phase diagrams of (la,y,sr,ca) 14 cu 24 o 41 : switching between the ladders and chains
DESCRIPTION
Phase diagrams of (La,Y,Sr,Ca) 14 Cu 24 O 41 : 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. - PowerPoint PPT PresentationTRANSCRIPT
Phase diagrams of Phase diagrams of (La,Y,Sr,Ca)(La,Y,Sr,Ca)1414CuCu2424OO4141: switching : switching between the ladders and chainsbetween the ladders and chains
T.Vuletic, T.Ivek, B.Korin-Hamzic, S.Tomic
B.Gorshunov, M.Dressel
C.Hess, B.Büchner
J.Akimitsu
Leibniz-Institut für Festkörper- und Werkstoffforschung, Dresden, Germany
Institut za fiziku, Zagreb, Croatia
1.Physikalisches Institut, Universität Stuttgart, Germany
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)
q1D materials: proximity (competition and/or coexistence) of superconductivity & magnetic/charge ordered phases
(La,Y,Sr,Ca)14Cu24O41 :
Task:
assemble phase diagrams to catalyze discussions on
the nature of superconductivity and charge-density wave
and their relationship with the spin-gap
spin chain/ladder composite q1D cuprates
strongly interacting q1D electron system
Motivation
U<0, t≠0
V>0: 2kF CDW
V<0: singlet SC
E.Dagotto et al., PRB’92ladders map onto 1D chain
with effective U<0 for hole pairing!
V.J.Emery, PRB’76
chai
n layer
t-J(-t’-J’) model for ladders
₪ pairing of the holes
superconducting or CDW correlations
₪ doped holes enter O2p orbitals form ZhangRice singlet with Cu spin
spin gap
b=
12.9
Åa=11.4 Å
Crystallographic structure (La,Y,Sr,Ca)14Cu24O41
cC
Chains: Ladders: cC=2.75 Å cL=3.9 Å
10·cC≈7·cL≈27.5 Å
cL
A14 Cu2O3 laddersCuO2 chains
cL/cC=√2
Bond configurations and dimensionality
cC
Chains: Ladders: cC=2.75 Å cL=3.9 Å
10·cC≈7·cL≈27.5 Å
cL
A14 Cu2O3 laddersCuO2 chains
90o - FM, J<0
180o - AF, J>0
Cu-O-Cu bonds
holes O2p orbitals
Cu2+ spin ½
Magnetic structure and holes distribution
(La,Y)y(Sr,Ca)14-yCu24O41
y≠0, all holes in chains
Sr14-xCaxCu24O41
x=0, around 1 hole in laddersincreases for x≠0
backtransfer to chains at low T
No charge ordering
2D AF dimer / charge order
Tco = 300 KT> Tco Nearest neighbor hopping
TTdc /2exp
Physics of chains:dc transport in (La,Y)y(Sr,Ca)14-yCu24O41
T< TcoMott’s variable range hopping
ddc TTT 1/1
00 /exp
Dimensionality of hopping: d=1
y=3
Tco = 330 K
y=3
y=5.2
co
dc
co- crossover frequency: ac hopping overcomes dc
No collective response
ac response in y=3
1;)(
,
sTA
TS
dc
ac
Quasi-optical microwave/FIR: hopping in addition to phonon
Hopping dies out
Chains Phase Diagram (La,Y)y(Sr,Ca)14-
yCu24O41
₪ Chains:
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
Chains in Sr14-xCaxCu24O41 : AF dimers/charge order
LRO below T*
only SRO for x=8&9
AF order for x≥11
Kataev et al., PRB’01
ESR signal due to Cu2+ spins in the chains
for T>T* broadening of ESR line due to the thermally activated hole mobility
Slope of H*(T) vs T is approximatelythe same for all x of Sr14-xCaxCu24O41 andfor La1Sr13Cu24O41 (nh=5, all in chains)
Upper limit: 1 hole transferredinto the ladders for all x
nh=5
nh=4
nh=6
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
Phase diagram for chains
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?
Phason: Elementary excitation associated with spatio-temporal variation of the CDW phase (x,t)
phason response to dc & ac field governed by: free carrier screening and pinning potential V0 of impurities or commensurability
Experimental fingerprints: mode at pinning frequency
broad radio-freq. modes centred at
enhanced effective mass nonlinear dc conductivity above sliding threshold ET=2kFV0/0
=
*/0 mV
1/0=200 / Vz
200
20*
z
m Littlewood, PRB ‘87
CDW
Ladders: charge response
Ladders: charge response
radio-frequency ac response:similar to phason responseCharge Density
Wave
1
01
1
iHF
Dielectric response:Generalized Debye function
1
01
1
iHF
₪ 104–105
₪0z
₪∞ 0.1 ns
2D phason response in ladder plane
pinned mode
Kitano et al.,
EPL’01
radio-freq. mode
enhanced effective mass m*=10 2-10 3
Ladders: Non-linear conductivity
good contacts and no unnested voltage
No ET, negligible non-linear effect
bad contacts, or large unnested voltageNo ET, “large”non-linear effect
“large” non-linear effect
small non-linear effect
Maeda et al., PRB’03
Blumberg et al., Science’02
Ladders: Non-linear conductivity
₪ order in ladders: CO of localized or CDW of itinerant electrons? analogy with AF/SDW
Phase diagram for ladders (corresponds to chains ph.diag.)
T*TCDW
suppresion of Tc and charge gaps
2D CDW in ladder planeunique to ladders? or common to low-D systems with charge order?
half-filled ladder in Hubbard model:CDW+pDW in competition with d-SC
Suzumura et al., JPSJ’04
FIN
CDW
SC
for x=0: Cross-over between paramagnetic and spin-gapped phase T* 200 K
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
Spin gap is present even for x=12, where SC sets-in
Polycrystalline
} Single crystal
Physics of ladders (Sr14-xCaxCu24O41): gapped spin-liquid
spin
ga
p
Physics of ladders (Sr14-xCaxCu24O41): superconductivity
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’04Fujiwara et al., PRL’03
₪ in x=0, the same, but no low-lying excitations and no SC!
Nagata et al., JPSJ’97
x=11.5
SC: x≥10 i T<12K, p= 3-8 GPa₪ pressure removes insulating phase
₪ x<11: insulating behavior
₪ : decreases with x
₪ c(300 K): 400-1200 (cm)-1 ₪ x≥11 i T>50K : metallic
Experiment:
temperature range: 2 K -700 K
dc transport, 4 probe measurements:lock-ins for 1 m-1 kdc current source/voltmeter 1 -100 M 2 probe measurements:electrometer in V/I mode, up to 30 Glock-in and current preamp, up to 1 Tac transport – LFDS(low-frequency dielectric spectroscopy) 2 probe measurements:lock-in and current preamp, 1 mHz-1 kHzimpedance analyzers, 20Hz-10MHz
Zagreb
Physics of ladders (Sr14-xCaxCu24O41): insulating phase(s)
Gorshunov et al., PRB’02Vuletic et al., PRL’03
Vuletic et al., submitted to PRB’04
₪ 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 0
-1for E||a, E||c ₪ c/a 10 c/a
No response along rungs for x=8,9
&Transition broadening
Increase in c/a at low-T for x=9
Long-range order in planes is destroyed
Anisotropic ac-response: 2D charge order in ladder plane
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
The nature of H.T. insulating phase is the key for CDW suppression
Ca-substitution
Pressure
Increase ladder/chain couplingincrease hchange V, U
b
Increase W change U/W
CDW suppresed due to changes in U/W, V, h (and disorder)
decrease lattice
parameters
HT phase: Mott-Hubbard insulator (1/2 filling, U/W>1) on-site U, inter-site V, hole-doping h, bandwidth W=4t
Pachot et al., PRB‘99
bbbaaaccc
H.T. phase persists – “disorder resistant”
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
Instabilities in 1D weakly interacting Fermi gas
T. Takahashi et al., PRB’97
M. Arai et al., PRB’97
inter-ladder hopping:
5-20% of intra-ladder
local density approximation
top of lower Hubbard band of ladders
finite DOS on EF
bands at 3 & 5.5 eV
optics: Mott-Hubbard gap 2 eV EF pulled down by doped holes
Osafune et al., PRL’97
Electronic structure (La,Sr,Ca)14Cu24O41
charge-transfer limit
1 electron, S=½ per copper site
doped holes enter O2p orbitals form ZhangRice singlet with Cu spin
chai
n
lad
der
layer
Hamiltonian reduces to Heisenberg spin ½ model + effective hopping term for ZR singlet motion
lattice formed of 1 kind of sites
two band model (oxygens!)
copper: strong on-site repulsion U
Zhang and Rice., PRB’88
Strong coupling limit for cuprates
Cu (3d9) and O (2p6) form the structure
Holes are localized in chains of fully hole doped Sr14-xCaxCu24O41
Chains: AF dimer / charge order complementarity
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
Physics of chains: Sr14-xCaxCu24O41
spin-gap
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
decrease V, increase the doping h, destabilizes CDW and p-DW, in favor of d-SC state.
h=2.8
CDW +p-DW
1.4 2.8 4.2 5.6
hole transferh
CDW +p-DW
(TMTTF)2AsF6 Charge order vs. CDW in ladders
NMR detects charge disproportionationD.S.Chow et al., PRL’00
In the vicinity of CO transition dielectric constant follows Curie lawF. Nađ et al., J.Phys.CM’00
Relaxation time is temperature independent – not phason like
Zagreb
CDW in the Ladders versus CO in the Chains
No splitting of 63Cu NMR line
ladder chain
Splitting of 63Cu NMR line
Charge disproportionation
Takigawa al., PRB 1998
Fukuyama, Lee, Rice
i
tiexii eErrQRrVK
dt
d
dt
dm
012
2
2
)(sin)(*
Phason: Elementary excitation associated with spatio-temporal variation of the CDW phase (x,t)
₪ Periodic modulation of charge density₪ Random distribution of pinning centers₪ Local elastic deformations (modulus K) of the phase (x,t) ₪ Damping ₪ Effective mass m*»1₪ External AC electric field Eex is applied
www.ifs.hr/real_science
)(sin10 rrQ
)( ii RrV
Phason dielectric response governed by: free carrier screening, nonuniform pinning
Phason CDW dielectric response
Phason CDW dielectric response
www.ifs.hr/real_science Littlewood
Max. conductivity close to the pinning
frequency
pinned mode - transversal
0- weak damping
=
*/0 mV
www.ifs.hr/real_science Littlewood
Longitudinal mode is not visible in diel. response since it exists only for =0!
Low frequency tail extends to 1/0=
strong damping»0
Screening:
200 / Vz
Max. conductivity close to the pinning
frequency
pinned mode - transversal
0- weak damping
=
*/0 mV
Phason CDW dielectric response
plasmon peak longitudinal
www.ifs.hr/real_science Littlewood
Experiments detect two modes
=
Nonuniform pinning of CDW gives the true phason mode a mixed character!
*/0 mV
0=200 / Vz
Longitudinal response mixes into the low-frequency conductivity
Phason CDW dielectric response
& 0 are related: 0 & z – from our experiments
0 – carriers condensed in CDW (holes transferred to ladders = 1·1027 m-3 = 1/6 of the total)
m* - CDW condensate effective mass
Sr14-xCaxCu24O41
Microwave conductivity measurements (cavity perturbation) peak at =60 GHz CDW pinned mode Kitano et al., 2001.
CDW effective mass m*≈100
www.ifs.hr/real_science m*
20
20
0 *
mz
0
'B
S
l
0
0''GG
S
l
GeneralizedDebye function
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Complex dielectric function
1
01
1
iHF∞
Debye.fja
www.ifs.hr/real_science
1
01
1
iHF∞
Debye.fja
Complex dielectric function
GeneralizedDebye function
₪ relaxation process
strength = (0) - ∞
₪ 0 – central relaxation time₪ symmetric broadening of the relaxation time
distribution 1 -
0
'B
S
l
0
0''GG
S
l
Eps im eps re
₪ We analyze real & imaginary part of the dielectric function
₪ We fit to the exp. data in the complex plane
₪ We get the temp. dependence , 0, 1-
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reim