Geometrical Correlation of Itinerant Electrons
Probed by Muons and Neutrons
Plan:•Introduction•LiV2O4-a model case
•Other pyrochlores•SummaryRyosuke Kadono
Institute for Materials Structure Science,High Energy Accelerator Research Organization (KEK),
andDepartment of Materials Structure Science,
The Graduate University for Advanced Studies

Method:

Muon Spin Rotation (µSR)a) Muons are produced with 100% spinpolarizaion and transported by a beamline for
implantention to sample.

b) The implanted muons stop between
atoms, where they start Larmor
precession according to the local
magnetic fields.

c) Muons emit positrons to the direction when theirspins were pointing upon decay, which aredetected by scintillation counters.
→The signal of scintillation counters oscillates
periodically due to the Larmor precession ofmuons.

Method:

Muon Spin Rotation (µSR)...How muons probe magnetic state of matter?

Diamagnetic

Paramagnetic

Magnetic Order...sensitive only
to the nn moments...sensitive only
to the nn moments...sensitive only
to the nn moments

µ+

µ+µ+

Time depend.

Time depend.

Fourier Trans.

Fourier Trans.

Time depend.

Freq.

0Amp.

Amp.

Amp..

Fourier Trans.

Freq. 00 Freq.

ωLMethod:

Muon Spin Rotation (µSR)...Unique time window for the spin dynamics
2$ 2%Spin relaxation rate: " # 2&µ + % 2Correlation Time of Spin Fluctuation
100

10−2

10−4

10−6

10−8

10−10

"=10−12 10−14 (s)!

SRNeutron
Muon (µSR)
NMR
ac-susceptibility

A unique “niche”
between NMR and neutron!

1, $µ = % µB
#cIssue:Geometrical Correlation of Itinerant Electrons

What would happen when frustration acts on metallic conduction?

Antiferroic correlation

Stage of itinerancy =highly symmetric crystal(Local picture)

Spin+m?

Charge+n?
?

+m ?+nFrustration
Pyrochlore lattice(Spinel)(=Large scale degeneracy)...so far extensively studied on local
spin/charge systems.

Muon Spin Rotation (µSR)：...One of the most sensitive probes for frustration
Electronic state of...
Normal metal

Poor metal
Geometrical Correlation...only reflecting
crystal symmetry(Single electron)...inhomogeneous spin/charge floweµ+

Amp.

µSR
Freq.

µSR
Amp.

µ+Freq.

Example:“Heavy Fermion” State in Metallic Spinels

YMn2(‘89), LiV2O4(‘97)
LiV2O4

A # (m* ) 2!

"0 ! mCT= " ! m**Quasiparticle
peak in photoemission spectra

T2 coefficient for Resistivity(according to specific heat, etc.)" + " 0 = AT 2

T*~20K

Mass enhancement ~102!

[Shimoyamada etal. ’06]

Sommerfeld coefficient[sc-LiV2O4, Urano et al. ’00]

LiV2O4: What is the origin of the HF-like behavior?
V3.5+• Conventional Heavy Fermion systems
Kondo-effectconduction electrons

kBTK

cubic

3d1.5eg

Tetragonal
distortion

t2g

Eg
A1g

Kondo singlet?

Local f electrons
Heavy Fermion=A new electronic state

Proposed Theoretical Models• Kondo scenario for 3d metals:

Quenched local moments

Anisimov et al., PRL 83 (1999) 364.

...competing interactions• Magnetic frustration:
Eyert et al., Europhys. Lett. 46 (1999) 762.

Fund coupling• Low-dimensional magnet:
Fulde et al., Europhys.Lett. 54 (2001) 779.

J?

?

Superexchange (AF) Magnetic frustration• Proximty to Mott Insulator:
Arita et al., PRL 98 (2007) 16402.
...

LiV2O4: Local moments develop below T*! ... µSR
Koda, Kadono et al., ‘05

Signal probing
local moments
Paramag.

single-crystal(Matsushita et al.)~ 0.1gµSR measured at
TRIUMF M15.

µSRAnalysis: Fits in time domain by
A0Gxy(t)=A0e-iφΣifiexp(iωit)exp(-Λit)
A0 : instrumental asymmetrye-iφ : initial phasefi : fractional yield of i-th component
ωi : precession frequency
Λi : relaxation rate

…three components (i=1-3) areenough to reproduce data.

µSR

T*~20KLiV2O4: Local inhomogeneity probed by µ+ Knight shift
K-χ plot:
The Knight shift vs bulk susceptibility…must be linear in normal metals.

cf. Typical example of HF metal:
CeRu2Si2 (TK~10-20 K)

poly-crystal
10 K↑ The broad lines exhibit highly non-linear
behavior below ~T*.
A broad distribution of hyperfine parameterAµ~ 6 ± 3 kOe/µB↑ no such anomaly(homogeneous metal)

LiV2O4: Spin fluctuation probed by LF-µSR
Spin-lattice relaxation: response to a longitudinal field (LF)...corresponding
to the components
observed in TF.

↓ There are two components withtheir fluctuation rate much different
with each other as inferred from theresponse to LF.
µSR in Li1-xZnxV2O4
with x=0, 0.05, 0.10

Quasi-static...hardlyquenced

Fluctuating...easily
quenched
Koda, Kadono et al., ‘04...fluctuation issuppressed forx>0 at low T.

LiV2O4: The ground state suggested from µSR
Two kinds of signals in µSR
suggests development of(a) weakly magnetic (~or nonmagnetic) state, and(b) inhomogeneous paramagnetic state fluctuating over afrequency range of ν~106-109/s.

...A snap shot"#!

$#!

ν << kBT*~ 1011/s...not like Kondo fluctuaion
One possibility:
quasi-1D chain correlations
for V3+ (S=1, Haldane?) andV4+ (S=1/2, Heisenberg) ions,[...a model suggested by Fuldeet al., ‘01]

Muon Site:…Center of O-octahedron, withnn V ions forming a hexagon ring.

Andeson’s Rule:
Each tetrahedron isoccupied by two
V3+ and V4+ ions.

LiV2O4: Inelastic Neutron Scattering (T<T*)
Antiferromagnetic correlation vs single-site fluctuation (SSF)
SSF...due to the Kondo coupling to conduction electrons
HF-system

LiV2O4S.-H. Lee et al., 2001

AFSSF(Kondo)
BG

Q ≅ 0.6 å−1
AF correlation?
(FS nesting?)
kBTK~ 100 meV (~1011/s)

No SSF?

(NB: phonon parts subtracted using LiTi2O4 data)LiV2O4: Inelastic Neutron Scattering (T>T*)
Paramagnetic response: observation of two components
A. P. Murani et al., 2004

T<T*

T>T*

T>T* (λ=2.2å, 5.1å)Q ≅ 0.6 å−1(λ=5.1å)Imaginary part of χ for “spin glass”" Qi $iQ""(Q,# ) = # % Q 22i ($i ) + #i=2 seems to be needed to reproduce
data. → ...in good accord with µSR.
!

µSR

LiV2O4: A New Class of Metal?
Implications from other experiments: Effect of Pressure
HF system:

LiV2O4: P-induced MI transition and reduction ofsymmetry (P > 10 GPa)T

LiV2O4?

AFFermi Liq.
QCP

Fd3m→R3m

10 K

W/UP∝W...getting further into theFermi liquid state with P.
TM-I: ρ min..

cf. Charge order in AlV2O4...not like a canonical HF system
Geometrical Correlation
New Class of Metallic State
Fd3m→R3m

V2.5+→V2.5±δMatsuo et al., 01Geometrical correlation: Other pyrochlore examples
Problem for A2B2O7: Structural and associated MI transition
Q: How to preserve cubic symmetry?
A: Let the t2g band half-filled (no orbital degeneracy).
egt2g
t2g half-filled
Structural phasetransition issuppressed by the lackof OD.

Ru5+ (4d3) S=3/2
Hg2Ru2O7 (MIT)Cd2Ru2O7 (CDW?)
Ca2Ru2O7 (Metal?)
Os5+(5d3)

S=3/2

Ion Radius
Ru5+< Os5+Cd2+ < Ca2+ < Hg2+Cd2Os2O7 (MIT)
Hg2Os2O7 (Metal)...It seems not trivial to obtain high quality specimens(some of them requires high pressure for synthesis).

Geometrical correlation: Other pyrochlore examples
Cd2Os2O7

ρ-T

Hg2Os2O7

MIT

Hg2Ru2O7

Metallic

TN~230K
88K
A.Koda et al.,’07µSRTMIMIT

ρ-T

A.Koda et al., ‘06

0

100
200
Temperature (K)K.H. Satoh et al., ‘08300

Geometrical correlation: Other pyrochlore examples“Metal”ness vs Frustration

T (K)

200

‘07

Cd2Os2O7●●Hg2Ru2O7

100

AF/SDW0?

Paramagnetic

Heavy Fermion state
Hg2Ru2O7 Takeshita et al.,100LocalAnomalous metal

Hg2Os2O7 ●P10-1
10-2
10-3
10-4
ρ at 2 K (Ohm cm)∝m/n

LiV2O4● -510Itinerant...suppression of MI
transition (by pressure)leads to HF-like behavior
similar to LiV2O4.

Geometrical correlation: Other pyrochlore examples
Other exotic ground states:
Fractional Charge Stated1d0

Chiral metal
Na4Ir3O8 (5d5,S=1/2)

d1d0Distribute charges according to the Anderson’srule....then put one electron into the lattice:“Hyper-Kagome”...If one can get it carrier-doped, andeven get superconducting, then...

P4132
Migration of a dopedelectron:(Fulde et al., ‘02)

Migration of host electron:
5 electrons split into
effectively 2.5 e charges.

P4332

Exotic superconductivity due to thelack of inversion symmetry?

(Nohara)Summary•Now it seems that time is mature to launch
an in-depth studies of GAC in combination
with a systematic and large-scale search for
new candidates for “frustrated metals”.

...to pin down the characteristic scales oftime/length with unprecedented precision.

104NowNeutron/SR•Both µSR, neutron scattering, and SR
should work together to elucidate themicroscopic details of the new metallic
ground state observed in cubicspinels/pyrochlores.

Our Goal:

Correlation length (nm)•Geometrically antiferroic correlation (GAC)
between electrons conducting on highly
symmetric orbits might give rise to new classof metallic state, where the HF behavior in
cubic spinels/pyrochlores might be one suchmanifestation.

103102

Goal
11010010−110−8µSR
10−9

10−10

10−11

Correlation time (s)10−12Collaborators (past, present, and future):
Material synthesis
ISSP-U. Tokyo
Okayama U.
U. Tokyo/RIKENµSR:
KEK-IMSS
JAEA-ASRC
KEK-IPNS
Neutron:
IMR-Tohoku U.
KEK-IMSS
Synchrotron Radiation:
Nagoya U.
KEK-IMSS

Y. Matsushita, H. Ueda, Y. Ueda, Z. Hiroi
M. Nohara
C. Urano, S. Kondo, A. Yamamoto, H. Takagi
A. Koda, W. Higemoto, K. Ohishi, S. Takeshita,
M. Hiraishi, M. Miyazaki, R. Kadono
W. Higemoto
M. Tanaka, Y. Yasu, S. Suzuki
M. Fujita, K. Yamada
S. Itoh, T. Yokoo
H. Sawa
Y. Murakami, S. Wakabayashi