Exotic Metals from Geometrical Frustration

Minoru NOHARADepartment of Physics, Okayama University

物構研シンポジウム ‘08

Topics(1) Pseudogap Metal in LiVS2

(2) High-Entropy Metal in CuRhO2

N. Katayama and H. TakagiUniversity of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. MatsunoRIKEN

D.Matsumura, Y.Nishihata, and J.MizukiJAEA

H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura, and H.Takagi

University of Tokyo

？

Topics(1) Pseudogap Metal in LiVS2

(2) High-Entropy Metal in CuRhO2

N. Katayama and H. TakagiUniversity of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. MatsunoRIKEN

D.Matsumura, Y.Nishihata, and J.MizukiJAEA

H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura, and H.Takagi

University of Tokyo

？

Valence Bond Solid in LiVO2

V3+, 3d2, S = 1

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

1st order transition from CW insulator to non-magnetic insulator at ~ 500 K.

dxy dzx

dyz

t2g

eg

Vanadium trimers

Weiss T = - 1500 K (AF), indicating strong frustration.

Valence Bond Solids are ubiquitous

heptmer in AlV2O4 Helical dimer in MgTi2O4

Octermer in CuIr2S4 Trimer in LiVO2

Pyrochlore Lattice

Triangular Lattice

!

1

2"# $ #"( )

EtMe3P[Pd(dmit)2]2

What kind of metal do we expect if VBS melts ?

In organic systems, BVS melts under pressure and superconductivity emerges.

Spin singlet in real space turns into spin singlet in k-space.

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

Inorganic Systems: VBS is stabilized by Pressure

Cell volume decreases at the VBS transition.

Trimer in Li0.8VO2 Octermer in CuIr2S4

Furubayashi et al., JPSJ 63, 3333 (1994).Cardoso et al., J. Solid State Chem. 72, 234 (1988).

Negative pressure by chemical substitution

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

LiVS2 LiVO2

Transition Temperature is reduced by replacing O to S.

Trimer at low temperatures in LiVS2

(a) (b)

110100

010

Electron Diffraction EXAFS, BL14B1, SPring-8

295 K (< Tc ) 350 K{1/3, 1/3, 0} superlattice

LiVS2

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

Metal-Insulator Transition in LiVS2

LiVO2

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

1.5

1.0

0.5

0.0

M /

H (

10-3

em

u/m

ol)

8006004002000T (K)

LiVS2-xSex

x = 00.1

0.6x = 1.0

x = 2.0

0.20.3

Pseudogap behavior in the metallic phase

10-2

10-1

100

101

102

ρ (Ω

cm)

4002000T (K)

x = 0.0

x = 2.0

LiVS2-xSex

VBS state is suppressed by Se doping.

Gradual decrease in susceptibility by approaching VBS phase, indicative local singlet.

Diffuse scattering due to local trimer formation.

800

600

400

200

0

Tem

pera

ture

(K)

2.01.51.00.50.0Se contents, x

70656055Volume (Å3/cell-f.u.)

LiVS2-xSex

LiVO2

Valence Bond Solid

ParamagneticInsulator

Metal

Pseu

doga

p

72

68

64

60Vol

ume

(Å/c

ell)

2.01.00.0Se contents, x

Conclusion

VBS can be melted by negative pressure.

VBS is robust from insulating to metallic side.

No superconductivity when VBS melts.

Short range correlation, or pseudogap, at the vicinity

of phase boundary.

Topics(1) Pseudogap Metal in LiVS2

(2) High-Entropy Metal in CuRhO2

N. Katayama and H. TakagiUniversity of Tokyo

M.Uchida, D.Hashizume, S.Niitaka, and J. MatsunoRIKEN

D.Matsumura, Y.Nishihata, and J.MizukiJAEA

H.Kuriyama, K.Takubo, T.Mizokawa, K.Kimura, and H.Takagi

University of Tokyo

？

Power Generation Peltier Cooling

Candle Radio

ワインセラー

Frustration can be a new route to thermoelectric materials

Refrigerator

currentcurrent

dT dT

TE materialTE material

σ2SPF =

TSZT

=

κσ2

1. Large “Power Factor” (PF)

Large Seebeck

High electrical conductivity

2. Large “Dimentionless Figure of Merit” (ZT)

S = !V /!T

Low thermal conductivity

Large PF

Requirements for thermoelectric materials

Hard to realize both “large Seebeck” and “high

k

EFE

k TB

Large Fermi surface

Symmetric band to EF

Small σ2SPF =

Boltzmann’s transport

Large

electron velocity

σ2SPF =

large

largek

EF

E

k TB

Large Fermi surface

large

Highly asymmetric band

Boltzmann’s transport

triangular lattice

hopping

charge current

entropy flow

Extended Heikes eq.

High-T limit / hopping conduction

Layered Rh oxides with d6 low-spin state

Cu

Rh

O

RhO2 layer

O-Cu-O dumbbell layer

Rh3+

eg

t2g

Cu+

Hole doping by substituting Mg2+ for Rh3+

Delafossite CuRhO2

CuRh1-xMgxO2

Band insulator

d6 low-spin state

10-3

10-2

10-1

100

101

102

ρ (Ω

cm)

12008004000

T (K)

x = 0.1

x = 0.05

x = 0

CuRh1-x Mgx O2

Large Seebeck and Metallic Conductivity Realized

polycrystalline samples

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

300

200

100

0Th

erm

oele

ctric

Pow

er (µ

V/K

)12008004000

Temperature (K)

x = 0.1

x = 0.05

CuRh1-xMgxO2

CuRhO2 atom 1DZ2 size 0.20

Z K.2 K.3 Z ! K M !

E F

Ener

gy (e

V)

0.0

1.0

-1.0

-2.0

CuRhO2

A W M

　“Pudding Mold Band” is present at Z point

Rh a1g Cu a1g

a

Z

Pudding Mold Band of Rh a1g centered at Z

Pocket of Cu a1g centered at W

a

　“Pudding Mold Band” is present at Z point

Z

a

collaboration with N. Bontemps (Paris)

　“Pudding Mold Band” scenario looks OK

0

50

100

150

200

250

0 100 200 300 400 500

S (µ

V/K

)

T (K)

nh0.035

0.055

0.0800.100

300

200

100

0

Ther

moe

lect

ric P

ower

(µ

V/K

)

12008004000Temperature (K)

x = 0.1

x = 0.05

CuRh1-xMgxO2

0

50

100

150

200

250

0 100 200 300 400 500

S (µ

V/K

)

T (K)

nh0.035

0.055

0.0800.100

Observation calculation

Kuroki & Arita

Spin & Orbital Scenario predicts High-T value of S

Spin & Orbitalentropy

(Heikes)

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

Charge configurationentropy

d6 LS d5 LS

hopping

Hexagonal

!

(P6 2c) Rhombohedral

!

(R3 m)

!

"Pauli = 0.25#10$3 emu/mol%Rh

!

"Pauli # 0.1$10%3emu/mol&Rh

Wiedemann – Frantz Law

!

"e# 2 mW/K $ cm for x = 0.1 at 300 K.

!

" = 650 mJ/K2mol

!

" = 650 mJ/K2mol

!

" = 45 mJ/K2mol

!

" = 38 mJ/K2mol

!

" = 48 mJ/K2mol

!

S = 160µV/K

!

S =kB

eln g4 " g3( ) "

kB

eln

x

1" x

!

g3 = 0

!

g4 = 2 " 3 = 6

Hexagonal

!

(P6 2c) Rhombohedral

!

(R3 m)

!

"Pauli = 0.25#10$3 emu/mol%Rh

!

"Pauli # 0.1$10%3emu/mol&Rh

Wiedemann – Frantz Law

!

"e# 2 mW/K $ cm for x = 0.1 at 300 K.

!

" = 650 mJ/K2mol

!

" = 650 mJ/K2mol

!

" = 45 mJ/K2mol

!

" = 38 mJ/K2mol

!

" = 48 mJ/K2mol

!

S = 160µV/K

!

S =kB

eln g4 " g3( ) "

kB

eln

x

1" x

!

g3 = 0

!

g4 = 2 " 3 = 6

Hexagonal

!

(P6 2c) Rhombohedral

!

(R3 m)

!

"Pauli = 0.25#10$3 emu/mol%Rh

!

"Pauli # 0.1$10%3emu/mol&Rh

Wiedemann – Frantz Law

!

"e# 2 mW/K $ cm for x = 0.1 at 300 K.

!

" = 650 mJ/K2mol

!

" = 650 mJ/K2mol

!

" = 45 mJ/K2mol

!

" = 38 mJ/K2mol

!

" = 48 mJ/K2mol

!

S = 160µV/K

!

S =kB

eln g4 " g3( ) "

kB

eln

x

1" x

!

g3 = 0

!

g4 = 2 " 3 = 6

!

+154 µV/K

!

+190 µV/K for x = 0.1

300

200

100

0

Ther

moe

lect

ric P

ower

(µ

V/K

)

12008004000Temperature (K)

x = 0.1

x = 0.05

CuRh1-xMgxO2

High T limit

“In-between-state” is ubiquitous theme in strongly correlated systems

kinetic term entropy term

Hubberd band better described

in real space

QP band better described

in k space

Band limit Atomic limit

a1g

Crossover between band limit & Atomic limit by PES

NaxCoO2

Isida & Fujimori, JPSJ 76, 103709 (2007).

“In-between-state” is ubiquitous theme in strongly correlated systems

d-electron system: high-Tc

Mott Physics Fermi Liq. & SCR

f-electron systems: heavy fermion

Atomic limit Band limit Band limitAtomic limit

localized f delocalized f

Conclusion

physics of “in-between-state”

material design from geometrical frustration

“pudding-mold band”

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

single band tight binding model

Band limit

？

Atomic limit

spin/orbitaldegeneracy

Geometrical Frustration

High-entropy metal (thermoelectric materials)