Kazuki Kasano

Shimizu Group

2008 5.28 Wed M1 Colloquium

Study of Magnetic Ordering in YbPd

Reference•R.Pott et al, Phys.Rev.Lett.54, 481-484 (1985)

1/13

Contents

Introduction - Heavy fermion compounds - Motivation

Measurements

Results

Summary

My study

（重い電子系化合物）

2/13

Introduction

Difference of specific heat

Normal metal

2/ ATTC

γ : Electronic specific heatAT2 : Lattice specific heat

C/T

T20

Heavy fermion compounds

CexLa1-

xCu6

log10

T

C/T

(J/K

2・

mol)

Decrease

Increase

三宅和正 著 「重い電子とは何か」 岩波書店

Electronic specific heat is differentfrom normal metal !

3/13

Introduction

Electronic specific heat

3

1

nmCElectronic

Electronic specific heat is given by free electron model.

m : effective mass of electrons （電子の有効質量）n : density of electrons （電子密度）

Electronic specific heat becomes large.

m becomes large.=Heavy !!

4/13

Introduction

Ce, Yb

Ce1s2

2s2 2p6

3s2 3p6 3d10

4s2 4p6 4d10 4f1

5s2 5p6 5d1

6s2

Xe shell

Localized or conductionelectron ?

Conduction electrons

n(r)

r/rBn(r) : Distribution of electronsrB : Bohr radius （ボーア半径）

Ce

Part of 4f electrons are mixed withconduction electrons !

RKKY interaction and Kondo effect

5/13

( 局在 )

Introduction

Two interactions

4f electron’s spin

Conduction electron’s spin

Spin singlet state

Kondo effect quenches spin !

Kondo effect RKKY interaction

RKKY interaction makesspin stable !

6/13

( スピン一重項基底状態 )

( 遮蔽する )

Introduction

Competition

In Ce and Yb compounds...

At high temperature,

there is no magnetic ordering.

At low temperature( ～ 10 K),

magnetic ordering occurs.

Kondo effect is dominant.RKKY interaction is dominant.

Competition !

7/13

( 競合 )

Introduction

Motivation

YbPd, Yb3Pd4, YbIr2

There had been few magnetic ordering.

Yb compounds

Magnetic ordering has been found frequently.

Ce compounds

8/13

Measurements

Specific heat (T = 1.5 ～ 300 K)

Thermal expansion (T = 1.5 ～ 300 K)

Electrical resistivity (T = 40 mK ～ 300 K)

Magnetic susceptibility (T = 40 mK ～ 300 K, H = 1.72 mGauss)

9/13

Results

T(K)

ΔC

(J/m

ol・

K)

T(K)

C(J/m

ol・

K)

T(K)Δ

α(1

0-6K

-1)

α(1

0-6K

-1)

Specific heat and thermal expansion125K

105K1.9K

125K105K

1.9K

•Specific heat is larger than LuPd.•Some anomalies are found.

•These anomalies are structural.•They are found at the same temperatures the case of specific heat.

10/13

Results

T(K)

ρ(1

0-6Ω

cm)

T(K)

χ(em

u/m

ol)

H =1.72(mGauss)

Electrical resistivity and magnetic susceptibility

0.5K

1.9K

0.5K

•Electrical resistivity is larger than LuPd.•At 0.5 K, a new anomaly is found.

•About under 2 K , the magnetic ordering occurs.•A hysteresis is found at 0.5 K.

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Summary

At high temperature

• Kondo effect is dominant and there is no magnetic ordering.• Two structural phase transitions are found at 125 , 105 K.

At low temperature

• RKKY interaction overcomes Kondo effect and magnetic ordering occurs at about 2 K .

• Magnetic phase transition is found at 0.5 K.

YbPd

12/13

My study13/13

Kondo effect RKKY interaction

Competition

YbPd

Pressure

What happen...?

Appendix

Electron

kg10110.9 31m

Force Interactionwith lattice

m changes !

This is effective mass.

m*

Effective mass

In vacuum In crystal

Appendix

JcfDc(εF)

k BT

)(2FccfRKKYB DJTk

))(

1exp(

FccfKB DJ

Tk

Jcf : c-f Exchange interactionDc(εF) : Density of state at Fermi energy

Doniach phase diagram

Appendix

Vale

nce

T(K)

Calculation of valence

Anomalies at 125K and 105K should be structural.They falsify the valence determination with the volume anomaly.As a result, YbPd become mixed-valent state.(Valence changes 2.82 at 300K to 2.80 near 0K)

（価数）