1. 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.

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. (I)CMR manganites: FM metal Rich phase diagram, several states competing. Common feature of many Strongly Correlated Electronic systems. PI Potential application in “read sensors”? CE-type Spin, charge, orbital order

4. Phase Competition in the Presence of Quenched Disorder First order or tetracritical Clean limit result: T W FMCO FMStripes Toy Model with disorder Burgy et al., PRL87, 277202 (2001). See also Nagaosa et al. SG T W FMCO T W FMCO See also Akahoshi et al. PRL 2003; Argyriou et al., PRL; De Teresa T*

5. CMR effect due to inhomogeneous states Resistor Network: FM up FM down Insulator Disorder H=0 H=0.01 Rotates easily MR ratios as large as 1000% at H=0.01. Field is small, but effective spin is large! T*Tc 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., …

6. Conjectured CMR State in Manganites High susceptibility to external magnetic fields: rapid rotation of preformed nano-moments (see also Cheong et al.) A similar picture will emerge in our high Tc analysis. Field=0 FM regions Field>0

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

8. New Trends: Inhomogeneities in cuprates. Are stripes universal? BiSCO (Hoffman et al.) PATCHES? LSCO (Yamada et al.) STRIPES? Ca2-x Nax Cu O2 Cl2 Hanaguri et al. TILES? YBCO Homogeneous? Large clusters and computational methods needed. Switch to phenomenology for underdoped region …

9. Homes’ Law Cuprates in all regimes follow the law. BCS SC follow the law in the dirty limit only. Homes et al., Cond-mat/0410719

10. A Spin-Fermion Model as a phenomenological model for HTSC S=1/2 J J’ t=1, 2D J~2 J’=0.05 t Charge DOF Spin DOF A.M. et al., PRL 84, 2690 (2000); PRL 88, 187001 (2002) (S classical)

11. 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. 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. Phenomenological SC vs. AF competition Tetracritical V=1-J/2

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

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

14. Theory vs Experiment Quasiparticle dispersion in 20x20 cluster 60% AF and 40% d-wave SC. Alvarez et al. sc AF ARPES Yoshida et al. Spin Glass region (no SC) AF background SC clusters arches in FS

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. Giant proximity effect? (Alvarez et al., PRB71, 014514 (2005)) “Colossal” Effects in underdoped regime? (``Giant proximity effect’’ Decca et al. PRL, and Bozovic et al. submitted to Nature). ``non-SC glass’’ ``Inhomogeneous’’ superconductors High susceptibility to ``external SC fields’’

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

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

19. Diagonal Term Stripes become more localized Shear mode

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 Stripes are induced in a uniform ground state Shear Mode Breathing Mode

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

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

25. Conclusions 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) 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. References

27. ---------------------------------------