物構研シンポジウム ‘08

Exotic Metals from Geometrical
Frustration
Minoru NOHARA

Department of Physics, Okayama University

Topics(1) Pseudogap Metal in LiVS2
N. Katayama and H. Takagi
University of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. Matsuno
RIKEN

D.Matsumura, Y.Nishihata, and J.Mizuki
JAEA(2) High-Entropy Metal in CuRhO2
H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura,and H.Takagi
University of Tokyo？

Topics(1) Pseudogap Metal in LiVS2
N. Katayama and H. Takagi
University of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. Matsuno
RIKEN

D.Matsumura, Y.Nishihata, and J.Mizuki
JAEA(2) High-Entropy Metal in CuRhO2
H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura,and H.Takagi
University of Tokyo？

Valence Bond Solid in LiVO2eg

V3+, 3d2, S = 1dyz
dxydzxW. Tian et al., Mater. Res. Bull. 39 (2004) 1319 .

Weiss T = - 1500 K (AF), indicating strong
frustration.
Vanadium trimers
1st order transition from CW insulator to
non-magnetic insulator at ~ 500 K.

t2g

Valence Bond Solids are ubiquitous
Pyrochlore Lattice

heptmer in AlV2O4Helical dimer in MgTi2O4
Triangular Lattice1( "# $ #" )2!

Octermer in CuIr2S4

Trimer in LiVO2

What kind of metal do we expect if VBS melts ?
EtMe3P[Pd(dmit)2]2

Shimizu et al., PRL 99, 256403 (2007).

In organic systems, BVS melts under pressure andsuperconductivity emerges.
Spin singlet in real space turns into spin singlet in k-space.

Inorganic Systems: VBS is stabilized by Pressure
Trimer in Li0.8VO2

Cardoso et al., J. Solid State Chem.
72, 234 (1988).

Octermer in CuIr2S4

Furubayashi et al., JPSJ 63, 3333 (1994).

Cell volume decreases at the VBS transition.

Negative pressure by chemical substitution
LiVS2

LiVO2W. Tian et al., Mater. Res. Bull. 39 (2004) 1319 .

Transition Temperature is reduced by replacing O to S.

Trimer at low temperatures in LiVS2
Electron Diffraction(a)

EXAFS, BL14B1, SPring-8(b)100110010

295 K (< Tc ){1/3, 1/3, 0}
superlattice

350 K

Metal-Insulator Transition in LiVS2
LiVS2

LiVO2W. Tian et al., Mater. Res. Bull. 39 (2004) 1319 .

VBS is robust irrespective of high temperature phases,
metallic in LiVS2 and semiconducting in LiVO2.

Pseudogap behavior in the metallic phase
LiVS2-xSex

x = 1.00.00ρ (Ωcm)

LiVS2-xSex

0100.3x = 2.0-20.6
0.5

101

10-1

1.0-3

M / H (10 emu/mol)

1.5x = 2.0x = 0.0

102

100

200

400T (K)0.2
0.1x=0Diffuse scattering due tolocal trimer formation.
200

400T (K)600800

VBS state is suppressed by Se doping.
Gradual decrease in susceptibility by approaching VBS phase,indicative local singlet.

Conclusion
380055

Volume (Å /cell-f.u.)
60
6572

LiVO2

VBS is robust frominsulating to metallic side.

64
600.0

400

1.0
Se contents, x

2.0

No superconductivity when
VBS melts.

LiVS2-xSex
2000

Short range correlation, orpseudogap, at the vicinityof phase boundary.

MetalValence Bond Solid0.0

VBS can be melted bynegative pressure.

68

Pseudogap

Temperature (K)Volume (Å/cell)

Paramagnetic
Insulator
600

700.5
1.0
1.5
Se contents, x2.0

Topics(1) Pseudogap Metal in LiVS2N. Katayama and H. Takagi
University of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. Matsuno
RIKEN

D.Matsumura, Y.Nishihata, and J.Mizuki
JAEA(2) High-Entropy Metal in CuRhO2
H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura,and H.Takagi
University of Tokyo？

Frustration can be a new route tothermoelectric materials
Power Generation

Peltier Coolingcurrent

current
TE material

TE materialdTdTCandle Radio

ワインセラー

Refrigerator

Requirements for thermoelectric materials
1. Large “Power Factor” (PF)2PF = S σ

Large Seebeck

S = !V /!THigh electrical conductivity

2. Large “Dimentionless Figure of Merit” (ZT) S 2σ 
TZT =  κ Large PF
Low thermal conductivity

Hard to realize both “large Seebeck” and “highelectron velocity

EEF

Large Fermi surface
kBT

kBoltzmann’stransport

Large
Symmetric band to EF

Small PF = S 2σ

triangular lattice

ELarge Fermi surface
large

EFkBT

k

Boltzmann’stransport

Highly asymmetric band
large

PF = S 2σlarge

Extended Heikes eq.

High-T limit / hopping conductionhopping

charge current
entropy flow

Layered Rh oxides with d6 low-spin state
Delafossite CuRhO2Band insulator

d6 low-spin state
RhO2 layereg

O-Cu-O
dumbbell layer

t2gCuRhO

Cu+Rh3+

Hole doping by substituting Mg2+ for Rh3+
CuRh1-xMgxO2

Large Seebeck and Metallic Conductivity Realized102

polycrystalline samples

100

Thermoelectric Power (µV/K)ρ (Ωcm)10

CuRh1-x Mgx O2

1x =010-1x = 0.05

-2

10x = 0.1
10400

800

300

200

1200

T (K)

Large Mg solubility of x = 0.1.
Large mobility of ~ 1 cm2/Vs.

x = 0.05
x = 0.1

10000-30

CuRh1-xMgxO2400800
Temperature (K)1200

“Pudding Mold Band” is present at Z point
CuRhO2 atom 1DZ2 size 0.20

1.0

CuRhO2

Rh a1gCu a1g
ZEF

Energy (eV)

0.0

a-1.0

Pudding Mold Band of Rh a1g centeredat Z
Pocket of Cu a1g centered at W
-2.0

Z

K.2
K.3
A W

Z !

K M
Ma!

“Pudding Mold Band” is present at Z point

Zacollaboration with N. Bontemps(Paris)

“Pudding Mold Band” scenario looks OKcalculation

CuRh1-xMgxO2300

250

nh0.035x = 0.05

2000.055

2500.055

x = 0.1

0.080
0.100

150

S (µV/K)

nh0.035

200200S (µV/K)

Thermoelectric Power (µV/K)

Observation

100100

0.080
0.100

150

100

50

5000 000100

200

300

T (K)

400

500

400
800
Temperature (K)

1200

0100

200

300

400

T (K)

Kuroki & Arita

500

!

$3
" = 650mJ/K=2 mol" =$345emu/mol%
mJ/K 2 mol Rh " = 38 mJ/K
" Pauli
0.25# 10

! = 0.25# 10" Pauli!

!
!

emu/mol% Rh

S = 160 µV/K!
!
!
Wiedemann–Frantz
FrantzLaw
Law
Wiedemann–!
Spin & Orbital Scenario predicts
High-Tvalueof xS= 0.1!at! 300 K!
"#2mW/K$cm
for
x = 0.1 at 300 K.
k"Bee # 2 mW/K $ cm
k B forx (Heikes)
S=

Thermoelectric Power (µV/K)!

200

x = 0.05
x = 0.1!
!

!
400
800
Temperature (K)High T limit

eln

1" x

g3 = 0g4 = 2 " 3 = 6
Spin & Orbital
Charge configuration!
entropy
entropy
22 mol2 2 mol
"
=650
mJ/K
"
=45mJ/K"=650mJ/Kmol"=45mJ/Kmol!
!
+154 µV/K!
! +190 µV/K for x = 0.1

10000ln( g4 " g3 ) "22 mol650mJ/K"=" = 650 mJ/K mol!
!

CuRh1-xMgxO2300e1200!

=
160µV/KµV/K
5 LS
dS6 =LS160d!

!

!

kkBB hoppingkkxx
S == lnln((gg44 ""gg33))"" BBlnln
1"xxeeee 1"
g33 == 00!

gg44 ==22""33==66

Koshibae et al. Phys. Rev. Lett. 87 (2001) 236603.

!

!!

!
!

“In-between-state” is ubiquitous theme in stronglycorrelated systems
NaxCoO2
kinetic term

entropy termBand limit

Atomic limit

QP bandbetter describedin k space

Hubberd band
better describedin real space

a1g

Crossover between band limit& Atomic limit by PES
Isida & Fujimori, JPSJ 76, 103709(2007).

“In-between-state” is ubiquitous theme in strongly
correlated systems
d-electron system: high-Tc

f-electron systems: heavy fermion

Atomic limit

Band limit

Atomic limit

Band limit

Mott Physics

Fermi Liq. & SCR

localized fdelocalized fConclusion
Geometrical Frustration

Band limit

Atomic limit？

physics of “in-between-state”
material design fromgeometrical frustration“pudding-mold band”
single band tight binding model

spin/orbital
degeneracy

Kuroki & Arita, JPSJ 76, 083707 (2007).

High-entropy metal (thermoelectric materials)