low spin state t g ↑ t g ↓ of Ru ) mainlyresponsible for the origin of the first order phase tran-sition. Therefore, in such a case where electron statesare localized, as in the Mott states, the observed q and q modulation in Na . Ru O may show CO-type mod-ulations due to inter-site Coulomb interactions. How-ever, localized charge-ordered states interact with itin-erant electrons of Na . Ru O through SOC and retainthe metallicity. IrTe is one of the rare examples showingsimilar behaviour with high SOC strength and unconven-tional CO. In this case, localized spin-orbit Mott statesare assisted by Ir dimerizations [42]. Thus, the elec-tronic behaviour of Na . Ru O is due to a subtle balancebetween itinerant and localized electrons [43]. C. Displacement pattern
We now describe the structure and its displaced Ruand Na ions in more detail. Na ions are present atthree different crystallographic sites inside the tunnelsformed by RuO octahedra, as shown in Fig. 6 (a) and(b). We observe a first-order phase transition with astrong anomaly in the electrical resistance and heat-capacity data. The superstructures have also been ob-served by SC-XRD for Na . Ru O . This can be un-derstood in terms of the Ru charge ordering, which hasbeen confirmed by both temperature-dependent bulk andSC-XRD measurements (see Fig. 1 and Fig. 2). In or-der to avoid complexity we ignored the q = (0, , )super-lattice reflections and analyzed the displacement-patterns by only considering the q = (0, , 0) super-structure mode with the same unit-cell size and the samespace group P m . The displacement-patterns of Na andRu are shown in Fig. 8 (a-d) and Fig. 9 (a) and (b), re-spectively. It is worth to note that Ru and Na ions aredimerized in comparison with the HT prototype phase Rutile octahedra Ramsdellite octahedra Hollandite octahedra Na Ru O : new tunnel type 1×2×3 : MO octahedral K ( a ) NaNaNa single double triple ( b ) ( c ) ( d ) FIG. 7. (Color online) Comparison of prototype tunnel structures including Na . Ru O by MO octahedra, where M is thetransition metal in (a) Rutile, (b) Ramsdellite and (c) Hollandite type tunnels. (d) An enlarged view is shown of the newtunnel type structure for Na . Ru O formed by 1 × × . Ru O for the HT-phase [695 K ≡ Prototype C m ], the intermediate-phase [450 K ≡ P m ] and the LT-phase [300 K ≡ Pseudo P m ( P a (˚A) b (˚A) c (˚A) β ( ◦ ) V (˚A )695 K 23.520 (11) 2.890 (1) 10.953 (6) 104.55(3) 720.6 (6)450 K 23.311 (2) 5.701 (4) 11.057 (7) 104.39(4) 1423.3(2)300 K 23.342 (2) 17.028 (16) 33.191 (3) 104.43(7) 12776.1(6) C /m along the crystallographic b -direction as shown bythe black solid and dashed rounded circles in Fig. 8 (a).From the intermediate-phase to the LT-phase, thestructure shows large Na ion displacements, and oneamong the three Na sites is displaced along the b -direction by about from its normal site. The displacedRuO and Na ions are shown by open arrows in Fig. 8(b) and (c) in the a -axis projection, which substantiallychanges the local environment of the structure. The ob-served large Na + ion displacements in Na . Ru O are ingood agreement with Fig. 8 (d), which shows the b -axisprojection of the structure shown in Fig. 8 (b) at 450 K.These Na ion displacements greatly affect the electronicstructure of Na . Ru O . This leads to displaced Ru ionsalong the a -direction, which forms zigzag chains alongthe crystallographic c -axis for both the intermediate andLT-phases as shown by the filled green arrow in Fig. 9(a) and (b), respectively. We observed that due to theshift of the Na ions, Ru electrons are favoured in theintermediate-phase as shown in the right panel of Fig. 9(a) and (b). However, Na octahedra sites are highly dis-torted face-sharing with both Ru O / Ru O octahe-dra and Ru-atoms form interactions with the alkali ionsthrough oxygen, which stabilize spd hybridization. Thishybridization strongly influences the 4 d Ru electrons and the electronic properties of Na . Ru O are greatly af-fected accordingly. Although such face-sharing sites oc-cur in both the intermediate and LT-phase structures, itis rather unusual to see such a site occupied by an alkaliion, Na, as we find in Na . Ru O .Therefore, the results of a structural investigation bythe temperature-dependent SC-XRD provides the directevidence for the formation of an unconventional chargeordering (CO). The system remains metallic, but partsof the Fermi surface may lose near the first order phasetransition. This then explains the abrupt increase in theexperimental resistivity at T C2 . Within this scenario thesuppression of super-lattice peaks above T C2 (Fig. 2 (c))can be interpreted as Na + ion motions in the Na . Ru O lattice [34] being responsible for the increased localizationof 4 d Ru electrons without the loss of metallicity. Thisscenario is very much consistent with magnetic suscepti-bility ( χ ), where short range magnetic correlations wereobserved. We think that these results are responsiblefor the origin of the first-order phase transition and pro-vide an unprecedented ionic displacement driven chargeordering in Na . Ru O .To conclude, we have presented evidence for a veryunusual charge ordering in Na . Ru O at room temper-ature while retaining metallicity by combining the re- b b b a NaRu
C 2 / mP 2 / m (450K)450 K; q=(0 ½ 0) c b c b
300 K; ignoring q=(0 1/3 1/3) a)b) c) +e y -e y y= ~
450 K; q=(0 ½ 0) d) O -e y +e y y= ~ FIG. 8. (Color online) (a) The P /m unit-cell of Na . Ru O at 450 K ( q =(0, , 0)). The reference solid blue line representsthe HT prototype phase C /m unit-cell. In the P /m unit-cell, black solid and dashed rounded lines indicate the dimerizationof Ru and Na ions along the crystallographic b -axis. The displacement pattern of Na ions at (b) 450 K and (c) 300 K in q =(0, , 0) mode on the bc -plane projection, while (d) ac -plane at 450 K is shown at each y -layer, 1 / /
4. The blue and redcolours in (b-d) indicate positive and negative direction shifts. sults of SC-XRD, electrical resistivity, specific heat, andsusceptibility χ ( T ). The temperature-dependent SC-XRD results show super-lattice peaks at q =(0, , 0)and q =(0, , ), clear evidence of symmetry break- ing with large ionic displacements. This helps mostprobably establish charge ordering (CO) in Na . Ru O .Na . Ru O hosts modest SOC of the Ru mixed valanceheavy d ions, which show several unique features such a c Na Ru
450 K; q=(0 ½ 0) mode a) a c Na Ru
300 K; q=(0 ½ 0) mode, ignoring q=(0 1/3 1/3) b) Ru Ru Ru Ru Na + Na + Ru Ru Ru Ru Na + Na + FIG. 9. (Color online) The displacement patterns of Ruions at (a) 450 and (b) 300 K with q =(0, , 0) mode on the ac -plane projection. The right panel of the figures shows thehighly distorted octahedrons local environment of displacedNa ions face sharing with different Ru O / Ru O octa-hedra at (a) 450 and (b) 300 K, respectively. as CO in the metallic state and large alkali metal Na iondisplacements in the tunnel lattice. More than one typeof electron scattering is involved in the resistivity, alter-natively making this material uniquely suitable examplefor several possible advanced applications such as in iontransport quantum computers and future energy storagematerials. Further, the higher value of γ indicates thatNa . Ru O belongs to the class of strongly correlatedelectron systems. ACKNOWLEDGMENTS
We thank Daniel I. Khomskii and Sang-Wook Cheongfor fruitful discussions. Work at the IBS CCES wassupported by Institute for Basic Science (IBS) in Korea(Grant No. IBS-R009-G1) [1] S. Sachdev,
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