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Phase diagrams of (La,Y,Sr,Ca) 14 Cu 24 O 41 : switching between the ladders and chains

Phase diagrams of (La,Y,Sr,Ca) 14 Cu 24 O 41 : switching between the ladders and chains. T.Vuletic, T.Ivek, B.Korin-Hamzic, S.Tomic B.Gorshunov, M.Dressel C.Hess, B.Büchner J.Akimitsu. Institut za fiziku, Zagreb, Croatia. 1.Physikalisches Institut, Universität Stuttgart, Germany.

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Phase diagrams of (La,Y,Sr,Ca) 14 Cu 24 O 41 : switching between the ladders and chains

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  1. Phase diagrams of (La,Y,Sr,Ca)14Cu24O41: switching between the ladders and chains T.Vuletic, T.Ivek, B.Korin-Hamzic, S.Tomic B.Gorshunov, M.Dressel C.Hess, B.Büchner J.Akimitsu Institut za fiziku, Zagreb, Croatia 1.Physikalisches Institut, Universität Stuttgart, Germany Leibniz-Institut für Festkörper- und Werkstoffforschung, Dresden, Germany Dept.of Physics, Aoyama-Gakuin University, Kanagawa, Japan B. Gorshunov et al., Phys.Rev.B66, 060508(R) (2002) T. Vuletic et al., Phys.Rev.B67, 184521 (2003) T. Vuletic et al.,Phys.Rev.Lett.90, 257002 (2003) T. Vuletic et al.,Phys.Rev.B71, 012508 (2005) T. Vuletic et al.,submitted to Physics Reports (2005)

  2. Motivation q1D materials: proximity (competition and/or coexistence) of superconductivity & magnetic/charge ordered phases (La,Y,Sr,Ca)14Cu24O41 : spin chain/ladder composite q1D cuprates strongly interacting q1D electron system Task: assemble phase diagrams to catalyze discussions on the nature of superconductivity and charge-density wave and their relationship with the spin-gap

  3. t-J(-t’-J’) model for ladders chain layer E.Dagotto et al., PRB’92 ladders map onto 1D chain with effective U<0 for hole pairing! U<0, t≠0 V>0: 2kF CDW V<0: singlet SC V.J.Emery, PRB’76 pairing of the holes superconducting or CDW correlations spin gap doped holes enter O2p orbitals  form ZhangRice singlet with Cu spin

  4. Crystallographic structure (La,Y,Sr,Ca)14Cu24O41 CuO2 chains A14 Cu2O3 ladders b=12.9 Å cC cL a=11.4 Å Chains: Ladders:cC=2.75 ÅcL=3.9 Å 10·cC≈7·cL≈27.5 Å cL/cC=√2

  5. Bond configurations and dimensionality CuO2 chains A14 Cu2O3 ladders cC cL Chains: Ladders:cC=2.75 ÅcL=3.9 Å 10·cC≈7·cL≈27.5 Å Cu-O-Cu bonds 180o - AF, J>0 90o- FM, J<0

  6. Magnetic structure and holes distribution (La,Y)y(Sr,Ca)14-yCu24O41 y≠0, all holes in chains No charge ordering Sr14-xCaxCu24O41 x=0, around 1 hole in ladders increases for x≠0 backtransfer to chains at low T 2D AF dimer / charge order Cu2+ spin ½ holes O2p orbitals

  7. T> Tco Nearest neighbor hopping Physics of chains:dc transport in (La,Y)y(Sr,Ca)14-yCu24O41 Tco= 300 K y=3 y=3 T< Tco Mott’s variable range hopping Tco = 330 K y=5.2 Dimensionality of hopping: d=1

  8. No collective response ac response in y=3 nco- crossover frequency: ac hopping overcomes dc Quasi-optical microwave/FIR: hopping in addition to phonon Hopping dies out

  9. Matsuda et al., PRB’96-98 Chains Phase Diagram (La,Y)y(Sr,Ca)14-yCu24O41 Chains: localized holes, hopping transport, 1D disorder driven insulator Unresolved issues... - Transport switches:chains  ladders in 1<y<0 range? - A phase transition: La-substituted  La-free materials?

  10. Chains in Sr14-xCaxCu24O41 : AF dimers/charge order AF order for x≥11 only SRO for x=8&9 ESR signal due to Cu2+ spins in the chains Kataev et al., PRB’01 nh=4 nh=5 nh=6 for T>T* broadening of ESR line due to the thermally activated hole mobility Slope of DH*(T) vsT is approximately the same for all x of Sr14-xCaxCu24O41 and for La1Sr13Cu24O41 (nh=5, all in chains) LRO below T* Upper limit: 1 hole transferred into the ladders for all x

  11. Principal results: merges with ph.diagram of chains in underdoped materials suppression of T* 2D ordering inferred from magnetic sector results Phase diagram for chains AF dimers order vanishes with holes transferred to ladders AF Néel order for x≥11 Kataev et al., PRB’01; Takigawa et al., PRB’98; Ohsugi et al., PRL’99; Nagata et al., JPSJ’99; Isobe et al., PRB’01

  12. What is important in the ladders in Sr14-xCaxCu24O41?

  13. W0= 1/t0= CDW Phason: Elementary excitation associated with spatio-temporal variation of the CDW phase F(x,t) phason response to dc & ac field governed by: free carrier screening and pinning potential V0 of impurities or commensurability Experimental fingerprints: mode at pinning frequency broad radio-freq. modes centred at enhanced effective mass nonlinear dc conductivity above sliding threshold ET=2kFV0/r0 Littlewood, PRB ‘87

  14. Ladders: charge response D 1300K

  15. Dielectric response: Generalized Debye function De 104–105 t01/sz t∞  0.1 ns radio-frequency ac response: similar to phason response Charge Density Wave Ladders: charge response D 1300K

  16. 2D phason response in ladder plane radio-freq. mode enhanced effective mass m*=102-103 pinned mode W0 Kitano et al., EPL’01

  17. Ladders: Non-linear conductivity bad contacts, or large unnested voltage No ET, “large”non-linear effect good contacts and no unnested voltage No ET, negligible non-linear effect

  18. Ladders: Non-linear conductivity small non-linear effect Maeda et al., PRB’03 “large” non-linear effect Blumberg et al., Science’02

  19. T* TCDW Phase diagram for ladders (corresponds to chains ph.diag.) suppresion of Tc and charge gaps 2D CDW in ladder plane unique to ladders? or common to low-D systems with charge order? order in ladders: CO oflocalized or CDW of itinerant electrons? analogy with AF/SDW half-filled ladder in Hubbard model: CDW+pDW in competition with d-SC Suzumura et al., JPSJ’04

  20. FIN CDW SC

  21. } Single crystal Polycrystalline NMR/NQR: Takigawa al., PRB’98; Kumagai et al., PRB’97; Magishi et al., PRB’98; Imai et al., PRL’98, Thurber et al., PRB’03 Physics of ladders (Sr14-xCaxCu24O41): gapped spin-liquid Inelastic neutron scattering:Katano et al., PRL’99, Eccleston et al., PRB’96 for x=0: Cross-over between paramagnetic and spin-gapped phase T*  200 K spin gap Spin gap is present even for x=12, where SC sets-in

  22. pressure removes insulating phase no superconductivity SC: x≥10 i T<12K, p= 3-8 GPa Nagata et al., JPSJ’97 x=0 x=11.5 Motoyama et al., EPL’02 Piskunov et al., PRB’04 NMR under pressure x=0 & x=12, p=3.2 GPa Fujiwara et al., PRL’03 in x=12 pressure only decreases spin gap, low lying excitations are present (Korringa behavior in T1-1) in x=0, the same, but no low-lying excitations and no SC! Physics of ladders (Sr14-xCaxCu24O41): superconductivity

  23. Physics of ladders (Sr14-xCaxCu24O41): insulating phase(s) Experiment: Zagreb temperature range: 2 K -700 K dc transport, 4 probe measurements: lock-ins for 1 mW-1 kW dc current source/voltmeter 1 W-100MW 2 probe measurements: electrometer in V/I mode, up to 30 GW lock-in and current preamp, up to 1 TW ac transport – LFDS (low-frequency dielectric spectroscopy) 2 probe measurements: lock-in and current preamp, 1 mHz-1 kHz impedance analyzers, 20Hz-10MHz x<11: insulating behavior D: decreases with x sc(300 K): 400-1200 (Wcm)-1 x≥11 i T>50K : metallic Gorshunov et al., PRB’02 Vuletic et al., PRL’03 Vuletic et al., submitted to PRB’04

  24. Broad screened relaxation modes E||a, E||c, x≤6 E||b, no response for any x Anisotropic ac-response: 2D charge order in ladder plane same Tc for E||a, E||c same t0-1for E||a, E||c Dec/Dea 10  sc/sa No response along rungs for x=8,9 & Transition broadening Increase in sc/sa at low-T for x=9 Long-range order in planes is destroyed

  25. HT phase: Mott-Hubbard insulator(1/2 filling, U/W>1) on-siteU, inter-siteV, hole-doping dh, bandwidth W=4t b b b Increase ladder/chain coupling increase dhchange V, U b decrease lattice parameters Ca-substitution Pressure a a a c c c Increase W change U/W Pachot et al., PRB‘99 CDW suppresed due to changes in U/W, V, dh(and disorder) H.T. phase persists – “disorder resistant” The nature of H.T. insulating phase is the key for CDW suppression nesting: strong e-e interactions – the concept not applicable, in principle – dimensionality change also contradicts disorder: renders Anderson insulator – but, this wouldn’t be removed by pressure

  26. Instabilities in 1D weakly interacting Fermi gas instabilities in the system proximity of SC and magnetic/charge order 4 possible scattering processes a-backward, q=2kF, short range interactions (Pauli principle or on-site U) b-forward, q=0, long range interactions c-Umklapp, q=4kF, in a half-filled band, lattice vector equals 4kF and cancels scattering momentum transfer d-forward, q=0

  27. Electronic structure (La,Sr,Ca)14Cu24O41 local density approximation Osafune et al., PRL’97 inter-ladder hopping: 5-20% of intra-ladder optics: Mott-Hubbard gap 2 eV EF pulled down by doped holes M. Arai et al., PRB’97 top of lower Hubbard band of ladders finite DOS on EF bands at 3 & 5.5 eV T. Takahashi et al., PRB’97

  28. Strong coupling limit for cuprates Zhang and Rice., PRB’88 two band model (oxygens!) copper: strong on-site repulsion U Cu (3d9) and O (2p6) form the structure charge-transfer limit lattice formed of 1 kind of sites chain layer 1 electron, S=½ per copper site ladder doped holes enter O2p orbitals  form ZhangRice singlet with Cu spin Hamiltonian reduces to Heisenberg spin ½ model + effective hopping term for ZR singlet motion

  29. Physics of chains: Sr14-xCaxCu24O41 T=50K X-ray difraction Cox et al., PRB’98 5 holes T= 5-20K INS Regnault et al., PRB’99; Eccleston et al., PRL’98 XRD Fukuda et al., PRB’02 NMR/NQR Takigawa al., PRB’98 6 holes 2cC 3cC 2cC 2cc Chains: AF dimer / charge order complementarity spin-gap Holes are localized in chains of fully hole doped Sr14-xCaxCu24O41

  30. Ladder plane dc conductivity anisotropy vs. Temperature anisotropy: approximately 10 for all x and temperatures increase at lowest T for x>8 more instructive picture if anisotropy is normalized to RT value

  31. Unconventional CDW in ladder system recently derived (extended Hubbard type) model for two-leg ladder with both on-site U and inter-site V|| along and Vacross ladder. Suzumura et al., JPSJ’04 CDW+p-DW CDW+p-DW 1.4 2.8 4.2 5.6 hole transfer dh dh=2.8 decrease V, increase thedopingdh, destabilizes CDW and p-DW, in favor of d-SC state.

  32. (TMTTF)2AsF6 Charge order vs. CDW in ladders D.S.Chow et al., PRL’00 NMR detects charge disproportionation In the vicinity of CO transition dielectric constant follows Curie law F. Nađ et al., J.Phys.CM’00 Zagreb Relaxation time is temperature independent – not phason like

  33. Splitting of 63Cu NMR line Charge disproportionation Takigawa al., PRB 1998 CDW in the Ladders versusCO in the Chains chain ladder No splitting of 63Cu NMR line

  34. Phason CDW dielectric response www.ifs.hr/real_science Fukuyama, Lee, Rice Periodic modulation of charge density Random distribution of pinning centers Local elastic deformations (modulus K) of the phase f(x,t) Damping g Effective mass m*»1 External AC electric field Eex is applied Phason: Elementary excitation associated with spatio-temporal variation of the CDW phase f(x,t) Phason dielectric response governed by: free carrier screening, nonuniform pinning

  35. Phason CDW dielectric response Littlewood W0= www.ifs.hr/real_science Max. conductivity close to the pinning frequency W0 pinned mode - transversal g0- weak damping

  36. Phason CDW dielectric response Littlewood W0= www.ifs.hr/real_science Max. conductivity close to the pinning frequency W0 pinned mode - transversal g0- weak damping plasmon peak longitudinal Screening: Low frequency tail extends to 1/t0= strong damping g»g0 Longitudinal mode is not visible in diel. response since it exists only for e=0!

  37. Phason CDW dielectric response Littlewood 1/t0= www.ifs.hr/real_science Nonuniform pinning of CDW gives the true phason mode a mixed character! W0= Longitudinal response mixes into the low-frequency conductivity Experiments detect two modes

  38. m* m* - CDW condensate effective mass Sr14-xCaxCu24O41 www.ifs.hr/real_science t0&sz– from our experiments r0– carriers condensed in CDW (holes transferred to ladders = 1·1027 m-3 = 1/6 of the total) W0&t0 are related: Microwave conductivity measurements (cavity perturbation)  peak at W0=60 GHz  CDW pinned mode Kitano et al., 2001. CDW effective mass m*≈100

  39. Complex dielectric function ∞ www.ifs.hr/real_science Debye.fja Generalized Debye function

  40. Complex dielectric function ∞ www.ifs.hr/real_science Generalized Debye function Debye.fja relaxation process strength = (0) - ∞ 0– central relaxation time symmetric broadening of the relaxation time distribution1 - 

  41. www.ifs.hr/real_science We analyze real & imaginary part of the dielectric function We fit to the exp. data in the complex plane We get the temp. dependence De, t0, 1-a Eps im eps re ere eim

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