Complexity as a result of competing orders in correlated materials
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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.

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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.

Supportedby NSF grants DMR-0443144

and 0454504.


Outline

  • 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:

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”?


Clean limit result:

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


H=0

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


Field=0

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.)


Theory:

Bi, tri, or

tetracritical

in clean limit.

Induced by

quenched disorder

(II) Similar Scenario in Cuprates?


LSCO (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 et al.,

Cond-mat/0410719

  • Cuprates in all regimes follow the law.

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


t

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

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


T*

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

Highly

inhomogeneous

Coulombic

centers, as in

Sr++. Each

provides 1h.


Random orientation of the local SC phases

in glassy underdoped region

T*

AF

or

CDW

Manganites

Cartoonish version of MC results

SC


SC clusters

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 a Landau-Ginzburg model with only AF and SC order parameters (no mobile electrons).

AF+SC SC AF

TRI

TETRA


``non-SC glass’’

``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))


Half-Breathing

along x

Half-Breathing

along y

Breathing

Shear

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

Adiabatic Phonons


Hamiltonian for Phonons

Diagonal Coupling:

Off-Diagonal Coupling:

Stiffness:


Diagonal Term

Shear mode

Stripes become more localized


Diagonal Term

Breathing mode

Shear mode

Half-Breathing mode


Off-Diagonal Term

The stripes become more dynamic


Diagonal Term on Uniform State

Shear Mode

Breathing Mode

Stripes are induced in a uniform ground state


Phonons in the t-J model

Half-breathing mode

Extended breathing mode

Phonons stabilize tiles and stripes

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


Quantum Phonons

Phonons stabilize stripes!

Half-breathing mode


Conclusions

  • 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

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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