Les échelles de spins conductrices: une approche pour les supras hauts Tc D.Jérome, Orsay avec les contributions de Y.Piskunov, P.Wzietek, P.Auban, C.Bourbonnais, H.Mayaffre, A.Revcolevschi,U.Ammerhal, G.Dhalenne and A.Yakubovsky.

Low dimensional magnets Chains: Heisenberg chain S=1/2 Almost ordered state at T=0, quantum fluctuations <Si.Sj> @1/ (ri-rj) , c(T=0) @1/J Gapless spin excitations Planes: Heisenberg antiferromagnet Long range ordered <Si.Sj> @ S2 cos Q. (ri-rj) Q=(p/a,p/a) Gapless excitations, spin waves Ladders: (even number of legs) Cu 2+ (S=1/2) J J ’ <Si.Sj> @ exp- (ri-rj) /x spin liquid N= x/a spins in a box --> Quantization D= J/N=J/2 --> spin gap

Ladders in organic compounds Chabousssant et-al, PRL, 79, 925, 1997 Cu 2+ (S=1/2) Cu-Cu superexchange via Cl

Spin gap in isotropic ladders From Dagotto and Rice, Science, 271, 618, 1996 Magnon and QP modes

Doping ladders, quasi-particles in spin ladders Ground state Hole in Cu2O3 ’ << Cost: J 2 J’  Bound quasiparticles Excited states -Magnon excitations with a modified gap -Excited quasiparticles t-J model, strong coupling Binding energy for a QP pair EB= J’-2t’-2t QP is a localized spin S=1/2 EB< Ds

Correlations, pairing, density waves, AF in doped ladders DMRG calculation Hayward et-al PRL 75, 926, 1995 Noack et-al 96 Power law Exponential decay Magnetism: exp-(x/r) -1, spin gapped Pairing: 1/r, power law like 1D systems @ negative U model d-wave pairing -0.08 -0.08 0.1 Noack et-al 96 Look for superconductivity in doped spin ladders ? E.Dagotto and T.M.Rice Science 271, 618, 1996

Spin ladders in La2Cu2O5 Hiroi and Takano Nature 377, 41, 1995

Hole doping in (La/Sr)2Cu2O5 Hiroi and Takano Nature 377, 41, 1995 No superconductivity obsereved AF ordering observed by NMR, mSR at 110K In La2Cu2O5 Interplay between spin liquid and AF due to the non frustrated interladder interaction

Spin ladders in cuprates : 2 versus 3 leg ladders Cu2O3 ladders M.Takano et - al 1996 SrCu2O3 Sr2Cu2O3 J=1000-1500K via Cu-O-Cu superexchange via 180° bond, antiferro J interladder due to Cu-O-Cu 90° bond, much smaller and ferro + frustration Azuma et al 1994

Structure of the ( Sr/Ca)14Cu24O41 series Mc Carron, 1998 Siegrist 1988 Nominal Cu valence +2.25 0.25 hole/Cu 14Cu(ladders)+10Cu(chains)/form.unit --> Non uniform distribution of holes

Faraday susceptibility Kato et-al Physica C, 263,482, 96 Carter et-al PRL 77, 1380, 96 No contribution from ladders:large spin gap Formation of a spin singlet dimerized ground state in chains. --> Local susceptibility measurements are needed for the study of the ladders.

Distribution of holes in chains and ladders from the optical conductivity Osafune et-al, PRL,78, 1980, 1997 Ca doping > transfer of spectral weight at low energy into the ladders Redistribution of holes between chains and ladders Ladder hole doping increases from 0.07 to 0.20 between Ca0 and Ca12

Transport in doped spin ladders Ca0------>Ca12 from H.Eisaki, University of Tokyo (private comm) x>8 ‘1D conductor’

Ca11.5 superconductivity under pressure Nagata et-al 1998

Superconductivity in Ca12,under pressure, Orsay Mayaffre et-al Science 1998 P.Auban et -al Synthetic Metal 1999 1D 2D 1D conductor becoming an anisotropic 2D conductor under pressure

Charge ordering in ladders vs doping From the dielectric response: CDW Destruction of the CO-CDW state upon doping A more 2D conductor under doping CDW gap decreases faster than the Spin gap Vuletic et-al PRL 90 , 2003

NMR in spin ladders

63 Cu NMR shifts, Knight shifts =>local susceptibility on the ladder subsytem No pressure dependence of Korb Gapped spin excitations c@ T -1/2 exp-Ds/T (Troyer formula at low temperature)

63 Cu Knight shifts =>local susceptibility in Ca12 under pressure No pressure dependence of Korb Gapped spin Excitations at low pressure c@ T -1/2 exp-Ds/T (Troyer formula) Low lying spin excitations in Ca12 under pressure

Spin gap and low lying modes seen by 17O NMR

Summary of the data for x= 0, 12

Spin gap versus Ca doping and pressure Piskunov et al EPJB 24,443 2001 see also Magishi et-al PRB 98 Relevance of the b- axis Pachot et-al PRB 59, 12048, 1999

Spin gap versus superconductivity in Ca12 Superconductivity detected by AC Susceptibility at 36 kbar Piskunov et-al EPJ B 24, 443, 2001

Spin gap versus Ca doping and pressure D(nh) / D0 Theory (DMRG) Noack et al PRL 94 - Up to Ca8 doping dependence of the gap is according to theory,gap with hole doping - Above Ca8 under pressure: more subtle! role of interladder coupling is possible ?

Existence d ’excitations électroniques sans gap dans Ca12 Relaxation sur O(1) et O(2)

Low lying modes in Ca12 Relation avec le Knight shift dans les mêmes conditions de pression

Magnon branches in spin ladders Triplet excitations q @ p q @ 0 E(kx)= J ’ + J coskx - One magnon branch (gapped) degenerate in zero magnetic field - Continuum of two magnons states

Nuclear relaxation mechanisms in undoped ladders Direct magnon process: no energy conservation wo<<Ds Two magnon Raman processes between thermally excited states Momentum transfer q=0 and q= p Relaxation and dynamical structure factor Naef and Wang, PRL, 84,1320,2000

Dynamical sructure factors derived from NMR relaxation Piskunov et-al, PRB, 69, 014510,2004 Use of the values for the spin gap determined experimentally

Ce qui a été appris par les mesures deT1 Détermination expérimentale des facteurs de structure dynamique S(q,w) Les processus multi-magnons q=0 et p contribuent au T1 dans les échelles dopées comme pour des échelles non dopées isolées. Mise en évidence du cross-over spin-gap/paramagnetism par le max de S(p,p)/S(0,0) à Tcr= Ds/2. Bonne corrélation entre les deux. La dynamique des échelles isolées n’est plus suivie en présence de porteurs libres à basse température, (Ca12 sous pression).

Spin gap versus superconductivity Piskunov et al EPJB 24,443,2001 P<Popt Gapped spin excitations and hole pairs with EB @Ds SC correlations cSC@ Ds/T Coherence lenght x@ t///Ds Josephson coupling between ladders Phase transition: -------------------------- P>Popt Deconfinement of holes Fermi liquid 2D Similar model SP AF in organics C.Bourbonnais and L.Caron, 1991

Where do the holes go upon Ca substitution and pressure? Use a local probe which is sensitive to the charge distribution on the ladders, the ion and vicinity Quadrupolar shifts of the NMR lines on 63Cu and 17Oxygen

Ladder sites and NMR spectrum Déplacements quadrupolaires du 1er ordre ou 2éme ordre

Comment les effets quadrupolaires apparaissent par rapport aux déplacements magnétiques

Les résultats bruts de RMN/RNQ

Spin ladders:hole distribution This experiment is quite accurate for variation of the hole density vs x and P but not for its absolute value Some calibration is needed, optics and X-ray absorption Backtransfer from ladders to chains Osafune and Nucker n = 0.06 hole/Cu(1) at 300K in Ca0

Pression et dopage a est peu sensible à la pression dans Ca12 Pachot et-al PRB 59, 12048, 1999 a est peu sensible à la pression dans Ca12

Le gap de spin en fonction des trous , 1 2 3 4 6 8 ? s e x p b a r k D ( L a , S r ) C a C u O D 1 4 - x x 2 4 4 1 D a r ? s t h e o C 9 ( 3 2 k b ) 8 1 5 L L a 5 ( 1 b a r ) D a 5 ( 3 2 k b a r ) 0.06 0.09 0.12 n h 0<x<8 , équivalence pression et dopage en Ca 8<x, dopage en Ca augmente le caractère 2D pression augmente les trous, nécessaire pour obtenir la supra

Le diagramme de Tallon 30 45 60 Pressure

Conclusion Possibilité de contrôler le caractère 2D et la densité de porteurs Ca et pression sont nécessaires pour obtenir les conditions de la supra Grande analogie avec le diagramme des hauts Tc Supra possible par le couplage de porteurs libres dans un conducteur devenu 2D