Complexity as a Result of Competing Orders in Correlated Materials.

1. 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.

2. 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)

3. 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”?

4. 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

5. 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

6. 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.)

7. Theory: Bi, tri, or tetracritical in clean limit. Induced by quenched disorder (II) Similar Scenario in Cuprates?

8. 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?

9. 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.

10. 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)

11. 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

12. T* Quenched disorder leads to clusters and T*, as in manganites. Highly inhomogeneous Coulombic centers, as in Sr++. Each provides 1h.

13. Random orientation of the local SC phases in glassy underdoped region T* AF or CDW Manganites Cartoonish version of MC results SC

14. 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

15. 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

16. ``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))

17. Half-Breathing along x Half-Breathing along y Breathing Shear See Y. Yildirim and A.M. cond-mat/0503292 Adiabatic Phonons

18. Hamiltonian for Phonons Diagonal Coupling: Off-Diagonal Coupling: Stiffness:

19. Diagonal Term Shear mode Stripes become more localized

20. Diagonal Term Breathing mode Shear mode Half-Breathing mode

21. Off-Diagonal Term The stripes become more dynamic

22. Diagonal Term on Uniform State Shear Mode Breathing Mode Stripes are induced in a uniform ground state

23. Phonons in the t-J model Half-breathing mode Extended breathing mode Phonons stabilize tiles and stripes A.M. and J. Riera (in preparation)

24. Quantum Phonons Phonons stabilize stripes! Half-breathing mode

25. 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.

26. 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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