From phenomenology to microscopic manybody theory in Pr skutterudites Y. Kuramoto Dpt. Phys., Tohoku

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From phenomenology to microscopic many-body
theory in Pr skutteruditesY. Kuramoto Dpt.
Phys., Tohoku Universitywith J. Ohtsuki (MC2)
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Drawn by H. Harima (2002)
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Why skutterudites?

• Diverse physical phenomena within the same
  crystal structure
• Unconventional superconductivity
• Metal-insulator transition
• Multipole order
• Kondo effect
• Unique crystal structure
• Nearly spherical arrangement of ligands
• Strong hybridization effects even for RPr, Nd,
• Loose cage of pnictogen gt rattling motion of R

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PrT4X12 (TFe, Ru, Os X P, As, Sb)
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H. Sato et al. J. Phys. Condens. Matter 15
(2003) S2063S2070
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H. Sato et al. J. Magn. and Magn. Mater. 258-259
(2003) 67
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Y. Aoki et al. Phys. Rev. B65, 064446 (2002)
PrFe4P12
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• T lt TA Sharp excitations
• T gt TA Quasielastic-like
• Strong hybridization in the HF phase above TA.

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PrOs4Sb12E.D. Bauer et al. Phys. Rev. B65,
100506R (2002)H. Kohgi et al. J.Phys.Soc.Jpn
72, 1002(2003)
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Neutron scattering of PrOs4Sb12
B
A
A
G4(2) (8K)
B
Kohgi et al. (2003)
Goremychkin et al. cond-mat/0404519
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PrRu4P12K. Matsuhira et al. Physica B 312-313
(2002) 829
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Neutron scattering of PrRu4P12 (Iwasa et al,
2004)
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Toward microscopic theory

• What are relevant parameters that control
  interactions between 4f electrons and
  environment?
• to be or not to be heavy
• types of electronic order
• CEF level structures (single-site theory)
• point charge energy
• p-f hybridization energy
• Temperature dependent CEF?

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J4 CEF levels in Oh and Th
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Point charge energy for CEF states
negative charge
Pr skutterudite Wx gt 0 ground state ?1
PrB6 Wx lt 0 ground state ?5
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Phenomenological Hamiltonian

• Lea, Leask, Wolf (1962)
• Takegahara, Harima, Yanase (2001)

J4 (Pr3)
y? 0 ) without four-fold rotation axis
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PrOs4Sb12
Point Charge Model
Neutron scatt.
G23 (205K)
G4(1) (135K)
G4(2) (8K)
G1
Kohgi et al.(2003)
Cf. H.Harima and K.Takegahara (2002)
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Hybridization of 4f and p electrons

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Pnictogen p molecular orbitals
au
(a)
tu
(b)
(d)
(e)
(c)
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Slater-Koster parametrization
hyb. parameter
Takegahara et al.(1980) Slater-Koster table
for f electrons
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Many-body matrix elements
Hybridization process
H.Takahashi and T.Kasuya (1985) Rare-earth
Pnictides C.W.Nielson and G.F.Koster (1963)
c.f.p. table
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Contrasting effects of f1 and f3
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Simplified model
tu(1)

• Taking only the au orbital near ?
• half filling for au

tu(2)
au
D3/D1 controlling relative importance of f 1
and f 3
m
tu(3)
Consistency with exp. results ) ?3/ ?1 lt1 is
likely.
tu(4)
Rare-Earth Pnictides
tu(5)
Franciosi et al.(1981),Lang et al.(1981), Martenss
on et al.(1982)
H.Harima and K.Takegahara (2003)
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Combined action of Coulomb and hybridization?
Point Charge (T 2, X-0.92)
Exp.
Hybridization
G23 (205K)
G4(2) (127K)
G1 , G23 , G4(1)
G4(1) (135K)

G23 (44K)
G4(2) (8K)
G4(1) (26K)
G1
G4(2)
G1
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Hyb. Point Charge
point charge only
Point Charge T 2 , X -0.92
hyb. au only
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Origin of narrow CEF splittings

• Point charge potential from positive transition
  ions and negative pnictogens
• ?1 singlet favored
• Hybridization between 4f and p electrons
• Anisotropic 4f states such as ?4(2) favored
• Competition between point charge and
  hybridization (material dependent!)
• narrow CEF splittings between ?1 and ?4(2)

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Hybridization gtEffective exchange

• Hybridization with pnictogen p states
• au symmetry near the Fermi level
• neglect of multiplet splitting of f 1, f 3

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Effective Hamiltonian for the quasi-quartet
Triplet states under Th (m0,)
Exchange interaction for the quasi-quartet
pseudo-spin S1, S2 R. Shiina JPSJ 73 (2004)
2257
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Resolvent method for dynamical response functions
NCA (Kuramoto 1983) Cf. Self-consistent ladder
app. (Maekawa et al 1985)
Green function gt Afms, B fmsy
? (w) gt AM, B M
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NCA for exchange models

• Ground state E(f2 singlet) 2? f
• Excited state E(f2 triplet) 2? f ? CEF
• Fictitious high-energy states to simulate J
• E(f1) ? f-U, U) 1 , V2/U finite
• Self-energy of each resolvent R?(z)

?
f1 K?(z-?)
f2 R?(z)
f2 R?(z)
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Resistivity in the CEF pseudo-quartet model by
the NCA
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Dynamical magnetic susceptibility
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Inelastic neutron scattering spectrum(
PrOs4Sb12?)
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Resistivity (PrOs4Sb12?)
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Inelastic neutron scattering spectrum(PrFe4P12?)
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Resistivity (PrFe4P12?)
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Summary

• Delicate balance between
• (1) f1 and f3 intermediate states,
• (2) Hybridization and ionic Coulomb interactions
• gt
• Quasi-quartet of CEF states
• Material-specific properties
• f-electron dynamics
• Kondo effects depend on CEF wave functions!
• Intersite interactions?

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Lea-Leask-Wolf diagram
PrB6
Skutterudite?
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Case of large y (1)
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Entropy of f2 Kondo systems
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Neutron scattering on PrFe4P12(Iwasa et al 2003)
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Neutron scattering spectrum
?1-?4(2)- ?4(1) ? Pr A and B? ?23 ?
K. Iwasa et al (2003)
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Density of states of 4f electrons (by J. Otsuki)
100 K 50 K 20 K 5 K
? f -1200 K, V2?c 120 K, D104 K ) TK 67 K
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?4f near the Fermi level
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?4f with various values of I at T 1K