Study of Magnetic Ordering in YbPd

1. 1/13 Study of Magnetic Ordering in YbPd • Reference • R.Pott et al, Phys.Rev.Lett.54, 481-484 (1985) Kazuki Kasano Shimizu Group 2008 5.28 Wed M1 Colloquium

2. 2/13 Contents • Introduction - Heavy fermion compounds - Motivation • Measurements • Results • Summary • My study （重い電子系化合物）

3. Introduction C/T 0 T2 3/13 • Difference of specific heat Heavy fermion compounds Normal metal CexLa1-xCu6 Increase C/T (J/K2・mol) Decrease log10T γ : Electronic specific heat AT2 : Lattice specific heat Electronic specific heat is different from normal metal ! 三宅和正 著 「重い電子とは何か」 岩波書店

4. Introduction 4/13 • Electronic specific heat 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. = Heavy !! m becomes large.

5. Introduction n(r) r/rB n(r) : Distribution of electrons rB : Bohr radius（ボーア半径） 5/13 • Ce, Yb Ce 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f1 5s2 5p6 5d1 6s2 Xe shell Ce (局在) Localized or conduction electron ? Conduction electrons Part of 4f electrons are mixed with conduction electrons ! RKKY interaction and Kondo effect

6. Introduction 6/13 • Two interactions • RKKY interaction • Kondo effect Conduction electron’s spin 4f electron’s spin Spin singlet state (スピン一重項基底状態) RKKY interaction makes spin stable ! Kondo effect quenches spin ! (遮蔽する)

7. Introduction 7/13 • Competition In Ce and Yb compounds... At low temperature(～10 K), magnetic ordering occurs. At high temperature, there is no magnetic ordering. RKKY interaction is dominant. Kondo effect is dominant. Competition ! (競合)

8. Introduction Ce compounds Magnetic ordering has been found frequently. Yb compounds There had been few magnetic ordering. 8/13 • Motivation YbPd, Yb3Pd4, YbIr2

9. 9/13 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)

10. T(K) C(J/mol・K) ΔC(J/mol・K) T(K) 10/13 Results • Specific heat and thermal expansion 125K 1.9K 105K Δα(10-6K-1) α(10-6K-1) 125K 1.9K 105K T(K) • These anomalies are structural. • They are found at the same • temperatures the case of • specific heat. • Specific heat is larger than LuPd. • Some anomalies are found.

11. Results H =1.72(mGauss) χ(emu/mol) ρ(10-6Ωcm) T(K) T(K) 11/13 • Electrical resistivity and magnetic susceptibility 1.9K 0.5K 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.

12. 12/13 Summary YbPd • 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.

13. My study 13/13 YbPd Kondo effect RKKY interaction Competition Pressure What happen...?

14. Appendix • Effective mass In vacuum In crystal m* Electron Force Interaction with lattice m changes ! This is effective mass.

15. Appendix • Doniach phase diagram kBT JcfDc(εF) Jcf : c-f Exchange interaction Dc(εF) : Density of state at Fermi energy

16. Valence T(K) Appendix • Calculation of valence （価数） 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)