Strongly correlated electron phenomena in filled skutterudites in - - PowerPoint PPT Presentation

Strongly correlated electron phenomena in filled skutterudites in filled skutterudites

• M. Brian Maple

University of California, San Diego

Workshop on Properties and Applications of Thermoelectric Materials, Hvar, September, 2008

Crystal structure of the filled skutterudites

• Filled skutterudites: MT X

(M = alkali metal alkaline earth rare earth actinide;

• Filled skutterudites: MT4X12 (M = alkali metal, alkaline earth, rare earth, actinide;

T = Fe, Ru, Os; X = P, As, Sb) (T = Pt, X = Ge; Dresden, Vienna)

• Binary skutterudites: TX3 (T = Co, Rh, Ir; X = P, As, Sb)

P t t C A Di d i Sk tt d N Prototype CoAs3: Discovered in Skutterud, Norway

• Cubic structure, Th symmetry
• T cations (Os)

sc sublattice

• T cations (Os) – sc sublattice
• X anions (Sb) – distorted corner sharing
• ctahedra centered by T cation
• M cations (Pr) – bcc sublattice

“Fill” atomic cages formed by X anions bcc structure (Im-3) a = 9 3068 Å a = 9.3068 Å

• W. Jeitschko & D. J. Braun, 77

PrOs4Sb12

Crystal structure of the filled skutterudites

After T. Yanagisawa (08)

• Many striking properties of filled skutterudites associated with M “filler ions”

Filled skutterudites

• Many striking properties of filled skutterudites associated with M filler ions

and the X atomic cages within which they reside – “Tunneling” and “rattling” of M “filler ions” in oversize X atomic cages “Rattling” of M “filler ions” can scatter phonons and reduce lattice contribution to the thermal conductivity κl Increases thermoelectric figure of merit g ZT = S2/(κe+κl)ρ ZT ~ 1.2 at T ~ 800 K (e.g., CeFe4-xCoxSb12) – Localized f-electron states of Ln and Ac ions hybridize with ligand states

• f 12 n.n. X ions

Large negative intra-atomic exchange interaction ⇒ “Kondo” physics g g g p y Admixture of fn and fn-1 configurations ⇒ “valence fluctuation” physics Can produce large value of S and, in turn, ZT

• Interplay between charge, spin, orbital, lattice degrees of freedom

– Competing interactions — readily “tuned” – “Knobs”: Chemical substitution pressure magnetic field Knobs : Chemical substitution, pressure, magnetic field – Wide variety of strongly correlated electron phenomena

Thermoelectric figure of merit of novel materials

After Tritt et al. 08

Filled skutterudites: correlated electron phenomena

• Conventional (BCS) superconductivity: e.g., LaFe4P12, PrRu4Sb12, PrRu4As12
• Unconventional superconductivity (spin triplet?): e.g., PrOs4Sb12
• Heavy fermion behavior: e.g., PrFe4P12, PrOs4Sb12, PrOs4As12
• Non-Fermi liquid behavior (QCP): e.g., CeRu4Sb12, CeRu4As12, PrFe4Sb12
• Ferromagnetic order (local moment): e.g., PrFe4As12, NdFe4Sb12, NdOs4Sb12
• Ferromagnetic order (itinerant): e.g., LaFe4As12, LiFe4Sb12, NaFe4Sb12
• Antiferromagnetic order: e.g., PrOs4As12
• Spin fluctuations: e.g., BaFe4Sb12, CaFe4Sb12, SrFe4Sb12

Spin fluctuations: e.g., BaFe4Sb12, CaFe4Sb12, SrFe4Sb12

• Antiferroquadrupolar order: e.g., PrFe4P12, PrOs4Sb12
• Hybridization gap semiconductivity (Kondo insulator behavior): e g

CeFe P

• Hybridization gap semiconductivity (Kondo insulator behavior): e.g., CeFe4P12,

CeOs4Sb12, CeOs4As12

• Metal-insulator transitions: e.g., PrRu4P12

g

4 12

Filled skutterudite arsenide & antimonide single crystals

NdOs4Sb12 (UCSD) “cubes” and

NdOs4Sb12

“rectangular parallelepipeds” PrOs As (ILTSR Wroclaw) PrOs4As12 (ILTSR, Wroclaw) “truncated octahra” Zygmunt Henkie

5 mm

PrOs4As12

“Skutterudite”

National Museum Washington D C

Skutterudite (CoAs3)

Washington, D.C.

1 mm

This talk Correlated electron behavior in La Ce and Pr based filled skutterudite

• Correlated electron behavior in La, Ce, and Pr-based filled skutterudite

compounds (particularly, arsenides and antimonides)

• La and Ce-based filled skutturudite compounds

p

• Pr-based filled skutterudite compounds

– Brief review of heavy fermion (HF) behavior & unconventional y ( ) superconductivity (SC) in PrOs4Sb12 – Experiments on pseudoternary systems Pr(Os1-xRux)4Sb12 & P Nd O Sb & Pr1-xNdxOs4Sb12 Insight into HF state & unconventional SC in PrOs4Sb12 HF b h i d tif ti (AFM) d t t i P O A – HF behavior and antiferromagnetic (AFM) ground state in PrOs4As12 – Comparison with correlated electron ground states of other PrT4X12 compounds compounds

• Overview — progress report on very active research area on worldwide

scale (Europe, Japan, North America, . . )

• More questions than answers, at this juncture!

University of California, San Diego E D Bauer LANL

Acknowledgements

Kobe University H Harima

• E. D. Bauer

LANL

• R. E. Baumbach
• N. P. Butch
• U. Maryland
• N. A. Frederick
• IPA. Inc.
• J. R. Jeffries

LLNL

• H. Harima

University of Waterloo, Canada

• R. W. Hill
• S. Rahimi

Université de Sherbrooke P.-C. Ho CSU, Fresno

• S. K. Kim

ISU, Ames

• J. Paglione
• U. Maryland
• T. A. Sayles

SOM, UCSD

• L. Shu

Université de Sherbrooke

• S. Li
• L. Taillefer

University of Tennessee & Oak Ridge National Laboratory

• L. Shu
• B. J. Taylor
• T. Yanagisawa

Hokkaido U

• W. M. Yuhasz

ISU, Ames

• V. S. Zapf

NHMFL, LANL I tit t f L T t & St t Laboratory

• T. Barnes

Songxue Chi Pengcheng Dai

• F. Ye

Institute of Low Temperature & Structure Research, Polish Academy of Sciences, Wroclaw

• T. Cichorek
• Z. Henkie
• A. Pietraszko

National Institute of Standards & Technology

• H. J. Kang
• J. W. Lynn

Rutherford Appleton Laboratory

• A. Pietraszko
• R. Wawryk

Niigata University

• T. Goto
• Y. Nemoto
• R. Bewley

Lawrence Livermore National Laboratory

• M. Fluss
• S. K. McCall

M W M Elf h

• H. Watanabe

Los Alamos National Laboratory

• J. B. Betts
• P. A. Goddard

A L d

• M. W. McElfresh
• U. Toronto
• C. S. Turel
• J. T. Wei

MPI Ch i l Ph i D d

• A. Lacerda
• J. Singleton

Research supported by US DOE and NSF

MPI Chemical Physics, Dresden A.C. Mota

• F. Steglich

La and Ce-based filled skutterudites

Correlated electron ground states in La filled skutterudites

LaT4X12

• Most La filled skutterudites are

superconducting – Highest T

c’s for T = Ru, X = As

– LaRu4As12: T

c = 10.3 K

E ti

T

• Exceptions

– LaFe4As12 Weak FM (θC = 5 2 K) Weak FM (θC 5.2 K) – LaFe4Sb12 Spin fluctuations (T

sf ~ 50 K)

X

sf

• Reflects tendency of Fe to form

local moments in LnFe4X12 Oft f X Sb

X

– Often for X = Sb – Occasionally for X = As – Rarely for X = P Rarely for X P

Weak ferromagnetism in LaFe4As12 P l t l θ 5 K Polycrystal – θC ≈ 5 K

• S. Tatsuoka et al., JPSJ (08)

Weak ferromagnetism in LaFe4As12 Single crystals – ILTSR, Wroclaw; UCSD; θC ≈ 5 K

Weak ferromagnetism in LaFe4As12 Polycrystal – θC ≈ 5 K

• S. Tatsuoka et al., JPSJ (08)

Correlated electron ground states in Ce filled skutterudites

CeT4X12 T

• Most are small gap semicon-

ductors (“Hybridization gap semiconductors” or “Kondo semiconductors or Kondo insulators”)

• First examples discovered in 1985

at UCSD: CeFe4P12, UFe4P12

X

at UCSD: CeFe4P12, UFe4P12 ∆ decreases with increasing a

• A few exhibit NFL behavior

– Suggests near QCP,

X

gg , possibly associated with valence or M-I transition

Unit cell volume Va vs Ln ion for LnT4X12 compounds

3 Depression of Va for Ce: VCe ≈ 3+: Kondo volume collapse VCe > 3+: valence fluctuations T l d i t f 4f0 d 4f1 vCe ≈ 3+ Temporal admixture of 4f0 and 4f1 Hybridization (Hyb) of localized f- vC > 3+

F R O

& conduction-electron states increases with decreasing Va vCe > 3+

Fe Ru Os P

Hyb Hyb

As

Va Va

Sb

• D. J. Braun & W. Jeitschko 80

Electrical resistivity of Ce filled skutterudites

Energy gap ∆ vs lattice constant a ∆ decreases with decreasing hybridization (increasing a) hybridization (increasing a)

• “hybridization gap semiconductors”

Magnetic susceptibility of Ce filled skutterudites

Magnetoresistivity of CeOs4As12

3

Intrinsic gap:

ρ-1(T,H) = ΣAiexp(-∆i/kBT)

i=1

(eqn. 3)

g p ∆1 = 73 K Donor, acceptor states in gap: ∆2 = 16 K ∆3 = 2.5 K

H(T)

• a. - 0
• b. - 0.3

c - 0 5

• c. - 0.5
• d. - 0.7
• e. - 1.0
• f. - 1.5
• g. - 2.0

h 3 0

• h. - 3.0
• i. - 5.0
• j. - 7.0
• k. - 9.0

Baumbach et al. 08

C(T) and χ(T) of CeOs4As12

χ(T) = χ0 + Cimp/(T - θ) χ0 ≈ 1.1 x 10-3 cm3/mol

• C(T)/T = γ + βT2

θ = 270 K χ0 1.1 x 10 cm /mol Cimp = 3.12 x 10-3 cm3/mol θ = -3 K θD = 270 K γ ≈ 12 mJ/mol K2 (H = 0) Wilson-Sommerfeld ratio: cimp ≈ 0.4% Ce3+ (µeff = 2.54µB)

• RW = (π2kB

2/3µeff 2)(χ0/γ) ≈ 1.1

• R. E. Baumbach et al., 08

Thermoelectric power of CeOs4As12

• R. E. Baumbach et al., 08

Non-Fermi liquid (NFL) behavior in CeRu4As12

ρ ~ T1.4

• R. E. Baumbach et al., 07

Non-Fermi liquid (NFL) behavior in CeRu4As12 NFL behavior NFL behavior ρ(T) ~ T1.4 C(T)/T ~ lnT C(T)/T ~ -lnT χ(T) ~ -lnT FL behavior ρ(T) ~ T2 C(T)/T ~ const χ(T) ~ const

• R. E. Baumbach et al., 07

Thermoelectric power of CeRu4As12

• R. E. Baumbach et al., 07

Pr-based filled skutterudites

PrOs4Sb12

• 1st Pr-based heavy fermion superconductor (Tc = 1.85 K) (Others based on Ce, U)

Why PrOs4Sb12 is interesting

1 Pr based heavy fermion superconductor (Tc 1.85 K) (Others based on Ce, U) Bauer, Frederick, Ho, Zapf, Maple, PRB (02)

• Nonmagnetic heavy Fermi liquid (m* ≈ 50 me)

U ti l t li d ti it id f

• Unconventional strong coupling superconductivity – evidence for:

– Several distinct SCing phases – Point nodes in energy gap ∆(k) – Izawa et al., JPSJ (03); gy g ( ) ( ) Chia et al., PRB (03) – Time reversal symmetry breaking – Aoki et al., PRL (03)

• Possible candidate for triplet spin superconductivity
• Possible candidate for triplet spin superconductivity
• High field ordered phase (HFOP): ρ(H,T) – Maple et al., JPSJ (02);

Ho et al., PRB (03); C(H,T) – Aoki et al., JPSJ (02); Vollmer et al., PRL (03);……. HFOP id tifi d ith tif d l d b d

• HFOP identified with antiferroquadrupolar order, based on

neutron diffraction at high H: Kohgi et al., JPSJ (03)

• SC appears to be near quadrupolar quantum critical point (QCP)
• Formation of heavy Fermi liquid &/or unconventional SCing state may involve

electric quadrupole, rather than magnetic dipole, fluctuations (Ce, U)

• Off-center rattling & tunneling – Goto et al., PRB (04); Cao et al., PRB (03)

Off center rattling & tunneling Goto et al., PRB (04); Cao et al., PRB (03)

• Multiband superconductivity – Seyfarth et al., PRL (05)

H–T phase diagram of PrOs4Sb12

QCP HFOP

• T. Yanagasawa (06)

HFOP

• Related to crossover of

CEF energy levels

• Identified with antiferro-

QCP Identified with antiferro- quadrupolar order: neutron diffraction Kohgi et al., JPSJ (03) QCP

• Anisotropic phase

boundary: M(H,T) Tayama et al., JPSJ (03)

• SC in vicinity of antiferro

Ho et al., PRB (03)

• SC in vicinity of antiferro-

quadrupolar QCP!

Low temperature specific heat of PrOs4Sb12

Superconducting state:

• Analyses of ∆C & dHc2/dT

at T

c confirm large value of

Normal state: C(T) = γT + βT3 + CSch(T) γ ≈ 500 mJ/mol K2, θD ≈ 200 K,

c

g γ derived from C(T) in normal state

• Structure in C(T) near T

c ⇒

γ ,

D

, Γ1 singlet g.s., Γ5 triplet 1st e.s., ∆ ≈ 7 K CSch(T) scaled by 0.56 50% t d ti l t S uc u e C( ) ea

c ⇒

two SCing phases? T

c1 ≈ 1.85 K, T c2 ≈ 1.70 K

• Single SCing transition at:

⇒ ~50% entropy → conduction electrons

• Single SCing transition at:

T

c2 – mechanical thinning

Seyfarth et al., PRL (06)

T

c1 – La or Ru substitution

Rotundu et al. PRB (04); Frederick et al. PRB (05)

S btl t t l ff t? Subtle structural effect?

Bauer, Frederick, Ho, Z f M l PRB (02) Zapf, Maple, PRB (02); Maple et al., JPSJ (02)

Pr3+ energy levels in CEF of PrOs4Sb12

• 9-fold degeneracy of Pr3+ J = 4 multiplet is lifted by CEF

INS t G hki t l PRL (04) 9 fold degeneracy of Pr J 4 multiplet is lifted by CEF

• CEF – tetrahedral Th symmetry (no 4-fold axis)
• Our CEF analyses – cubic Oh symmetry (simpler, adequate)
• INS measurements Goremychkin et al.,PRL (04)

Pr3+ energy levels: Γ3 nonmagnetic doublet (~200 K) Γ3 nonmagnetic doublet ( 200 K) Γ4 triplet (~130 K) Γ5 triplet (~7 K) Γ singlet (0 K) Γ1 singlet (0 K)

• Confirms previous evidence for Γ1 singlet ground state:

C(H,T) – Aoki et al., JPSJ (03), Rotundu et al., PRL (04)

• Magnetic & quadrupolar excitations within Γ1- Γ5 two level system presumably

M(H,T) – Tayama et al., JPSJ (03) Neutron diffraction at high H – Kohgi et al., JPSJ (03) g q p

1 5

y p y involved in formation of HF state &/or unconventional SC in PrOs4Sb12; Two possible scenarios: [based on theories by Fulde et al. (70, 78)] (1) exchange scattering → enhancement of m* (e.g., Pr metal: m* ≈ 4 me) ( ) g g ( g ,

e)

(2) aspherical Coulomb scattering → increase of electron pairing interaction (3) other more exotic mechanisms?

CEF fits to C(T), χ(T) & ρ(T) for PrOs4Sb12 Pr3+ energy levels in CEF Pr energy levels in CEF INS measurements

Goremychkin et al., PRL (04)

RRR ≈ 80

Γ3 doublet (~200 K) Γ4 triplet (~130 K) Γ triplet (~7 K) Γ5 triplet ( 7 K) Γ1 singlet (0 K)

PrOs4Sb12: Possible superconducting phase diagram

Zero magnetic field T

c1 = 1.85 K, T c2 =1.70 K

C(T):

M l t l 02 Maple et al., 02 Vollmer et al., 02 Aoki et al., 02

α(T): ( )

Oeschler et al., 04

λ(T):

Broun et al., 03 Chi t l 03

T*(H)

Chia et al., 03

T

c3 ≈ 0.6 K

Hc1(T), Ic(T):

Cichorek et al., 05

T

c3

T

c2T c1

Cichorek et al., 05

Finite magnetic field T

c1(H), T c2(H)

C(H,T), χac(H,T): ( , ), χac( , )

Measson et al., 04 (0.3 K) Grube et al., 06 (0.1 K)

T*(H)

Change in energy gap symmetry at T ≈ 0 6 K;

κ(H,φH,T):

Izawa et al., 03

Change in energy gap symmetry at T

c3 ≈ 0.6 K;

nodeless gap (T > T

c3), gap with point nodes (T < T c3)

PrOs4Sb12: Probing the superconducting energy gap symmetry

• Experimental evidence for both isotropic gap & gap with point nodes
• Isotropic:

λ(T) (µSR) (H = 200 Oe) MacLaughlin et al.,02 λ(T) (tunnel diode) Chia et al 03 05 (T > T ) λ(T) (tunnel diode) Chia et al., 03, 05 Sb-NQR Kotegawa et al., 03 Electron tunneling Suderow et al., 04 (T > T

c3)

ect o tu e g Sude o et a , 0

• Point nodes

C(T) Maple et al., 02 κ(H,φH,T) Izawa et al., 03 (T < T

c3)

λ(T) (tunnel diode) Chia et al., 03 Distortion of FLL Huxley et al., 04 κ(T) at low T Seyfarth et al., 06; Hill et al., 07 Andreev spectroscopy C. S. Turel et al., 07

• Change in energy gap symmetry at T

c3 ≈ 0.6 K; nodeless gap (T > T c3),

gap with point nodes (T < T

c3)

Sb NQR measurements on PrOs4Sb12

PrOs4Sb12 — Kotegawa et al., PRL (03) PrRu4Sb12 — Yogi et al., PRB (03)

PrRu4Sb12: Coherence peak T

1

( ∆/k T) T1

• 1 ~ exp(-∆/kBT)

2∆/kBT

c ≈ 3.1

Weak coupling BCS SC PrOs4Sb12: No coherence peak p T1

• 1 ~ exp(-∆/kBT); (T < 1.3 T

c)

2∆/kBT

c ≈ 5.3

Strong coupling unconventional Strong coupling unconventional SC

Low-T thermal conductivity of PrT4Sb12 (T = Os, Ru)

• Measurements of κ(T) to 40 mK

under same conditions for both PrOs4Sb12 and PrRu4Sb12 κ(T) described by relation: κ/T = κo/T + βT2

• Results consistent with

– Gap nodes for PrOs4Sb12 – Absence of gap nodes for Absence of gap nodes for PrRu4Sb12 (known BCS SC)

• Measurements on PrOs4Sb12 at

variance with those of Seyfarth et y

• al. (06) which yield isotropic gap

(thinned sample – one SCing transition at T

c2)

R W Hill et al 07

• Origin of T

c1 and T c2?

(SCing fraction at T

c1 grows with

increasing x to 1 at x ≈ 0.05 in Pr(Os Ru ) Sb system)

• R. W. Hill et al., 07

Pr(Os1-xRux)4Sb12 system)

Time-reversal symmetry breaking (TRSB) in PrOs4Sb12

Zero field µSR measurements A ki

t l 03 M L hli t l 05

• Zero field µSR measurements Aoki et al., 03; MacLaughlin et al., 05
• Small, spontaneous internal field in SCing state

Cooper pairs with nonzero spin and/or orbital moments i i

∆ idth f i t l

⇒ non-s-wave pairing

∆: width of internal field distribution Λ: relaxation rate in 0 field (ZF) and in 0.01 T ( )

• Y. Aoki et al., 03

Penetration depth λ(T) measurements on PrOs4Sb12

Tunnel diode oscillator technique: E E Chia et al

03

Tunnel diode oscillator technique: E. E. Chia et al., 03 Superfluid density: ρ (T) = [λ2(0)/λ2(T)] ρs(T) = [λ (0)/λ (T)] λ(T), ρs(T) ~ T2 (0.1 K – 0.55 K) ⇒ point nodes in energy gap Polar plots of gap functions

BCS nodeless

• pt. nodes

II, III: Maki et al., 03

T

c3

, , A, B: Ichioka et al., 03

Pr(Os Ru ) Sb & Pr Nd Os Sb Pr(Os1-xRux)4Sb12 & Pr1-xNdxOs4Sb12

Pr(Os1-xRux)4Sb12: Evolution of SCing & normal state properties with x

• PrOs4Sb12: Unconventional SC; heavy FL
• PrRu4Sb12: Conventional BCS SC; non-heavy FL: γ ~ γ(PrOs4Sb12)/10

P (O R ) Sb C titi b t ti l d BCS SC

• Pr(Os1-xRux)4Sb12: Competition between unconventional and BCS SC

9.31 9.30

Pr(Os1-xRux)4Sb12

9 28 9.29

a (Å)

9.27 9.28

Vegard’s law

9.26 0.2 0.4 0.6 0.8 1

x

• N. A. Frederick et al., PRB (03)

Pr(Os1-xRux)4Sb12: ∆Eg.s.-1e.s. vs x

• N. A. Frederick et al., PRB (04)

ρ(x,T), χ(x,T), C(x,T) measurements

Pr(Os1-xRux)4Sb12: Evolution of SCing & normal state properties with x

O S SC PrOs4Sb12: Unconventional SC; HF PrRu4Sb12: Conventional BCS SC; non-HF γ(PrRu4Sb12) ≈ γ(PrOs4Sb12)/10 λ(T) measurements

Chia et al., 05

T T ( ) T ( )

• T > T

char(x) ≡ T c3(x):

λ(T), ρs(T) ~ BCS ∆(k) ~ constant T T ( )

Nodeless

• Pt. nodes
• T < T

c3(x):

λ(T), ρs(T) ~ T2 ∆(k) → 0 at point nodes T ( ) t 0 3

• T

c3(x) → 0 at x ≈ 0.3

No TRSB at x = 0.1

• L. Shu et al., 06

∆C/T

c

Note: Hc2(0) ~ orbital Hc2(0)

P-C Ho et al 07 After N. A. Frederick et al., 04, 05; M. B. Maple et al., 06

• P. C. Ho et al, 07

Hc2 vs T for Pr(Os1-xRux)4Sb12

X ≤ 0 5 X ≥ 0 5 X ≤ 0.5 X ≥ 0.5 Sh f H (T) Shapes of Hc2(T) curves:

• x < ~0.5 – Conventional – convex (linear near T

c, zero slope near 0 K)

• x > ~0.5 – Anomalous – nearly linear

3

P.-C. Ho et al., 07

(possible mechanisms: T-dependent exchange scattering from Pr3+ CEF energy levels, two band superconductivity (e.g., MgB2))

Pr(Os1-xRux)4Sb12: High field ordered phase (HFOP) Hc2(0)

• HFOP no longer detectable by means of ρ(T)

measurements for x > ~0.1

• Correlates with changes in SCing state

P.-C. Ho et al., 07

Correlates with changes in SCing state

• Evidence for quadrupolar pairing mechanism?

Pr1-xNdxOs4Sb12: T – x phase diagram

• Pr

Nd Os Sb : Interplay between unconventional SC and FM order

• Pr1-xNdxOs4Sb12: Interplay between unconventional SC and FM order

– PrOs4Sb12: Unconventional (possibly, triplet spin) SC – NdOs4Sb12: FM order (θC ≈ 0.8 K)

P.-C. Ho et al., 05

xcr

Upper critical field Hc2(T) of Pr1-xNdxOs4Sb12

magnetic order

xcr T ~ 0 K

Hc2(0) P.-C. Ho et al., 07

PrOs4As12

PrOs4As12: H-T phase diagram

• Single crystals: Z.Henkie
• Kondo lattice:

TK ~ 1 K

• Heavy fermion behavior:

γ ~ 1 J/mol K2 γ ~ 1 J/mol-K2

• Two ordered phases:

AFM: Low H Unknown: High H (quadrupolar?) AFM structure: Alternating (100) AFM structure: Alternating (100) planes of FMicallyordered Pr µ’s,

• ppositely oriented with one

another

• W. M. Yuhasz et al., 06;
• M. B. Maple et al., 06

PrOs4As12: ρ(T,H)

ρ(T) minimum negative magnetoresistance ⇒ Kondo lattice ρ(T) minimum, negative magnetoresistance ⇒ Kondo lattice Single ion Kondo scaling analysis for S = 1 ⇒ TK ~ 1 K

• P. Schlottmann, Z. Phys. B Cond. Matt. (83)

PrOs4As12: C/T vs T in magnetic fields

PrOs4As12: Ce/T vs T in magnetic fields

• Ce(T) data:

UCSD (0 ≤ H ≤ 5 T) LLNL (6 T ≤ H ≤ 16 T)

• Ce(T) fits:

Resonance level model

• K. D. Schotte, U. Schotte, 75

– Spin: S = 1 (triplet CEF g.s.) p ( p g ) – Level width: ∆ = kBTK ≈ 3.5 K – Zeeman splitting of resonances: gµ H resonances: gµBH

• Similar to behavior of PrFe4P12

Aoki et al., 02

PrOs4As12: γ(0) vs H

AFM Unknown order

dHvA measurements on PrOs4As12

P.-C. Ho, J. Singleton et al., 07

dHvA measurements on PrOs4As12

• Mass enhancement due to spin

fl t ti i t d ith fluctuations associated with AFM phase – decrease with H in paramagnetic state

• At 25 T m

3 5 times greater

• At 25 T, mexp ~ 3 - 5 times greater

than mth

P.-C. Ho, J. Singleton et al., 07

PrOs4As12: Analysis of ρ(T,H) in AFM state

AFM nkno n PM

(a) lnρ vs ln T plots; lines – AFM with energy gap ∆ (N. Hessel-Anderson ‘80)

unknown

(b) ln(ρ - ρo) vs lnT plots; lines – power law ρ(T) = ρo + ATn

Correlated electron ground states in Pr filled skutterudites

PrT4X12 T X

Concluding remarks Filled skutterudites exhibit wide variety of correlated electron phenomena

• Filled skutterudites exhibit wide variety of correlated electron phenomena
• Phenomena extremely sensitive to changes in elemental constituents
• Reflection of coupling between charge spin orbital and lattice
• Reflection of coupling between charge, spin, orbital and lattice

degrees of freedom and competing interactions

• Focused on the La, Ce, and Pr-based filled skutterudite arsenides

and antimonides (Left out other interesting cases: e.g., Sm, Eu, Yb, alkali metal, alkaline earth-based filled skutterudites)

• PrOs Sb :
• PrOs4Sb12:

– First example of Pr-based heavy fermion superconductor Unconventional type of strong coupling superconductivity – Unconventional type of strong coupling superconductivity – Possible new superconducting electron pairing mechanism — electric quadrupole (rather than magnetic dipole) fluctuations

• Role of “tunneling” and “rattling” of filler ions in strongly correlated

electron physics of filled skutterudites

• Growing class of novel materials — opportunity for exploring for other

examples of correlated electron behavior