1. Experimental methods for the determination of magnetic, electrical and thermal transport properties of condensed matter Janez Dolinšek FMF Uni-Ljubljana & J. Stefan Institute, Ljubljana

2. Magnetic, electrical and thermal transport properties -Magnetic susceptibility -Electrical resistivity -Thermoelectric power -Hall coefficient -Thermal conductivity

3. 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

4. Complex Metallic Alloys Intermetallic compounds Giant unit cells Cluster arrangement of atoms Inherent disorder: Configurational Chemical or substitutional Partial or split occupation quasicrystals∞ YbCu 4.5 7448 at. / u. c. Ψ-Al-Pd-Mn1480 at. / u. c. β-Al 3 Mg 2 1168 at. / u. c. λ-Al 4 Mn586 at. / u. c. Al 39 Fe 2 Pd 21 248 at. / u. c. Mg 32 (Al,Zn) 49 162 at. / u. c. Re 14 Al 57 71 at. / u. c. elem. metals<5 at. / u. c. Mg 32 (Al,Zn) 49

5. 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

6. Sample preparation Czochralski methodBridgman methodFlux-grown method Single-crystal is cut in bar-shaped samples The first solidification zone Coexistence of solid and liquid phases

7. Czochralski method Al-Co-Ni decagonal QC

8. Experimental methods Magnetization and magnetic susceptibility measurement … magnetic susceptibility SQUID magnetometer 5 T

9. Experimental methods Measurement of the electrical conductivity Electrical resistance: R = U/I Specific resistivity: PPMS – Physical Property Measurement System 9 T

10. Experimental methods Thermoelectric effect

11. Experimental methods Measurement of the thermoelectric power Thermal conductivity measurement

12. Experimental methods Measurement of the Hall coefficient Hall coefficient

13. Magnetization vs. magnetic field Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe) i-Al 64 Cu 23 Fe 13 FM contributionlinear term Curie magnetizations ferromagnetic component linear term

14. Magnetic susceptibility Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe) i-Al 64 Cu 23 Fe 13 Curie-Weiss susceptibility temperature-independent term temperature-dependent correction Curie-Weiss susceptibility temperature-independent term

15. Electrical resistivity Y-Al-Ni-Co o-Al 13 Co 4 PTC of the resistivity – predominant role of electron-phonon scattering mechanism (Boltzmann type)

16. Electrical resistivity Al 4 (Cr,Fe)i-Al 64 Cu 23 Fe 13  is nonmetallic with NTC slow charge carriers pseudogap in  (  ) specific distribution of Fe

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

18. Hall coefficient Y-Al-Ni-Co o-Al 13 Co 4 Al 4 (Cr,Fe) 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

19. Thermal conductivity Y-Al-Ni-Coo-Al 13 Co 4 Al 4 (Cr,Fe) 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

20. Thermal conductivity i-Al 64 Cu 23 Fe 13 long wave phonons (Debye model) electronic part hopping of localized vibrations  300K < 1.7 W/mK lower than SiO 2 (2.8 W/mK)

21. Thank you for your attention !