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Complexity as a Result of Competing Orders in Correlated Materials. Adriana Moreo Dept. of Physics and ORNL University of Tennessee, Knoxville, TN, USA. Supported by NSF grants DMR-0443144 and 0454504. Outline. CMR manganites (short overview) High-Tc cuprates Phonons (new results)

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Complexity as a result of competing orders in correlated materials

Complexity as a Result of Competing Orders in Correlated Materials.

Adriana Moreo

Dept. of Physics and ORNL

University of Tennessee, Knoxville,

TN, USA.

Supportedby NSF grants DMR-0443144

and 0454504.


Outline
Outline Materials.

  • CMR manganites (short overview)

  • High-Tc cuprates

    • Phonons (new results)

      Common theme emerging:

      Clustered states and dramatic effects as a result of small perturbations (complexity)


Cmr manganites
CMR manganites: Materials.

PI

CE-type

Spin, charge,

orbital order

FM

metal

Rich phase diagram, several states

competing. Common feature of many

Strongly Correlated Electronic systems.

Potential application in

“read sensors”?


Phase competition in the presence of quenched disorder

Clean limit result: Materials.

T

T

T*

CO

FM

CO

FM

FM

Stripes

W

W

SG

T

First order or

tetracritical

See also

Akahoshi et al.

PRL 2003;

Argyriou et al.,

PRL; De Teresa

Toy Model with disorder

Burgy et al., PRL87, 277202 (2001). See also Nagaosa et al.

CO

FM

W

Phase Competition in the Presence of Quenched Disorder


Cmr effect due to inhomogeneous states

H=0 Materials.

Rotates easily

H=0.01

MR ratios as large as 1000% at H=0.01.

CMR effect due to inhomogeneous states

Tc

T*

Field is small, but effective spin is large!

Elastic effects (see also

Bishop, Egami,…) are important for

this to occur in both D=2 and 3

(Burgy et al, PRL 92, 097202 (04)).

See also K. Yang, H. Ahn et al., …

Resistor Network:

FM up FM down Insulator Disorder


Conjectured cmr state in manganites

Field=0 Materials.

Field>0

FM regions

Conjectured CMR State in Manganites

A similar picture

will emerge in our

high Tc analysis.

High susceptibility to external magnetic fields:

rapid rotation of preformed nano-moments

(see also Cheong et al.)


Ii similar scenario in cuprates

Theory: Materials.

Bi, tri, or

tetracritical

in clean limit.

Induced by

quenched disorder

(II) Similar Scenario in Cuprates?


New trends inhomogeneities in cuprates are stripes universal

LSCO Materials.(Yamada et al.)

Ca2-x Nax Cu O2 Cl2

STRIPES?

Hanaguri et al.

TILES?

BiSCO (Hoffman et al.)

Switch to phenomenology

for underdoped region …

PATCHES?

Large clusters and computational methods needed.

New Trends: Inhomogeneities in cuprates. Are stripes universal?

YBCO

Homogeneous?


Homes law
Homes’ Law Materials.

Homes et al.,

Cond-mat/0410719

  • Cuprates in all regimes follow the law.

  • BCS SC follow the law in the dirty limit only.


A spin fermion model as a phenomenological model for htsc

t Materials.

Charge DOF

Spin DOF

J

S=1/2

t=1, 2D

J~2

J’=0.05

S=1/2

J’

A Spin-Fermion Model as aphenomenological model for HTSC

A.M. et al., PRL 84, 2690 (2000); PRL 88, 187001 (2002) (S classical)


Phenomenological SC vs. AF competition Materials.

Monte Carlo results for ``mean-field-like’’ model of mobile electrons coupled to classical AF (A.M. et al., PRL 88, 187001 (2002)) and SC order parameters (Alvarez et al., cond-mat/0401474). Two parameters: J and V.

V=1-J/2

Tetracritical


Quenched disorder leads to clusters and t as in manganites

T* Materials.

Quenched disorder leads to clusters and T*, as in manganites.

Highly

inhomogeneous

Coulombic

centers, as in

Sr++. Each

provides 1h.


Cartoonish version of mc results

Random orientation of the local SC phases Materials.

in glassy underdoped region

T*

AF

or

CDW

Manganites

Cartoonish version of MC results

SC


Theory vs experiment

SC clusters Materials.

arches in FS

Quasiparticle dispersion in

20x20 cluster 60% AF and

40% d-wave SC.

Alvarez et al.

AF background

sc

AF

ARPES

Yoshida

et al.

Spin Glass region (no SC)

Theory vs Experiment


Effects of Quenched Disorder on Materials.a Landau-Ginzburg model with only AF and SC order parameters (no mobile electrons).

AF+SC SC AF

TRI

TETRA


Giant proximity effect alvarez et al prb71 014514 2005

``non-SC glass’’ Materials.

``Inhomogeneous’’

superconductors

“Colossal” Effects in underdoped regime?

(``Giant proximity effect’’ Decca et al. PRL, and Bozovic et al. submitted to Nature).

High

susceptibility

to ``external

SC fields’’

Giant proximity effect? (Alvarez et al., PRB71, 014514 (2005))


Adiabatic phonons

Half-Breathing Materials.

along x

Half-Breathing

along y

Breathing

Shear

See Y. Yildirim and A.M. cond-mat/0503292

Adiabatic Phonons


Hamiltonian for phonons
Hamiltonian for Phonons Materials.

Diagonal Coupling:

Off-Diagonal Coupling:

Stiffness:


Diagonal term
Diagonal Term Materials.

Shear mode

Stripes become more localized


Diagonal term1
Diagonal Term Materials.

Breathing mode

Shear mode

Half-Breathing mode


Off diagonal term
Off-Diagonal Term Materials.

The stripes become more dynamic


Diagonal term on uniform state
Diagonal Term on Uniform State Materials.

Shear Mode

Breathing Mode

Stripes are induced in a uniform ground state


Phonons in the t j model
Phonons in the t-J model Materials.

Half-breathing mode

Extended breathing mode

Phonons stabilize tiles and stripes

A.M. and J. Riera (in preparation)


Quantum phonons
Quantum Phonons Materials.

Phonons stabilize stripes!

Half-breathing mode


Conclusions
Conclusions Materials.

  • Experiments + theory have revealed nano-scale inhomogeneities in TMOs. Intrinsic PS or first-order transitions smeared by disorder maybe at work.

  • The mixed-phase states appear to cause the CMR. They may contribute to the unusual behavior of underdoped cuprates. ``Colossal’’ effects may extend beyond manganites.

  • Phononic degrees of freedom in cuprates seem to produce competing charge inhomogeneous states like stripes and tiles due to breathing and half-breathing modes. Buckling modes will be studied.


Collaborators
Collaborators Materials.

G. Alvarez (ORNL) C. Sen (FSU)

E. Dagotto (UT/ORNL) M. Mayr (Stuttgart)

T. Hotta (Tokai) S. Yunoki (Trieste)

J. Riera (Argentina) Y.Yildirim (UT)

References

  • A. M. et al., Science 283, 2034 (1999).

  • J. Burgy et al., PRL 87, 277202 (2001).

  • G. Alvarez et al., PRB71, 014514 (2005).

  • Y. Yildirim et al., cond-mat/0503292.



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