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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,

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Présentation au sujet: "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,"— Transcription de la présentation:

1 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.

2 Ladders: (even number of legs) exp- (r i -r j ) / spin liquid J J N= /a spins in a box --> Quantization = J/N=J/2 --> spin gap Planes: Heisenberg antiferromagnet Long range ordered S 2 cos Q. (r i -r j ) Q=( /a, /a) Gapless excitations, spin waves Chains: Heisenberg chain S=1/2 Almost ordered state at T=0, quantum fluctuations (r i -r j ), (T=0) J Gapless spin excitations Low dimensional magnets Cu 2+ (S=1/2)

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

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

5 Doping ladders, quasi-particles in spin ladders Hole in Cu 2 O 3 Cost: J 2 J Bound quasiparticles Ground state Excited states -Magnon excitations with a modified gap -Excited quasiparticles t-J model, strong coupling Binding energy for a QP pair E B = J-2t-2t QP is a localized spin S=1/2 E B < s <<

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

7 Spin ladders in La 2 Cu 2 O 5 Hiroi and Takano Nature 377, 41, 1995

8 Hole doping in (La/Sr) 2 Cu 2 O 5 Hiroi and Takano Nature 377, 41, 1995 AF ordering observed by NMR, SR at 110K In La2Cu2O5 Interplay between spin liquid and AF due to the non frustrated interladder interaction No superconductivity obsereved

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

10 Structure of the ( Sr/Ca) 14 Cu 24 O 41 series Mc Carron, 1998 Siegrist 1988 Nominal Cu valence hole/Cu 14Cu(ladders)+10Cu(chains)/form.unit --> Non uniform distribution of holes

11 Kato et-al Physica C, 263,482, 96 Carter et-al PRL 77, 1380, 96 Faraday susceptibility 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.

12 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

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

14 Ca11.5 superconductivity under pressure Nagata et-al 1998

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

16 Vuletic et-al PRL 90, 2003 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

17 NMR in spin ladders

18 No pressure dependence of K orb 63 Cu NMR shifts, Knight shifts =>local susceptibility on the ladder subsytem Gapped spin excitations exp- s /T (Troyer formula at low temperature)

19 63 Cu Knight shifts =>local susceptibility in Ca12 under pressure Low lying spin excitations in Ca12 under pressure Gapped spin Excitations at low pressure exp- s /T (Troyer formula) No pressure dependence of K orb

20 Spin gap and low lying modes seen by 17 O NMR

21 Summary of the data for x= 0, 12

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

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

24 n h ) / Spin gap versus Ca doping and pressure 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 ?

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

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

27 q 0 q Magnon branches in spin ladders - One magnon branch (gapped) degenerate in zero magnetic field - Continuum of two magnons states E(k x )= J + J cosk x Triplet excitations

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

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

30 Ce qui a été appris par les mesures deT 1 Détermination expérimentale des facteurs de structure dynamique S(q, ) Les processus multi-magnons q=0 et contribuent au T 1 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( )/S(0,0) à T cr = s /2. Bonne corrélation entre les deux. La dynamique des échelles isolées nest plus suivie en présence de porteurs libres à basse température, (Ca12 sous pression).

31 Spin gap versus superconductivity P

P opt Deconfinement of holes Fermi liquid 2D Similar model SP AF in organics C.Bourbonnais and L.Caron, Piskunov et al EPJB 24,443,2001

32 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

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

34 Comment les effets quadrupolaires apparaissent par rapport aux déplacements magnétiques

35 Les résultats bruts de RMN/RNQ

36 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 Osafune and Nucker n = 0.06 hole/Cu(1) at 300K in Ca0 Backtransfer from ladders to chains

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

38 Le gap de spin en fonction des trous 0

39 Le diagramme de Tallon Pressure

40 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


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