[PPT] - Thermomagnetic properties of the strongly correlated semimetal PowerPoint Presentation

SLIDE 1

Thermomagnetic properties

f the strongly correlated semimetal

CeNiSn

Niels Oeschler

Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

MAX-PLANCK-INSTITUT

FÜR CHEMISCHE PHYSIK FESTER STOFFE

SLIDE 2

Acknowledgements:

Measurements:

U. Köhler, MPI CPfS, Dresden, Germany
P. Sun, MPI CPfS, Dresden, Germany
S. Paschen, Vienna University of Technology, Austria
F. Steglich, MPI CPfS, Dresden, Germany

Samples:

T. Takabatake, Hiroshima University, Japan

MAX-PLANCK-INSTITUT

FÜR CHEMISCHE PHYSIK FESTER STOFFE

SLIDE 3

Outline

Introduction

Thermoel. and thermomagn. effects
Exp. setup

Correlated semimetal CeNiSn

Results

Resistivity and Hall effect Thermopower Nernst effect and Righi-Leduc effect

Discussion

Field-dependent thermopower Nernst effect

Summary

SLIDE 4

Introduction

Thermoel. and thermomagn. Effects

Charge transport: J = σE - σSΔT Heat transport: JQ = σSTE - κΔT Thermal conductivity: κ = JQ/ΔTx Thermopower: S = -Ux/ΔTx

x y z JQ heater bath B

ΔTx Ux

SLIDE 5

Introduction

Thermoel. and thermomagn. Effects

Charge transport: J = σE - σSΔT Heat transport: JQ = σSTE - κΔT Thermal conductivity: κ = JQ/ΔTx Thermopower: S = -Ux/ΔTx Nernst effect: ν = -Uy/ΔTxB Righi-Leduc effect: L = -κy/B ΔTy/ΔTx

x y z JQ heater bath B

Uy ΔTy

SLIDE 6

Introduction

Thermomagn. Effects: Ettingshausen cooling

j B

source/hot sink/cold

ΔT

Lc Lh

j B infinite stage Ettingshausen device

α

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = Δ

h c hot max

1 L L T T

2

2 cold mag max

T Z T = Δ κ υ σ T B T Z

2 mag

) ( =

Thermomagn. figure of merit ZmagT

SLIDE 7

Kondo Insulator

2π/a E k N(E) EF EF

unperturbed conduction band unperturbed 4f band hybridized bands

2π/a E k

(a) (d) (c) (b)

N(E)

Heavy fermion metals

ρ ~ -lnT at T ≈ TK
enhanced DOS at EF below ~TK

metal-like behavior at low T Kondo insulator

ρ ~ -lnT at T ≈ TK
gap below ~Tg

insulating behavior at low T

SLIDE 8

Introduction

Experimental Setup:

4He cryostat

horizontal 7T magnet

ptimized for small samples with

low κ ΔT: chromel-AuFe thermocouples U: copper wires, nanovoltmeter

SLIDE 9

CeNiSn

samples

rthorhombic crystal structure

chains of Cerium ions along a easy a axis Czochralski method annealed by SSE energy scales crystal field levels: kBΔCEF ≈ 230K, 460K Kondo temp.: TK ≈ 56 K pseudogap Δ/kB ≈ 10 K below T ≈ 10 K no ordering down to 25 mK

c a b Ce Ni Sn c b a

SLIDE 10

CeNiSn

gap structure

pseudogap opens around 10K residual states at EF metallic ρ, large Sommerfeld coeff.

gap suppression

magnetic fields ~10 T // a
pressure ~ 2 GPa
substitution (Ce/La and Ni/Cu,Co) ~ 10 %

dI/dV

T. Ekino et al., Phys. Rev. Lett. 75, 4262 (1995)
K. Izawa et al., J. Phys. Soc. Jpn. 65, 3119 (1996)

V (mV)

SLIDE 11

CeNiSn - Kondo Insulator?

G. Nakamoto et al., J. Phys. Soc. Jpn. 64(12), 4834 (1995)

sensitive dependence on sample purity (ρ, MR, RH) residual DOS near EF (NMR, cP, ρ, κ)

⇒ CeNiSn – Kondo semimetal

K. Izawa et al., J. Phys. Soc. Jpn. 65, 3119 (1996)
H. Ikeda and K. Miyake, J. Phys. Soc. Jpn. 65, 1769 (1996)

SLIDE 12

Experimental

Single crystals (#5)

Czochralski + SSE
best available samples
Orientation: Laue, χ, ρ (a/c)
ca. 4 x 4 x 0.8 mm³
Measurements: q // b; B // a, c

Measurements:

Thermal conductivity
Thermopower at +B and –B
Nernst effect
Thermal Hall effect

1.5 5 10 50 50 100 150 200

0 T 1 T 2 T 4 T 7 T

ρ (μΩ cm)

T (K)

CeNiSn No.3 j // b, B // a

G. Nakamoto et al., J. Phys. Soc. Jpn. 64(12), 4834 (1995)

SLIDE 13

Results: Thermopower

1.5 5 10 50 100

40
20

20 40

sample No 1 sample No 3

CeNiSn #5 B = 0 T q//b S (µV/K) T (K)

Kondo system with CEF splitting
largest negative S ever observed
very precise orientation !

CeNiSn #4

G. Nakamoto et al., Physica B 306 & 307, 840 (1995)

S (µV/K) 60 40 20 T (K)

0 10 20 30 40

b-axis

J. Sakurai et al., Physica B 306 & 307, 834 (1995)

CeNiSn type unknown

SLIDE 14

Field-dep. Thermopower

1.5 2 3 4 5 6 7 89 10 20 30 40

40
20

20 40 CeNiSn #5, No. 3 q//b, B//a

0 T 1 T 2 T 4 T 7 T

S (µV/K) T (K)

B // a: - enhanced values of |S|

shift of the minimum to lower T

B // c:

similar, but less pronounced

literature:

strong sample

dependence at low T

no comparable results

in field

SLIDE 15

Nernst effect

large values of N below 10 K (opening of the gap)

scaling for B // a (easy axis!)
shift of minimum for B // c

q // b, B // a B // c

1.5 5 10 50

120
100
80
60
40
20

2 4 6 8 10

20
15
10
5

4 T 7 T 0.5 T 1 T 2 T

N (µV/K) T (K)

ν (µV/KT)

T (K)

1.5 5 10 50

120
100
80
60
40
20

2 4 6 8 10

15
10
5

5.5 T 7 T 1 T 2 T 3 T

N (µV/K) T (K)

ν (µV/KT)

T (K)

SLIDE 16

Discussion: Thermopower

2 4 6 8 10

40
30
20
10

10 Ulong/ΔT T (K) + 2 T

2 T

variation due to

sample dependence
misorientation
non-negligible Nernst contribution

SLIDE 17

Discussion: Thermopower

2 4 6 8 10

40
30
20
10

10 Ulong/ΔT T (K) + 2 T

2 T

variation due to

sample dependence
misorientation
non-negligible Nernst contribution

2 4 6 8 10

40
30
20
10

Ulong/ΔT T (K) (U+-U-)/(2ΔT) N(2T)

(U+-U-)/2ΔT N (2T)

SLIDE 18

Discussion: Thermopower

2 4 6 8 10

40
30
20
10

10 Ulong/ΔT T (K) + 2 T

2 T

variation due to

sample dependence
misorientation
non-negligible Nernst contribution

7 deg

2 4 6 8 10

40
30
20
10

Ulong/ΔT T (K) (U+-U-)/(2ΔT) N(2T)

N (2T) (U+-U-)/2ΔT

SLIDE 19

Discussion: Thermopower

2 4 6 8 10

40
30
20
10

10 Ulong/ΔT T (K) + 2 T

2 T

variation due to

sample dependence
misorientation
non-negligible Nernst contribution

7 deg

2 4 6 8 10

40
30
20
10

Ulong/ΔT T (K) (U+-U-)/(2ΔT) N(2T)

first systematic study of S(T,B) including:

best available samples
precise orientation
correction for the Nernst signal

N (2T) (U+-U-)/2ΔT

SLIDE 20

Field-dep. Thermopower

1.5 2 3 4 5 6 7 89 10 20 30 40

40
20

20 40 CeNiSn #5, No. 3 q//b, B//a

0 T 1 T 2 T 4 T 7 T

S (µV/K) T (K)

B // a: - enhanced values of |S|

shift of the minimum to lower T

B // c:

similar, but less pronounced

literature:

strong sample

dependence at low T

no comparable results

in field

SLIDE 21

Discussion: Thermopower

2 4 6 8 1.5 2.0 2.5 3.0 3.5 B // a B // c Tmin (K) B (T)

position of the minimum

effect larger for B // a

SLIDE 22

Discussion: Thermopower

2 4 6 8 1.5 2.0 2.5 3.0 3.5 B // a B // c Tmin (K) B (T)

position of the minimum

effect larger for B // a
extrapolation // a: Bc = 14 T

(MR: 18 T)

shift ~ closing of the gap

SLIDE 23

Discussion: Thermopower

position of the minimum

effect larger for B // a
extrapolation // a: Bc = 14 T

(MR: 18 T)

shift ~ closing of the gap

(ΔE from tunneling spectroscopy)

2 4 6 8 1.5 2.0 2.5 3.0 3.5

8 10 12 14 16 18

B // a B // c Tmin (K) B (T)

ΔE

ΔE (meV)

T. Ekino et al., Physica B 230-232, 635 (1997)

SLIDE 24

Discussion: Thermopower

position of the minimum

effect larger for B // a
extrapolation // a: Bc = 14 T

(MR: 18 T)

shift ~ closing of the gap

(ΔE from tunneling spectroscopy)

2 4 6 8 1.5 2.0 2.5 3.0 3.5

8 10 12 14 16 18

B // a B // c Tmin (K) B (T)

ΔE

ΔE (meV)

T. Ekino et al., Physica B 230-232, 635 (1997)

2 4 6 8

50
45
40
35
30
25

B // a B // c Smin (µV/K) B (T)

value at the minimum

effect larger for B // a
change of the DOS near EF due

to Zeeman splitting (cP)

similar results for S(T) at low T
K. Izawa et al., J. Phys. Soc. Jpn. 65, 3119 (1996)
S. Paschen et al., Phys. Rev. B 62, 14912 (2000)

SLIDE 25

Discussion: Thermopower

F

ln

E

N S ε ∂ ∂ ∝

V-shaped DOS in field similar analysis for CP(T,B) (enhanced γ value in field)

increasing B

K. Izawa et al., J. Phys. Soc. Jpn. 65, 3119 (1996)

SLIDE 26

Results: Nernst effect

large values of N below 10 K (opening of the gap)

scaling for B // a (easy axis!)
shift of minimum for B // c

→ open question: weak sensitivity to magnetic fields // a q // b, B // a B // c

1.5 5 10 50

120
100
80
60
40
20

2 4 6 8 10

20
15
10
5

4 T 7 T 0.5 T 1 T 2 T

N (µV/K) T (K)

ν (µV/KT)

T (K)

1.5 5 10 50

120
100
80
60
40
20

2 4 6 8 10

15
10
5

5.5 T 7 T 1 T 2 T 3 T

N (µV/K) T (K)

ν (µV/KT)

T (K)

SLIDE 27

Discussion: Nernst effect

Boltzmann approximation:

F

* 3

2 B 2 n E

m T k N ε τ π ∂ ∂ =

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

xx yx

σ σ = ΘH tan

with Hall angle Large Nernst coefficient:

Low charge carrier concentration
Small Fermi energy

Nernst effect: νa = νn - εyy/κyy Lxy νn: normal Nernst coeff. νa: adiabatic Nernst coeff. due to transverse temp. gradient For CeNiSn, ΔTy ≈ 0, Lxy ≈ 0 (below resolution limit) → νa = νn

νn νn

SLIDE 28

Discussion: Nernst effect

N

Behnia et al., Phys. Rev. Lett. 98, 076603 (2007)

How to obtain large Nernst coefficients?

SLIDE 29

Discussion: Nernst effect

N

Bi normal semimetal

Behnia et al., Phys. Rev. Lett. 98, 076603 (2007)

How to obtain large Nernst coefficients?

SLIDE 30

Discussion: Nernst effect

N

Bi normal semimetal PrFe4P12 URu2Si2 correlations, unconventional

rder

Behnia et al., Phys. Rev. Lett. 98, 076603 (2007)

How to obtain large Nernst coefficients?

SLIDE 31

Discussion: Nernst effect

N

Bi normal semimetal PrFe4P12 URu2Si2 correlations, unconventional

rder

CeRu2Si2 CeCoIn5 enhanced mass

Behnia et al., Phys. Rev. Lett. 98, 076603 (2007)

How to obtain large Nernst coefficients?

SLIDE 32

Discussion: Nernst effect

N

Bi normal semimetal PrFe4P12 URu2Si2 correlations, unconventional

rder

CeRu2Si2 CeCoIn5 enhanced mass NbSe2 bipolar Nernst effect

Behnia et al., Phys. Rev. Lett. 98, 076603 (2007)

How to obtain large Nernst coefficients?

SLIDE 33

Discussion: Nernst effect

Boltzmann approximation:

F

* 3

2 B 2 n E

m T k N ε τ π ∂ ∂ =

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

BUT: CeNiSn with two types of charge carriers

xx yx

σ σ = ΘH tan

with Hall angle

SLIDE 34

Discussion: Nernst effect

Boltzmann approximation:

F

* 3

2 B 2 n E

m T k N ε τ π ∂ ∂ =

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

BUT: CeNiSn with two types of charge carriers

xx yx

σ σ = ΘH tan

with Hall angle

B

Hall effect

j

V. Oganesyan and I. Ussishkin, Phys. Rev. B 70, 054503 (2004)
A. Pourret et al., Phys. Rev. Lett. 96, 176402 (2006)

B

Nernst effect

q

SLIDE 35

B

Discussion: Nernst effect

Boltzmann approximation:

F

* 3

2 B 2 n E

m T k N ε τ π ∂ ∂ =

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

BUT: CeNiSn with two types of charge carriers

xx yx

σ σ = ΘH tan

with Hall angle

B

Hall effect

B

Nernst effect

q

V. Oganesyan and I. Ussishkin, Phys. Rev. B 70, 054503 (2004)
A. Pourret et al., Phys. Rev. Lett. 96, 176402 (2006)

j

SLIDE 36

Discussion: Nernst effect

1.5 5 10 50

120
100
80
60
40
20

2 4 6 8 10

20
15
10
5

4 T 7 T 0.5 T 1 T 2 T

N (µV/K) T (K)

ν (µV/KT)

T (K)

q // b, B // a

1.5 5 10 50

0.04
0.02

0.00

CeNiSn No.3 j // b, B // a

RH (cm

3/C)

T (K)

1 T 2 T 4 T 7 T

sign change in RH but not in N

SLIDE 37

Discussion: Nernst effect

1.5 5 10 50

120
100
80
60
40
20

0.5 T 1 T 2 T 4 T 7 T

N (µV/K) T (K)

q // b, B // a relevant mechanism:

pening of the gap ↔

enhanced values of N low Fermi energy TK TK Tgap

SLIDE 38

Discussion: Nernst effect

ν ~ T/B tan ΘH Increase below Tg No scaling Hall coefficient stronger suppressed in field

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

xx yx

σ σ = ΘH tan

νn

SLIDE 39

Discussion: Nernst effect

ν ~ S/B tan ΘH Increase below Tg No scaling Maximum in S tan ΘH shifts in contrast to N/B → Multiband effects must be included

F H 2 B 2 n

tan 3 E Be T k N Θ ≈ π

νn

SLIDE 40

Discussion: Nernst effect

CeNiSn N T (K)

CeNiSn

ν

CeNiSn ( = 2 K) T CeNiSn ( = 2 K) T PrFe P

4 12

PrFe P

4 12

T = 1.2 K NB Z T =

mag

CeNiSn (T = 2K) CeNiSn (2K)

νB (µV/K) ZmagT = (N2σT)/κ

ZmagT: Low, since high κ (single crystals) High, since small MR

SLIDE 41

Discussion: Nernst effect

CeNiSn N T (K)

CeNiSn ν

ZmagT: Low, since high κ (single crystals) High, since small MR

CeNiSn ( = 2 K) T CeNiSn ( = 2 K) T PrFe P

4 12

PrFe P

4 12

T = 1.2 K NB Z T =

mag

CeNiSn (T = 2K) CeNiSn (2K)

νB (µV/K) ZmagT = (N2σT)/κ

1.5 5 10 50 50 100 150 200

0 T 1 T 2 T 4 T 7 T

ρ (μΩ cm)

T (K)

CeNiSn No.3 j // b, B // a

SLIDE 42

Summary

thermopower:

first systematic study of S(T,B) taking into account the Nernst signal
reported sample dependence partly due to misorientation/ Nernst signal
low-T thermopower governed by the pseudogap opening
Unusal field dependence due to gap closing and Zeeman splitting

SLIDE 43

Summary

thermopower:

first systematic study of S(T,B) taking into account the Nernst signal
reported sample dependence partly due to misorientation/ Nernst signal
low-T thermopower governed by the pseudogap opening
Unusal field dependence due to gap closing and Zeeman splitting

Nernst coefficient:

large signal below gap opening
scaling for B//a
high relevance of the pseudogap
potential of correlated semiconductors for Ettingshausen cooling (low

ρ(B))