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

Janez Dolinšek FMF 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 insulator Combination 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 Mg 32 (Al,Zn) 49

quasicrystals YbCu 4.5

Ψ-Al-Pd-Mn β-Al 3 Mg 2 λ-Al 4 Mn Al 39 Fe 2 Pd 21 Mg 32 (Al,Zn) 49 Re 14 Al 57 elem. metals ∞ 7448 at. / u. c.

1480 at. / u. c.

1168 at. / u. c.

586 at. / u. c.

248 at. / u. c.

162 at. / u. c.

71 at. / u. c.

<5 at. / u. c.

Quasicrystals

• Discovered in1984 • Thermodynamically stable samples have appeared after 1990 • Well-ordered but nonperiodic solids • Diffraction patterns with non-crystallographic point symmetry Periodic tiling Penrose tiling (quasiperiodic) Diffraction pattern of a decagonal quasicrystal

Sample preparation

Bridgman method Czochralski method Flux-grown method •The first solidification zone •Coexistence of solid and liquid phases Single-crystal is cut in bar-shaped samples

Czochralski method Al-Co-Ni decagonal QC

Experimental methods Magnetization and magnetic susceptibility measurement

  M H

… magnetic susceptibility

SQUID magnetometer 5 T

Experimental methods Measurement of the electrical conductivity

Electrical resistance: R

=

U

/

I Specific resistivity:

 

R l S

PPMS – Physical Property Measurement System 9 T

Experimental methods Thermoelectric effect

Experimental methods Measurement of the thermoelectric power



U



S



T

Thermal conductivity measurement j

q 

P S

    

T

Experimental methods Measurement of the Hall coefficient Hall coefficient

R

H

 1

ne R

H   H

B



j

x

E

y 

B



U I

H  

B d

Magnetization vs. magnetic field Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe)

M



M

0

L

(  ,

H

,

T

) 

kH

FM contribution linear term

i-Al 64 Cu 23 Fe 13

ferromagnetic component

M



M

1

B

(

g

1 ,

J

1 ) 

M

2

B

(

g

2 ,

J

2 ) 

kH

Curie magnetizations linear term

Magnetic susceptibility Y-Al-Ni-Co i-Al 64 Cu 23 Fe 13 Al 4 (Cr,Fe)

temperature-independent term   

0j



T C j

 

j

Curie-Weiss susceptibility temperature-independent term  (

T

)   0 

T C

  

A

2

T

2 

A

4

T

4 Curie-Weiss susceptibility temperature-dependent correction

o-Al 13 Co 4

Electrical resistivity Y-Al-Ni-Co o-Al 13 Co 4

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

Electrical resistivity Al 4 (Cr,Fe)

 is nonmetallic with NTC slow charge carriers

v τ



L wp



e 2 j

 

Bj g

(  F )

v

 

NBj j 2



j

 

e 2 g

(  F )

L 2 j

 ( 

j j

) pseudogap in  (  ) specific distribution of Fe  (  ) 

A

   1      1  1  2   2 1         1      2  2  2   2 2     

i-Al 64 Cu 23 Fe 13

Thermoelectric power Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe) i-Al 64 Cu 23 Fe 13

Hall coefficient

• •

R

H values of QCs and CMAs are typical metallic

R

H ’s exhibits pronounced anisotropy • Fermi surface is strongly anisotropic • consists of hole-like and electron-like parts

Y-Al-Ni-Co Al 4 (Cr,Fe) o-Al 13 Co 4

Thermal conductivity

• • Total  is a sum of the electronic  el and the phononic  ph contribution  el is estimated from the Wiedemann-Franz law:  el

=



2 k

B

2 T



(T)/3e 2

• WF law valid when elastic scattering of electrons is dominant

Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe)

Thermal conductivity i-Al 64 Cu 23 Fe 13

electronic part hopping of localized vibrations  (

T

)   el (

T

)   D (

T

)   H (

T

) long wave phonons (Debye model) •  300K < 1.7 W/mK lower than SiO 2 (2.8 W/mK)

Thank you for your attention !