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

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

Introduction  Difference of specific heat Normal metal γ : Electronic specific heat AT 2 : Lattice specific heat C/T T2T2 0 Heavy fermion compounds Ce x La 1- x Cu 6 log 10 T C/T (J/K 2 ・ mol) Decrease Increase 三宅和正 著 「重い電子とは何か」 岩波書店 Electronic specific heat is different from normal metal ! 3/13

Introduction  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. m becomes large. = Heavy !! 4/13

Introduction  Ce, Yb Ce 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 1 5s 2 5p 6 5d 1 6s 2 Xe shell Localized or conduction electron ? Conduction electrons n(r) r/r B n(r) : Distribution of electrons r B : Bohr radius （ボーア半径） Ce Part of 4f electrons are mixed with conduction electrons ! RKKY interaction and Kondo effect 5/13 ( 局在 )

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

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

Introduction  Motivation YbPd, Yb 3 Pd 4, YbIr 2 There had been few magnetic ordering. Yb compounds Magnetic ordering has been found frequently. Ce compounds 8/13

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) 9/13

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

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

Summary  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. YbPd 12/13

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

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

Appendix J cf D c (ε F ) kBTkBT J cf : c-f Exchange interaction D c (ε F ) : Density of state at Fermi energy  Doniach phase diagram

Appendix Valence T(K)  Calculation of valence 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) （価数）