Coherent Kondo State in a Dense Kondo Substance : Ce x La 1-x Cu 6 A.Sumiyama et al., J.Phys.Soc.Jpn.55(1986) Shimizu-group Katsuya TOKUOKA

Contents Introduction ■ Dilute Kondo effect ■ Coherent Kondo effect Experimental data about Ce x La 1-x Cu 6 Summary

The simple metallic resistivity Impurity scattering T (K) 10 2 R / R 290K Residual resistivity （残留抵抗 ） The resistivity decreases monotonically as the temperature decreases. potassium C.Kittel Introduction to Solid State Physics

Kondo effect Discovery of the resistivity minimum in dilute magnetic alloys( 希薄磁性合金 ).(1930’s) The electrical resistivity increases steeply as the temperature decreases In the low temperature region. Jun Kondo has derived the logarithmic increase of the resistivity in the low temperature region. (1964) → 40 th anniversary in 2004 ! de Haas et al., Physica 1 (1934)

Dilute Kondo effect( 希薄系近藤効果 ) T > T K T < T K But this Kondo effect does not appear if the metal contains a large amount of magnetic impurities. Spin singlet ( スピン一重項 ) S = 0 de Haas et al., Physica 1 (1934) 1115 T K : 近藤温度

A new type Kondo effect In Ce compounds, although it contains a large amount of magnetic impurities (>10%), Kondo effect appeared. Y.Ōnuki et al., J.Phys.Soc.Jpn. 53 (1984) Temperature dependence of resistivity in CeCu6

f - electron |r R(r)| 2 r (a.u.) Lanthanoides La 3+ Ce 3+ Pr 3+ … 4f-electrons Closed shell 5s 2 5p 6 f - electron is localized.

Coherent (Dense) Kondo effect ( 高濃度近藤効果 ) T > T K T < T K f-localized ( 局在 ) f-itinerant ( 遍歴 ) In Ce compounds, the Kondo effect appears. Y.Ōnuki et al., J.Phys.Soc.Jpn. 53 (1984) Heavy fermion state ( 重い電子状態 ) Dilute

Coherent Kondo substance CeCu 6 Coherent Kondo substance Pauli paramagnet ( パウリ常磁性 ) (no magnetic ordering) Large specific heat coefficient ( 電子比熱係数 ) Crystal structure of CeCu6 Y.Onuki et al., J.Phys.Soc.Jpn. 54 (1985) γ= 1.6 J / mole·K 2 The effective mass ( 有効質量 ) is 1000 times or more as large as the free electron mass !

Motivation LaCu6 is a normal metal which has the same structure. (no f – electrons) To clarify the process from the incoherent Kondo state to the coherent Kondo state, we can investigate the compound : Ce x La 1-x Cu 6 (x=0-1). Dilute (incoherent) Dense(Coherent) Ce density x : 0 1

Experiment Single crystals of Ce x La 1-x Cu 6 were grown by the Czochralski pulling method. a large single crystal ! Measurements ・ electrical resistivity from 300 K~ 18 mK ・ magnetoresistance ( 磁気抵抗効果 )

Temperature dependence of electrical resistivity Electrical resistivity increases as temperature increases in the low temperature region. A maximum appeared around 5-15 K for an x value of f-electrons are itinerant in the low temperature region. Temperature dependence of electrical resistivity in Ce x La 1-x Cu 6

Magnetic resistivity ρ m = ρ Ce x La 1-x Cu 6 - ρ LaCu 6 (magnetic resistivity) ρ( T ) = ρ 0 + ρ e-e (T) + ρ m (T) The normal metal ρ( T ) = ρ 0 + ρ e-e (T) (Matthiessen’s rule) The magnetic substance

Magnetic resistivity Dilute x = – 0.50 Coherent x = 0.73 – 1.0 Consecutive change from dilute to coherent Temperature dependence of magnetic resistivity in Ce x La 1-x Cu 6

Magnetoresistance A effective method to investigate heavy fermion system In normal metal Cyclotron motion → The resistivity increases. Heavy fermion system magnetization → The resistivity decreases due to magnetic ordering. Ｉ H b c a

Magnetic field dependence of resistivity Magnetoresistance at 1.5 K Dilute Kondo system ρhas a Maximum around 20 kOe. Because of the suppression of the coherent Kondo effect, the resistivity increases. Itinerant localized The coherent Kondo effect is suppressed by applied magnetic field. Magnetic field dependence of resistivity in CeCu 6

Summary Dilute Kondo effect appears for x = – Coherent Kondo effect appears for x = 0.73 – 1.0. Consecutive change from dilute Kondo state to coherent Kondo state occurs. The coherent Kondo effect is suppressed by applying a magnetic field.