Experimental methods for the determination of magnetic, electrical and thermal transport properties of

condensed matterJanez DolinšekJanez Dolinšek

FMF Uni-Ljubljana & J. Stefan Institute, LjubljanaFMF Uni-Ljubljana & J. Stefan Institute, Ljubljana

Magnetic, electrical and thermal transport properties

- Magnetic susceptibility- Electrical resistivity- Thermoelectric power- Hall coefficient- Thermal conductivity

Introduction

• Why to measure magnetic, electrical and thermal transport properties of solid materials ?

• Ever-present demand for new materials with novel/improved physical-chemical-mechanical properties• Novel materials preparation techniques were developed• High-quality single crystals available

• Complex metallic alloys (CMAs) and quasicrystals (QCs) offer unique physical properties or combinations of properties

Electrical conductor + thermal insulatorCombination of hardness + elasticity+ small friction coefficient

• Potential applications in high technology

Complex Metallic Alloys

• Intermetallic compounds• Giant unit cells• Cluster arrangement of atoms• Inherent disorder:

• Configurational• Chemical or substitutional• Partial or split occupation

quasicrystals ∞YbCu4.5 7448 at. / u. c.Ψ-Al-Pd-Mn 1480 at. / u. c.β-Al3Mg2 1168 at. / u. c.λ-Al4Mn 586 at. / u. c.Al39Fe2Pd21 248 at. / u. c.Mg32(Al,Zn)49 162 at. / u. c.Re14Al57 71 at. / u. c.elem. metals <5 at. / u. c.

Mg32(Al,Zn)49

Quasicrystals

• Discovered in1984

• Thermodynamically stable samples have appeared after 1990

• Well-ordered but nonperiodic solids

• Diffraction patterns with non-crystallographic point symmetry

Penrose tiling (quasiperiodic)Periodic tiling Diffraction pattern of a decagonal quasicrystal

Sample preparation

Czochralski methodBridgman method Flux-grown method

Single-crystal is cut in bar-shaped samples

•The first solidification zone

•Coexistence of solid and liquid phases

Czochralski method

Al-Co-Ni decagonal QC

Experimental methods

Magnetization and magnetic susceptibility measurement

H

M … magnetic susceptibility

SQUID magnetometer 5 T

Experimental methods

Measurement of the electrical conductivity

Electrical resistance:

R = U/I

l

SR

Specific resistivity:

PPMS – Physical Property Measurement System 9 T

Experimental methods

Thermoelectric effect

Experimental methods

Measurement of the thermoelectric power

Thermal conductivity measurement

TS

P qj

TSU

Experimental methods

Measurement of the Hall coefficient

BI

dU

Bj

E

BR

H

x

yHH

Hall coefficient

neH1

R

Magnetization vs. magnetic fieldY-Al-Ni-Co o-Al13Co4

Al4(Cr,Fe)

i-Al64Cu23Fe13

kHTHLMM ),,(0

kHJgBMJgBMM ),(),( 222111

FM contribution linear term

Curie magnetizations

ferromagnetic component

linear term

Magnetic susceptibilityY-Al-Ni-Co

o-Al13Co4Al4(Cr,Fe)

i-Al64Cu23Fe13

44

220)( TATA

T

CT

j

j0j T

C

Curie-Weisssusceptibility

temperature-independent term

temperature-dependent correction

Curie-Weisssusceptibility

temperature-independent term

Electrical resistivityY-Al-Ni-Co o-Al13Co4

PTC of the resistivity – predominant role of electron-phonon scattering mechanism (Boltzmann type)

Electrical resistivityAl4(Cr,Fe) i-Al64Cu23Fe13

is nonmetallic with NTC

slow charge carriers

j

j2j2

j2j

2

NBjBjj

Lgevge

)(

)()( FF

wpLvτ

pseudogap in ()

22

22

2

21

21

1 11)(

A

specific distribution of Fe

Thermoelectric power Y-Al-Ni-Co o-Al13Co4

Al4(Cr,Fe) i-Al64Cu23Fe13

Hall coefficient

Y-Al-Ni-Co o-Al13Co4Al4(Cr,Fe)

• RH values of QCs and CMAs are typical metallic

• RH’s exhibits pronounced anisotropy

• Fermi surface is strongly anisotropic

• consists of hole-like and electron-like parts

Thermal conductivity

Y-Al-Ni-Co o-Al13Co4 Al4(Cr,Fe)

• Total is a sum of the electronic el and the phononic ph contribution

• el is estimated from the Wiedemann-Franz law: el=2kB2T(T)/3e2

• WF law valid when elastic scattering of electrons is dominant

Thermal conductivity

i-Al64Cu23Fe13

)()()()( HDel TTTT

long wave phonons

(Debye model)

electronic part hopping of localized vibrations

• 300K < 1.7 W/mK lower than SiO2 (2.8 W/mK)

Thank you for your attention !