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 Dear colleagues, my intention is to provide you with an overview of the quasi-one-dimensional cuprates. This work was done in close cooperation of Zagreb dielectric spectroscopy group and Stuttgart group, where quasi-optical microwave and far infrared mesurements are performed. We also thank to colleagues which provided samples. Our detailed charge response study, allowed us to assemble phase diagrams for the materials. It seems that our contribution was necessary for completion, besides the plethora of data produced in the field in last 10 years. Dept.of Physics, Aoyama-Gakuin University, Kanagawa, Japan B. Gorshunov et al., Phys.Rev.B 66, 060508(R) (2002) T. Vuletic et al., Phys.Rev.B 67, 184521 (2003) T. Vuletic et al., Phys.Rev.Lett. 90, 257002 (2003) T. Vuletic et al., Phys.Rev.B 71, 012508 (2005) T. Vuletic et al., submitted to Physics Reports (2005)

Motivation (La,Y,Sr,Ca)14Cu24O41 : Task: 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: In general, in q1D materials sc competes with magnetic/charge orders which render materials insulating. This competition appears also in q1D cuprates. Another interesting issue here is that this is also a strongly interacting q1D electron system, and later it will show that some concepts we know from other q1D, mostly density wave systems do not apply here. So our task could have been recognized as to catalyze discussions on the nature of superconductivity and charge-density wave and their relationship with the spin-gap, which is an important property of these materials. assemble phase diagrams to catalyze discussions on the nature of superconductivity and charge-density wave and their relationship with the spin-gap

t-J(-t’-J’) model for ladders E.Dagotto et al., PRB’92 ladders map onto 1D chain with effective U<0 for hole pairing! chain layer U<0, t≠0 V>0: 2kF CDW V<0: singlet SC V.J.Emery, PRB’76 In fact, the theory quite early recognized that the spin gap which occurs for spins arranged in ladders might lead to superconductivity (or CDW, that is) if the ladders are hole doped. Pure ladder materials were soon after sinthetized, however doping did not lead to SC. pairing of the holes  superconducting or CDW correlations spin gap doped holes enter O2p orbitals  form ZhangRice singlet with Cu spin

Crystallographic structure (La,Y,Sr,Ca)14Cu24O41 b=12.9 Å a=11.4 Å A14 Cu2O3 ladders CuO2 chains cC Chains: Ladders: cC=2.75 Å cL=3.9 Å 10·cC≈7·cL≈27.5 Å cL Only when good crystals of composites of chains and ladders were synthetized SC was discovered below 10-12K, however, only when more than 3GPa were applied. The structure of the composite is arranged in a following manner. The chains and ladders separately form layers. Metal A atoms are coordinated to ladders, as they fit into the openings of ladders. Then the two systems are stacked in alternating manner. cL/cC=√2

Bond configurations and dimensionality Cu2O3 ladders CuO2 chains 90o - FM, J<0 180o - AF, J>0 Cu-O-Cu bonds cC Chains: Ladders: cC=2.75 Å cL=3.9 Å 10·cC≈7·cL≈27.5 Å cL {{{{{It is important to note that the subsystems are incomensurate with 1-to-sqrt2 ratio. Due to this, the bonds formed are never 90 degree, and Copper and its four coordinated oxygens form irregular tetragons and even distorted tetrahedrons. Obviously the intrinsic disorder in the material is strong.}}}}} Here we can recognize more easily why ladders are regarded as q1D system and not 2D. Ladders are decoupled by 90 degree bonds and also bytriangular, frustrated arrangement of Coppers between neighboring atoms.

2D AF dimer / charge order 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

Physics of chains: dc transport in (La,Y)y(Sr,Ca)14-yCu24O41 T> Tco  Nearest neighbor hopping 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

ac response in y=3 No collective response nco- crossover frequency: ac hopping overcomes dc Quasi-optical microwave/FIR: hopping in addition to phonon Hopping dies out THere is no collective response in radio frequency, no pinnedmode.It was interesting to observe how the achopping contribution eventually died out

Chains Phase Diagram (La,Y)y(Sr,Ca)14-yCu24O41 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? Matsuda et al., PRB’96-98 So the chains were recognized as a 1D disordered insulator. Hey are also a paramagnet which at low T orders magnetically.Chains are ferro (when there are no holes) but organize antiferomagnetically. With more holes, less La content AFdimer pattern starts to apear. But unresolved issue is how the transport switches from chains to ladders

Chains in Sr14-xCaxCu24O41 : AF dimers/charge order ESR signal due to Cu2+ spins in the chains Kataev et al., PRB’01 only SRO for x=8&9 AF order for x≥11 nh=4 nh=5 nh=6 for T>T* broadening of ESR line due to the thermally activated hole mobility Slope of DH*(T) vs T is approximately the same for all x of Sr14-xCaxCu24O41 and for La1Sr13Cu24O41 (nh=5, all in chains) That is chains in fully doped materials keep the same number of holes, so the additional one is gradually doped to ladders. We also note another AF order in the chains at high x in these materials. LRO below T* Upper limit: 1 hole transferred into the ladders for all x

Phase diagram for chains Principal results: merges with ph.diagram of chains in underdoped materials suppression of T* 2D ordering inferred from magnetic sector results 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

What is important in the ladders in Sr14-xCaxCu24O41? Now we are finished with the chains, what is important in the ladders. There is CDW suppressed by Ca content, not by worsened nesting and dimensionality. It is somewhat strange CDW. SC is obtained only in the presence of pressre, which increses dimensionality, and seemingly gives a regular HTC SC, despite the presence of spingap and Dagoto’s elegant ideas.

CDW W0= 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 W0= Experimental fingerprints: mode at pinning frequency broad radio-freq. modes centred at enhanced effective mass nonlinear dc conductivity above sliding threshold ET=2kFV0/r0 1/t0= We identified CDW through its phason response, charaterized by pinned mode and broad radiofreq modes. There should also be some nonlinearity. We also estimated effective mass from these results. Littlewood, PRB ‘87

Ladders: charge response 1300K

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

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

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

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

Phase diagram for ladders (corresponds to chains ph.diag.) TCDW 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 of localized 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

FIN CDW SC

Physics of ladders (Sr14-xCaxCu24O41): gapped spin-liquid 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 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 Polycrystalline } Single crystal spin gap Spin gap is present even for x=12, where SC sets-in

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

Physics of ladders (Sr14-xCaxCu24O41): insulating phase(s) Experiment: temperature range: 2 K -700 K dc transport, 4 probe measurements: lock-ins for 1 mW-1 kW dc current source/voltmeter 1 W-100 MW 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) lock-in and current preamp, 1 mHz-1 kHz impedance analyzers, 20Hz-10MHz Zagreb 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

Anisotropic ac-response: 2D charge order in ladder plane Broad screened relaxation modes E||a, E||c, x≤6 E||b, no response for any x 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

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 Ca-substitution Pressure Increase ladder/chain coupling increase dhchange V, U b Increase W change U/W CDW suppresed due to changes in U/W, V, dh (and disorder) decrease lattice parameters HT phase: Mott-Hubbard insulator (1/2 filling, U/W>1) on-site U, inter-site V, hole-doping dh, bandwidth W=4t Pachot et al., PRB‘99 a c H.T. phase persists – “disorder resistant”

Instabilities in 1D weakly interacting Fermi gas 4 possible scattering processes instabilities in the system proximity of SC and magnetic/charge order 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

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

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

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

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

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=2.8 dh decrease V, increase the doping dh, destabilizes CDW and p-DW, in favor of d-SC state.

(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

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

Phason CDW dielectric response 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) in the third term, which is the elastic energy associated with the local deformations Random distribution of pinning centers taken into account in the fourth term Phason dielectric response governed by: free carrier screening, nonuniform pinning www.ifs.hr/real_science

Phason CDW dielectric response Max. conductivity close to the pinning frequency W0 pinned mode - transversal g0- weak damping in the third term, which is the elastic energy associated with the local deformations Random distribution of pinning centers taken into account in the fourth term www.ifs.hr/real_science Littlewood

Phason CDW dielectric response 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 in the third term, which is the elastic energy associated with the local deformations Random distribution of pinning centers taken into account in the fourth term Longitudinal mode is not visible in diel. response since it exists only for e=0! www.ifs.hr/real_science Littlewood

Experiments detect two modes Phason CDW dielectric response Nonuniform pinning of CDW gives the true phason mode a mixed character! W0= 1/t0= in the third term, which is the elastic energy associated with the local deformations Random distribution of pinning centers taken into account in the fourth term Longitudinal response mixes into the low-frequency conductivity Experiments detect two modes www.ifs.hr/real_science Littlewood

m* - CDW condensate effective mass Sr14-xCaxCu24O41 W0 & t0 are related: t0 & sz – from our experiments r0 – carriers condensed in CDW (holes transferred to ladders = 1·1027 m-3 = 1/6 of the total) Microwave conductivity measurements (cavity perturbation)  peak at W0=60 GHz  CDW pinned mode Kitano et al., 2001. in the third term, which is the elastic energy associated with the local deformations Random distribution of pinning centers taken into account in the fourth term CDW effective mass m*≈100 www.ifs.hr/real_science m*

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

Complex dielectric function Generalized Debye function ∞ relaxation process strength  = (0) - ∞ 0 – central relaxation time symmetric broadening of the relaxation time distribution 1 -  www.ifs.hr/real_science Debye.fja

ere eim 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 eim ere www.ifs.hr/real_science Eps im eps re