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
Mg32(Al,Zn)49
quasicrystals
YbCu4.5
Ψ-Al-Pd-Mn
β-Al3Mg2
λ-Al4Mn
Al39Fe2Pd21
Mg32(Al,Zn)49
Re14Al57
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
Al-Co-Ni decagonal QC
Czochralski method
Experimental methods
Magnetization and magnetic
susceptibility measurement
 
M
… magnetic susceptibility
H
SQUID magnetometer 5 T
Experimental methods
Measurement of the electrical
conductivity
Electrical resistance:
R = U/I
Specific resistivity:
S
 R
l
PPMS – Physical Property
Measurement System 9 T
Experimental methods
Thermoelectric effect
Experimental methods
Measurement of the
thermoelectric power
Thermal conductivity
measurement
U  ST
q
j 
P
S
    T
Experimental methods
Measurement of the
Hall coefficient
Hall coefficient
RH 
RH 
H
B

Ey
jx  B

UH d
I B
1
ne
Magnetization vs. magnetic field
Y-Al-Ni-Co
o-Al13Co4
M  M 0 L (  , H , T )  kH
FM contribution
linear term
i-Al64Cu23Fe13
Al4(Cr,Fe)
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-Al64Cu23Fe13
temperature-independent term
 (T )   0 
C
T 
Curie-Weiss
susceptibility
 A2T
temperature-independent term
   0j 
C
j
T 
j
Curie-Weiss
susceptibility
 A4T
4
temperature-dependent
correction
o-Al13Co4
Al4(Cr,Fe)
2
Electrical resistivity
Y-Al-Ni-Co
o-Al13Co4
PTC of the resistivity – predominant role of electron-phonon scattering
mechanism (Boltzmann type)
Electrical resistivity
Al4(Cr,Fe)
i-Al64Cu23Fe13
 is nonmetallic with NTC
slow charge carriers
vτ  L wp
 j   Bj   NBj 
L j ( j )
2
2
2
j
2
e g ( F ) v  j  e g ( F )

j
pseudogap in ()
specific distribution of Fe

 1
 ( )  A  
1


     1   
2
2
1

1
2

2
2

     2    2



 

Thermoelectric power
Y-Al-Ni-Co
Al4(Cr,Fe)
o-Al13Co4
i-Al64Cu23Fe13
Hall coefficient
• 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
Y-Al-Ni-Co
Al4(Cr,Fe)
o-Al13Co4
Thermal conductivity
• 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
Y-Al-Ni-Co
o-Al13Co4
Al4(Cr,Fe)
Thermal conductivity
i-Al64Cu23Fe13
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 SiO2 (2.8 W/mK)
Thank you for your attention !