Complexity in Transition Metal Oxides Adriana Moreo Dept. of Physics and ORNL University of Tennessee, Knoxville, TN, USA. Supported by NSF grants DMR-0443144 and 0454504.
Collaborators G. Alvarez (ORNL) E.Dagotto(UT/ORNL) A.Feiguin(Microsoft) T. Hotta (Japan) M. Mayr (Germany) M. Moraghebi (UW) J. Verges (Spain) S. Yunoki (Italy)
Outline Motivation Models and Techniques Results Conclusions
Motivation I: Colossal Magnetoresistance (CMR) Drastic reduction of resistivity with small H- fields. Potential application in read sensors? Tomioka and Tokura, (1999).
Motivation II: Understand the complex phase diagram that experiments are unveiling. A-type AF CE-type Cheong et al.
Motivation III: Transfer what we learned in the context of manganites to other transition metal oxides, in particular, high Tc cuprates. D-wave SC. Pseudogap Stripes?
Structure of the Manganites La, Sr Mn O n=2 Bilayer ( ) 2 7 ( R, D) Mn O n 3 + 1 3 n+ 1 n
Theoretical Models Strong coupling between correlated itinerant electrons and localized spins are believed to be responsible for magnetic and electronic properties. Mn [ ] 5 2 Ar 3d 4 : s 3d orbital 3 Mn + g [ ] 4 Ar 3 : d e ( ) d d x 2 y 2, 2 2 r 3z 5 fold degenerate g S=3/2 (localized) t ( ) 2 d, d, d xy yz zx
Manganites t e g J H t 2g S=3/2 S=1/2 J AF t=1 3d Mn e- J >8 H (prevents double occupancy) J ~0.05 (small but AF relevant)
The Lattice Kondo Model 1 orbital approximation H ( + + c ) i σ c j σ + c j σ ci + J si Si + J AF Si S j = t,,,, σ i, j i i, j Heavy Fermions: J/t<<1 Manganites: J/t >8, J<0 Cuprates: J/t~2 PRL84, 2690 (2000) J/t
Two Orbitals plus Jahn-Teller phonons H = t ab c + c J S c + σ c + ij ia, σ jb, σ H i ia, σ ia, σ i, j, a, b, σ i, a, σ r Q 2 Q = Q Q 3 2 + g ab cia, σq ib, σ + i, a, σ Q 2 Q 3 k 2 () i c tr Q () i + 2 g: electron-phonon coupling k: phonon stiffness i λ = g / Q 3 k
Computational Techniques Partition Function S i phonons = Z = DQ DS tr e e g ( βh ) ( sinθ cosφ,sinθ sinφ, cosθ ) i t 2g spins i Monte Carlo simulation over classical spins. Quantum itinerant electrons treated exactly. No sign problems. All temperatures and densities are accessible. Classical approximation tested in 1D comparing with Lanczos. Dynamical properties can be calculated straightforwardly. e g i electrons i i
AF FM Results J H / t AF insulator metal FM, AF, Phase Separation and Spin Incommensuration observed. No canted states in this model! <n> Yunoki et al. PRL80, 845 (1998). n=1 n<1
2 Orbitals and J-T Phonons PS CO PS Precursor of CE All the stable phases observed experimentally are obtained. PS is driven by orbital degrees of freedom. Precursor of A-type AF metal.
Influence of 1/r Coulomb interaction or Droplets, stripes or other nanometer size patterns may form (as in studies of high Tc and stripes). In 1D the PS state evolved into CDW state with increasing repulsion (Malvezzi et al. PRB 99).
Experimental Evidence of Phase coexistence HM A.M. et al., Science 283, 2034 (1999). Renner et al., Nature 02 BiCaMnO STM Uehara et al., Nature 99 LaPrCaMnO Elec. Micros.
Phase Competition in the Presence of Quenched Disorder Manganites FM Stripes First order Toy Model with disorder Burgy et al., PRL87, 277202 (2001).
Real-Space Spin Configurations Paramagnetic Clustered Percolated FM down FM up Insulator Disorder T>T* To <T<T* 1 T<To 1 Conjectured CMR state in manganites (see also Cheong et al.)
Random Resistor Network Resistor Network: FM up FM down Insulator Disorder H=0 Rotates easily H=0.01 MR ratios as large as 1000% at Hs=0.01 (Burgy et al.,prl 87, 277202 (2001).
Conjectured CMR State in Manganites A similar picture will emerge in our high Tc analysis. Field=0 FM regions Field>0 High susceptibility to external magnetic fields: rapid rotation of preformed nano-moments (see also Cheong et al.)
(II) Similar Scenario in Cuprates? Theory: Bi, tri, or tetracritical in clean limit. Induced by quenched disorder
New Trends: Inhomogeneities in cuprates. Are stripes universal? YBCO Homogeneous? BiSCO (Hoffman et al.) PATCHES? LSCO (Yamada et al.) STRIPES? Switch to phenomenology for underdoped region Ca2-x Nax Cu O2 Cl2 Hanaguri et al. TILES? Large clusters and computational methods needed.
Lessons from Models for High Tc Superconductivity Sorella et al., PRL 88, 117002 (2002) Hubbard and t-j computational investigations are reaching the limits of what can be done. Fortunately, dominant tendencies in t-j model have been identified. SC appears in t-j simulations due to short-range AF, as in 2-leg ladders However, other studies show stripes: Several phases in competition. Haas et al. PRB51, 5989 (95): CDW states can be Stabilized. Third state? J/t
A Spin-Fermion Model as a phenomenological model for HTSC t S=1/2 S=1/2 J t=1, 2D J~2 J =0.05 Charge DOF J Spin DOF A.M. et al., PRL 84, 2690 (2000); PRL 88, 187001 (2002) (S classical) H ( + + c ) i σc j σ + c j σ ci σ + J si Si + J Si S j = t,,,, ' i, j i i, j 1 1 + 2 ij D < i, j> Vi < i, j> ( ) ijc c + h. c. i j ij = ij i ij e ϕ
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., PRB71,014514(2005)). V=1-J/2 Two parameters: J and V. Tetracritical
Quenched disorder leads to clusters and T*, as in manganites. T* Highly inhomogeneous Coulombic centers, as in Sr++. Each provides 1h.
Cartoonish version of MC results Random orientation of the local SC phases in glassy underdoped region T* Manganites SC AF or CDW
SC clusters Theory vs Experiment arches in FS Quasiparticle dispersion in 20x20 cluster 60% AF and 40% d-wave SC. Alvarez et al. AF background sc AF Spin Glass region (no SC) Fujimori et al. ARPES Yoshida et al.
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
Giant proximity effect? Alvarez et al., PRB71, 014514 (2005) ``non-sc glass ext SC = 0 ``Inhomogeneous superconductors ext SC = 0.2 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 ρ1 ext SC i ( i, zˆ ) cos( ψ ) i i
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. Plenty of work to do! Are these truly new stable states? Calculations in Mn- and Cu-oxide contexts with more realistic models? Experimental confirmation?
High Tc Cuprates STM Gap Maps 560A x 560A Underdoped Bi-2212, Tc=79K Overdoped Bi-2212 Mixture of two different short-range electronic orders. Long-range characteristics of granular SC. SC domains ~3nm. Lang et al., Nature 02.
Evolution with Magnetic Field H=0.001 H=0.005 H=0.008 H=0.009 H=0.003 H=0.002 H=0.004 H=0.006 H=0.01 H=0.007 H = 0.001 0.1% of natural scale 0.001t~1 Tesla
New: Correlated disorder (Idea: each doped element distorts a finite region around) 3D alpha=3 16^3 J1-J2 Dc=3 for Alpha<2.5 64^3 cluster Random Field Ising Model with power-law correlated disorder 64^3 3D and 2D are now similar Spin up Spin down Insulator
Experimental phase diagrams with and without disorder Dramatic changes with and without disorder. CO phase affected the most. Tokura, Ueda, et al., 2002
New: CE-phase is sensitive to disorder X=0.5 FM-AF transition is first-order and ``bicritical looking. Disorder affects the CE phase strongly, similarly as in experiments (Aliaga et al., unpublished)
The Spin-Fermion Model t S=1/2 S=1/2 J t=1, 2D J~2 J =0.05 Charge DOF J Spin DOF H ( + + c ) i σ c j σ + c j σ ci σ + J si Si + J Si S j = t,,,, ' i, j i i, j
Snapshots 12x12, T=0.01t No phase separation No long-range coulomb!
See PRL84, 2690 (2000). Magnetic Correlations 8x8 Q max = ( π δ, π ) π π δ Cheong et al., PRL67, 1791 (1991). Yamada et al., PRB57, 6165 (1998). 0 π T=0.01t~50K T=0.05t~250K
Charge Correlations 8x8 Q = ( 2δ,0) max π T=0.01t T=0.05t 0 2δ π
Pseudogap Sato et al., PRL83, 2254 (1999). Similar as in manganites. A.M. et al., Science 283, 2034 (1999) and Dessau et al., PRL81, 192 (1998). 8x8 <n>~0.85
Pairing Correlations For similar results on the t-j model see Sorella et al., PRL88, 117002 (2002). P( 6) 0.1 K SC = 500 exp 300K sc 12x12 T=0.01t
nop 0.75 T c 0.02 0.04t 150K
Optical Conductivity 12x12 T=0.01t Perp. to stripes Par. to stripes
Doping Dependence 12x12 T=0.01
Temperature Dependence 1/ω
1/D shows linear behavior above Tc. Optimal Doping
Underdoped and Overdoped <n>=0.875 T 1.5 <n>=0.68 Linear above T*
Conclusions Experimental and theoretical work agree that nanoscale phase separation is present in CMR materials. Two mechanisms for phase separation : electronic or disorder-induced near first-order transitions. A state with preformed FM clusters has a CMR effect. A scale T* > Tc is predicted for cluster formation. Similar results for some high-tc compounds as well. Self-generation of inhomogeneities appears to be a phenomenon far more frequent than previously believed! And it has highly nontrivial consequences (CMR, T*, PG, ).
Conclusions PS, FM and CO/OO dominate the phase diagram for manganites. Several experiments suggest mixed-states in agreement with our calculations. Disorder enhanced inhomogeneous states generate CMR. Inhomogeneity may also play a role in high Tc superconductivity.
Possible theories of CMR This talk
New: CMR at low-t even in clean-limit, due to first-order transition FM-CO CE H=0.0 CE-phase H=0.0 T H=0.025 FM FM phase ~100 K H=0.05~50T FM CE g H=0.05 Aliaga et al., x=0.5 Technique: lead-cluster-lead
Structure of the Manganites ( La, Sr) MnO4 2 ( La, Sr) Mn2O7 3 ( La, Sr) MnO3 Moritomo et al., Nature 380, 141 (1996). ( R, D) Mn O n 3 + 1 n+ 1 n
Ionic arrangement in the perovskite structure
Stripes and pseudogap in the spin-fermion model
Disorder caused by doping in Manganites
Numerical evidence of cluster coexistence
Disorder effects metal insulator large clusters equal density disorder-induced phase separation
Percolative metallic path across an insulating sample
3D example
Extended Phase Diagram at x=0.45 Tomioka et al.
Phase Diagram
Pseudogap
Temperature dependence of the Elastic and quasielastic intensity at the momentum corresponding to the CE clusters. Argyriou et al.
Experimental Test of Predictions T*>Tc Weak disorder Tomioka et al. Strong disorder De Teresa et al. Argyriou et al.
Three active degrees of freedom: Charge Spin Orbital Antiferromagnetic, staggered orbitals staggered charge.
Collaborators and Areas of Research G. Alvarez (FSU) J. Burgy (FSU) E. Dagotto (FSU) A. Feiguin (Argentina) T. Hotta (Japan) M. Mayr (Germany) J. Verges (Spain) S. Yunoki (Italy) Quasi 1D Nanostructures Transition Oxides Diluted Magnetic Semiconductors
The Lattice Kondo Model 1 orbital approximation H ( + + c ) i σ c j σ + c j σ ci J H si Si + J AF Si S j = t,,,, σ i, j i i, j Models with two orbitals and electronphonon couplings need to be considered to study orbital degrees of freedom.