les échelles de spins conductrices: une approche pour les supras hauts tc d.jérome, orsay avec les...
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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,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