Transcript Studying Manganites, Cuprates and Heavy Fermions with the

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)
Common theme emerging:
Clustered states and dramatic effects as a
result of small perturbations (complexity)
(I)
CMR manganites:
PI
CE-type
Spin, charge,
orbital order
FM
metal
Potential application in
“read sensors”?
Rich phase diagram, several states
competing. Common feature of many
Strongly Correlated Electronic systems.
Phase Competition in the Presence
of Quenched Disorder
T
Clean limit result:
CO
FM
W
T
FM CO
T*
T
FMStripes
W
CO
FM
SG
First order or
tetracritical
Toy Model with disorder
Burgy et al., PRL87, 277202
(2001). See also Nagaosa et al.
See also
Akahoshi et al.
PRL 2003;
Argyriou et al.,
PRL; De Teresa
W
CMR effect due to inhomogeneous
states
H=0
Rotates easily
Tc
H=0.01
T*
Field is small,
but effective
spin is large!
MR ratios as large as 1000% at H=0.01.
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
A similar picture
will emerge in our
high Tc analysis.
Field=0
Field>0
FM regions
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?
LSCO (Yamada et al.)
STRIPES?
Hanaguri et al.
TILES?
BiSCO (Hoffman et al.)
PATCHES?
Ca2-x Nax Cu O2 Cl2
Switch to phenomenology
for underdoped region …
Large clusters and computational methods needed.
Homes et al.,
Cond-mat/0410719
Homes’ Law
• 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
J
S=1/2 J’
S=1/2
Charge DOF
Spin DOF
t=1, 2D
J~2
J’=0.05
A.M. et al., PRL 84, 2690 (2000); PRL 88, 187001 (2002) (S classical)


H  t  ci, c j ,  c j , ci ,  J  si  Si  J '  Si  S j
i, j

i

1
1
  |  ij |2    ij ci c j   h.c.
D i , j Vi
i , j 
i, j
 ij |  ij | e
iij
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.
Tetracritical
V=1-J/2
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
Spin Glass region (no SC)
ARPES
Yoshida
et al.
AF
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 extSC  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’’
ˆ  |  i | cos i 
| ext
SC |  1 i, z
i
See Y. Yildirim and A.M. cond-mat/0503292
Adiabatic Phonons
Half-Breathing
along x Q
( 3)
Half-Breathing
along y
Breathing
Q (1)
Q ( 4)
Qi(1)   ui ,   ui   , 

Shear
Q ( 2)
Hamiltonian for Phonons
Diagonal Coupling :
H
( j)
e  ph
   Q
( j)
i
ni
i
Off-Diagonal Coupling :
ti , j  t   [u (i)  u ( j )]
u (i)  ui , x  ui  x , x  ui , y  ui  y , y
Stiffness :
H ph    [ui ,  ]2
i ,
J 'i , j  J ' '[u (i)  u ( j )]
Diagonal Term
Shear mode
 0
2
Stripes become more localized
 1
Diagonal Term
Breathing mode
Shear mode
2
Half-Breathing mode
Off-Diagonal Term
 0
  0.2
The stripes become more dynamic
  0.1
  0.6
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
A.M. and J. Riera (in preparation)
Phonons stabilize tiles and stripes
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)
E. Dagotto (UT/ORNL)
T. Hotta (Tokai)
J. Riera (Argentina)
C. Sen (FSU)
M. Mayr (Stuttgart)
S. Yunoki (Trieste)
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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