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