Study of superconductivity on βpyrochlore KOs2O6 Kitaoka Lab. Hirofumi Naruwa Ref.) Z. Hiroi et al., Phys. Rev. B 76 (2007) 014523 M.Yoshida et al., Phys. Rev. Lett. 98 (2007) 197002 Contents ・Introduction Cage compounds Influence to Tc from the guest in the cage BCS superconductivity Crystal structure of KOs2O6 ・Experimental results & discussion Rattling of KOs2O6 1/T1T of KOs2O6 and RbOs2O6 Specific heat of KOs2O6 Superconductivity of KOs2O6 ・Summary Cage compounds Ag cage compound Ag6O8AgNO3 Introduction Silicon clathrate compounds NO3 Ag Si Ag6O8 cage ・Cage compounds have Polyhedral cages and guest molecules 多面体の inside the cages. ・Guest molecules influence the physical properties very much. Influence to Tc from the guest in the cage Ag6O8AgNO3 Ag6O8AgX Ag6O8cage Ag6O8cage NO3 X O Ｎ O Ag6O8AgHF2 Ag6O8cage Introduction Ag6O8AgBF4 Ag6O8cage BF4 HF2 F H F B O F Tc=1.04K 1.0 (cm) (cm) 0.8 80 Tc=1.38K F F F Tc=0.3K Ag O AgHF 6 8 2 (I = 0.1 mA) 0.6 60 0.4 40 0.2 20 0 0.5 Ag O AgNO 6 8 the superconducting property is affected by the presence of molecules inside the cages 3 (I = 1.0 mA) 1.0 1.5 T (K) 2.0 K. Kawashima et. al., JPSJ BCS superconductivity Introduction Cooper-pair electron-phonon coupling constant + λ λ Superconductivity is caused by the formation of Cooper-pairs. Hg 20 Nb3Sn 18 1.6 ⊿C/γTc 14 12 1.2 λ Nb Cn Ｔｃ(K) C/ γT Cs Sn 0.8 Nb 10 8 6 Hg Sn 4 Al 2 0.4 Al 0 1.4 T / Tc Nb3Sn 16 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 ⊿C (Tc)/γTc the jump of specific heat is a good measure for strength of the Cooper pairing interaction 0.4 0.6 0.8 1.0 1.2 1.4 1.6 λ Tc tends to be higher in the materials, which has a stronger Cooper pairing interaction 1.8 Crystal structure of KOs2O6 βpyrochlore KOs2O6 Introduction KOs2O6 O alkali metal RbOs2O6 K rattling OsO6 K CsOs2O6 from Hiroi Lab. HP KOs2O6 Tc=9.6K RbOs2O6 Tc=6.3K CsOs2O6 Tc=3.3K compare these three β pyrochlore materials to study why Tc of KOs2O6 is the highest Rattling of KOs2O6 Experimental results & discussion βpyrochlore KOs2O6 lattice constant Einstein frequency rattling ωE（Ｋ） rion K Cs Rb K lattice constant / rion 8 harmonic oscillation 7 6 5 4 K free space 3 2 phonon 1 rattling 0 Cs Rb K ⇒ Rattling would be prominent in K-compound. 1/T1T of KOs2O6 and RbOs2O6 Experimental results & discussion T1(Nuclear spin-lattice relaxation time) pulse magnetic field t YBa2Cu3O7 T1 Al (high-temperature cuprate superconductor) (BCS superconductor ) Coherent peak Tc 1/T1T=const 1/ T1 (s-1) 1/ T1 (s-1) external magnetic field ∝ T3 ∝ exp(-⊿/kBT) T(K) T(K) RbOs2O6,KOs2O6 Coherent peak ⇒BCS 1/T1T=const KOs2O6 RbOs2O6 87Rb-NMR 1/ T1∝ exp(-⊿/kBT) ⇒BCS 1/ T1∝ exp(-⊿/kBT) exp(-⊿/kBT ) specific heat of KOs2O6 Experimental results & discussion Hg Nb3Sn Cp/ T (mJ K-2mol-1) 1.6 1.2 λ Nb Sn 0.8 Al 0.4 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 ⊿C (Tc)/γTc Tc(Cs) Tc(Rb) Tc(K) T(K) λ increase Cs＜Rb＜K 20 18 Nb3Sn 16 14 Cs＜Rb＜K Ｔｃ(K) 12 Nb 10 Tc increase 8 6 Hg Sn 4 2 Al 0 0.4 0.6 0.8 1.0 1.2 λ 1.4 1.6 1.8 superconductivity of KOs2O6 βpyrochlore BCS 8 Experimental results & discussion lattice constant / rion 7 cage 6 5 4 K 3 rattling 2 free space 1 0 Cs Rb K phonon Rattling would be prominent in K-compound. ⇒Cs＜Rb＜K λ increase + λ K λ K This electron pair links more strongly than BCS one. coefficient of electronic specific heat K K harmonicitic potential anharmonicitic potential CsOs2O6 RbOs2O6 KOs2O6 effective mass large Summary Summary ・Free space for the guest atoms seem to influence superconductivity of βpyrochlore. ・ The results from specific heat and 1/T1T were different from those of BCS superconductors. It may be due to the rattling in free space.