Transcript Level Splitting in Frustrated non

Inhomogeneous Level
Splitting in PrxBi2-xRu2O7
Collin Broholm and Joost van Duijn
Department of Physics and Astronomy
Johns Hopkins University
Collaborators
Ruthenium pyrochlores
K. H. Kim
N. Hur
D. Adroja
Q. Huang
S.-W. Cheong
T. G. Perring
Rutgers
Rutgers
ISIS
NIST
Rutgers
ISIS
Iridium pyrochlores
Satoru Nakatsuji
Yo Machida
Yoshiteru Maeno
Toshiro Sakakibara
Takashi Tayama
3/12/04
Kyoto
Kyoto
Kyoto
ISSP
ISSP
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Outline
 Introduction
 Bulk properties of 4dn and 5dn pyrochlores
 Spin correlations on TM sites
 Crystal field excitations on RE sites
 Level splitting in PrxBi2-xRu2O7
 Ground state doublet spin dynamics
 Model of inhomogeneous level splitting
 Discussion and Conclusions
 Possible relevance for other non-Kramers
doublet systems
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The pyrochlore structure A2B2O7


Aand BJsites
Si  Son
j
vertices
of cornerij
sharing tetrahedra
2
1
J trivalent
S  cst
3+ 2site is
 A
RE with 8-fold O2coordination
Nearest neighbor exchange selects
a
manifold
states
by
B4+ of
site
is characterized
tetravalent
Zero-spin tetrahedra
TM with 6-fold O2coordination
 Can have both A3+
and B4+ magnetism

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B=Ru site magnetism of Y2Ru2O7
Taira et al. (2000)
Taira et al. (1999)
□ Neutron Diffraction reveals long range magnetic order
□ ZFC/FC hysteresis suggests some form of disorder that produces
glassy canted AFM
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“Strong Coupling” Transition in Y2Ru2O7
T=90
T=1.5KK
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PM and AFM Spin Fluctuations
1.5 K
1.5 K
90 K
90 K
□ Phase Transition pushes significant spectral weight into “resonance”
□ The Q-dependence of scattering reflects the form factor for AFM
cluster degrees of freedom
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2 Magnetic Ions
2 Phase Transitions
R2Ru2O7
Er2Ru2O7
M. Ito et al. (2001)
Pr3+
Yb3+
N. Taira et al. (2003)
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Metal Insulator Transition
 Bi-doping increase
bandwidth causing
Mott Hubbard MIT
 Magnet order is
found only in the
insulating state
 Electronic DOS at
EF is enhanced
close to the MIT
Yoshii and Sato (1999)
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A Highly Entropic Metallic State
2.0
PrxBi2-xRu2O7
C/T (J/mol K )
1.6
x=2.0
1.4
3K
4K
4
C (J/mol K)
1.8
2
5
3
2
1
1.2
1.5
0
0.0
1.0
1.0
1.2
0.8
0.5
1.0
1.5
2.0
Pr (x)
Y2Ru2O7
0.6
0.9
0.4
0.4
0.2
0.0
0.0
0
20
40
60
2
T (K)
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80
100
K. H. Kim et al.
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Praseodymium Crystal Field levels:
116 meV
5K
Pr1.2Bi0.8Ru2O7
105 meV
85 meV
50 meV
200 K
10 meV
0
Five transitions from GS implies it is doublet:
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GS   4   4  
1
11
Fluctuations in metallic Pr1.2Bi0.8Ru2O7
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Inhomogeneous Level Splitting
 Broad Spectrum unchanged
Upon heating to kBT

 Wave vector dependence
Follows Pr form factor2
Neutron Scattering measures
the level splitting spectrum
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Inhomogeneous two level system
 The level distribution function:
 Singlet-singlet susceptibility:
  
1  e 
       g B             
1  e   e  / 2 Z    
2
 Sample averaged susceptibility

 ( )    ( )    d     g B 
0
2
1  e 
 (|  |)
1  e   e  / 2 Z    
 Fluctuation-dissipation theorem yields
  
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 
  / 2
S

1

e

e
Z    



2
1

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Data Collapse Confirms “quenched broadening”
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C(T)/T (J/mole-f.u./K2)
C(T)/T (J/mole-f.u./K2)
Specific heat of ()-split doublet
exp   2 exp    H z 
d H 2
d
C T ,HkB kB         H z   2 d 
2
4
1  exp  1  exp    H z 
0 0
 

  Hz  
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
2
2
g


H


 B z
2
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Susceptibility of ()-split doublet
For gapless spectrum low
T limiting form is ~lnT
  T   2  g B 

2

0
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 
1  e  
d
 
  / 2
 1 e  e
Z  
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Clues to origins of level splitting
 T-independent distribution function 
⇒ Static not dynamic phenomenon
 Continuous not discrete spectrum
⇒ Large rare defect or density wave producing
distribution of environments
 Same distribution describes all x<1.2
⇒ Distribution may not come from Bi doping
 Magnetic field enters in quadrature
⇒ Electrostatic not magnetostatic inhomogeneity
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Where else might this occur?
 Elements that can have non-Kramers
doublet ground states:
Pr3+ , Pm3+, Sm2+, Eu3+, Tb3+, Ho3+,
Tm3+, Yb2+, and U4+
 Nominally cubic and stoichiometric
systems may have clandestine level
splitting disorder
 Doping effects may be controlled by the
induced level splitting
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Other Materials to Reconsider
 Tb2Ti2O7: A non ordering magnet with
mysterious low energy mode
 Ho2Ti2O7: Long range ordered with unusual
thermodynamics
 YbBiPt: Ultra heavy fermion system with
mysterious low E mode (Robinson et al
(1995).
 LiHoxY1-xF4 quantum spin glass. Strain
induced level splitting adds an effective
transverse field
 TbxY2-xTi2O7: Dilution has added effect of
neutralizing Tb through level splitting
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Metal insulator transition in R2Ir2O7
Yanagishima and Maeno (2001)
Nakatsuji et al.
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Conclusions
 Ir and Ru pyrochlores offer MIT transitions
with frustrated magnetism
 Y2Ru2O7 : “strong coupling” transition
 Spectral weight pushed to finite E resonance
 Q-dependence unaffected by ordering
 PrxBi2-xRu2O7 : static inhomogeneous
distribution of level splittings
 Neutrons: “T-independent” broad spectrum
 C(T)/T: broadened Schottky anomaly
 (T): possible logarithmic divergence at low T
 Watch out for level splitting in non-Kramers
ions, which are “not really magnets”
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