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.

Ladders: (even number of legs)

<Si.Sj> exp- (ri-rj) /spin liquid

J ’

J

N= /a spins in a box --> Quantization = J/N=J/2 --> spin gap

Planes: Heisenberg antiferromagnetLong range ordered

<Si.Sj> S2 cos Q. (ri-rj) Q=(/a,/a)Gapless excitations, spin waves

Chains: Heisenberg chain S=1/2Almost ordered state at T=0, quantum fluctuations<Si.Sj> (ri-rj) , (T=0) JGapless spin excitations

Low dimensional magnets

Cu 2+ (S=1/2)

Ladders in organic compounds

Chabousssant et-al, PRL, 79, 925, 1997Cu 2+ (S=1/2)

Cu-Cu superexchange via Cl

Magnon and QP modes

Spin gap in isotropic ladders

From Dagotto and Rice, Science, 271, 618, 1996

Doping ladders, quasi-particles in spin ladders

Hole in Cu2O3

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 EB= J’-2t’-2tQP is a localized spin S=1/2

EB< s

<<

Correlations, pairing, density waves, AFin doped ladders

DMRG calculationHayward et-alPRL 75, 926, 1995Noack et-al 96

Magnetism: exp-(/r) -1, spin gappedPairing: 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

0.1

-0.08 -0.08

Noack et-al 96

d-wave pairing

Spin ladders in La2Cu2O5

Hiroi and TakanoNature 377, 41, 1995

Hole doping in (La/Sr)2Cu2O5

Hiroi and TakanoNature 377, 41, 1995

AF ordering observed by NMR, SR at 110KIn La2Cu2O5

Interplay between spin liquid and AF due to the non frustrated interladder interaction

No superconductivity obsereved

Spin ladders in cuprates : 2 versus 3 leg ladders

J=1000-1500K via Cu-O-Cu superexchange via 180° bond, antiferroJ interladder due to Cu-O-Cu 90° bond, much smaller and ferro + frustration

Cu2O3 ladders M.Takano et - al 1996

Azuma et al 1994

Sr2Cu2O3

SrCu2O3

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

Kato et-al Physica C, 263,482, 96Carter et-al PRL 77, 1380, 96

Faraday susceptibility

No contribution from ladders:large spin gapFormation 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 laddersCa0------>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 -alSynthetic Metal 1999

1D conductorbecoming an anisotropic 2D conductor under pressure

1D2D

Vuletic et-al PRL 90 , 2003

Charge ordering in ladders vs doping

From the dielectric response: CDWDestruction of the CO-CDW state upon dopingA more 2D conductor under dopingCDW gap decreases faster than the Spin gap

NMR in spin ladders

Kα

=Korb,α

+Ks,α

No pressure dependence of Korb

63 Cu NMR shifts, Knight shifts =>local susceptibilityon the ladder subsytem

Gapped spin excitationsexp-s/T

(Troyer formulaat low temperature)

63 Cu Knight shifts =>local susceptibility in Ca12 under pressure

Low lying spin excitations in Ca12 under pressure

Kα

=Korb,α

+Ks,α

Gapped spin Excitations at low pressureexp-s/T (Troyer formula)

No pressure dependence of Korb

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 24,4432001see alsoMagishi 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

0,0 0,1 0,2 0,3 0,40,0

0,2

0,4

0,6

0,8

1,0

1,2

?sexp,bar

?sexp,3kbar

?stheor

Ca9(3kbar)Ca8(3kbar)

Ca(3kbar)Ca(bar)Ca5(3kbar)

Ca9(bar)

Ca8(bar)

Ca(3kbar)

Ca5(bar)

Ca0(3kbar)

Ca(bar)

Ca0(bar)

La5(3kbar)

La5(bar)

(La,Sr)4-xCaxCu4O4

?s(nh)/?s(nh

=0)( )K

nh

n h) /

0

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 ?

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

q 0

q

Magnon branches in spin ladders

- One magnon branch (gapped) degenerate in zero magnetic field- Continuum of two magnons states

E(kx)= J ’ + J coskx

Triplet excitations

Nuclear relaxation mechanisms in undoped ladders

Direct magnon process: no energy conservationo<<s

Two magnon Raman processes between thermally excited statesMomentum transfer q=0 and q=

Relaxation and dynamical structure factorNaef 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,)

Les processus multi-magnons q=0 et 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()/S(0,0)à Tcr= s/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

P<Popt

Gapped spin excitations and hole pairs with EB s

SC correlations SCsCoherence lenght t//s

Josephson coupling between laddersJ S≈

ξct⊥2 /Δ

Phase transition: JSχSC(TC)=1 TC≈t⊥2 /ΔS

P>Popt

Deconfinement of holes Fermi liquid 2D

Tc≈t⊥e−1g*

Similar model SP AF in organics C.Bourbonnais and L.Caron, 1991

SPIN GAP

METALCDW

Popt

SC

BCSBEPressure

T* : Pair Formation

Temperature

--------------------------

Piskunov et alEPJB 24,443,2001

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 lineson 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

Osafune and Nucker

n = 0.06 hole/Cu(1)at 300K in Ca0

Backtransferfrom ladders to chains

Pression et dopage

Pachot et-al PRB 59, 12048, 1999

a est peu sensible à la pression dans Ca12

Le gap de spin en fonction des trous

0<x<8 , équivalence pression et dopage en Ca8<x, dopage en Ca augmente le caractère 2D pression augmente les trous, nécessaire pour obtenir la supra

0,0 0,1 0,2 0,3 0,40,0

0,2

0,4

0,6

0,8

1,0

1,2

?s

exp, 1 bar

?s

exp, 32 kbar

?s

theor

Ca9 (32 kbar)Ca8 (32 kbar)

Ca12 (32 kbar)Ca12 (1 bar)Ca5 (32 kbar)

Ca9 (1 bar)

Ca8 (1 bar)

Ca2 (32 kbar)

Ca5 (1 bar)

Ca0 (32 kbar)

Ca2 (1 bar)

Ca0 (1 bar)

La5 (32 kbar)

La5 (1 bar)

(La,Sr)14-xCaxCu24O41

nh

0.120.06 0.09

Le diagramme de Tallon

30 45 60Pressure

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 libresdans un conducteur devenu 2D