Quasiparticle spin susceptibility in heavy-fermion superconductors : An NMR study compared with specific heat results

Hideki Tou; Kenji Ishida; Yoshio Kitaoka

doi:10.1143/JPSJ.74.1245

paper

Quasiparticle spin susceptibility in heavy-fermion superconductors : An NMR study compared with specific heat results

arXiv:cond-mat/0308562 · doi:10.1143/JPSJ.74.1245

Abstract

Quasi-particle spin susceptibility ( $χ^{q p}$ ) for various heavy-fermion (HF) superconductors are discussed on the basis of the experimental results of electronic specific heat ( $γ_{e l}$ ), NMR Knight shift ( $K$ ) and NMR relaxation rate ( $1/ T_{1}$ ) within the framework of the Fermi liquid model for a Kramers doublet crystal electric field (CEF) ground state. $χ_{γ}^{q p}$ is calculated from the enhanced Sommerfeld coefficient $γ_{e l}$ and $χ_{T_{1}}^{q p}$ from the quasi-particle Korringa relation $T_{1} T (K_{T_{1}}^{q p})^{2} = co n s t .$ via the relation of $χ_{T_{1}}^{q p} = (N_{A} μ_{B} / A_{h f}) K_{T_{1}}^{q p}$ where $A_{h f}$ is the hyperfine coupling constant, $N_{A}$ the Abogadoro's number and $μ_{B}$ the Bohr magneton. For the even-parity (spin-singlet) superconductors CeCu $_{2}$ Si $_{2}$ , CeCoIn $_{5}$ and UPd $_{2}$ Al $_{3}$ , the fractional decrease in the Knight shift, $δ K^{o b s}$ , below the superconducting transition temperature ( $T_{c}$ ) is due to the decrease of the spin susceptibility of heavy quasi-particle estimated consistently from $χ_{γ}^{q p}$ and $χ_{T_{1}}^{q p}$ . This result allows us to conclude that the heavy quasi-particles form the spin-singlet Cooper pairs in CeCu $_{2}$ Si $_{2}$ , CeCoIn $_{5}$ and UPd $_{2}$ Al $_{3}$ . On the other hand, no reduction in the Knight shift is observed in UPt $_{3}$ and UNi $_{2}$ Al $_{3}$ , nevertheless the estimated values of $χ_{γ}^{q p}$ and $χ_{T_{1}}^{q p}$ are large enough to be probed experimentally. The odd-parity superconductivity is therefore concluded in these compounds. The NMR result provides a convincing way to classify the HF superconductors into either even- or odd- parity paring together with the identification for the gap structure, as long as the system has Kramers degeneracy.

11 pages, 3 tables, 5 figures, RevTex4(LaTex2e)

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Coexistence of Antiferromagnetism and Superconductivity near the Quantum Criticality in Heavy Fermion Compound CeRhIn $_{5}$

Quasiparticle spin susceptibility in heavy-fermion superconductors : An NMR study compared with specific heat results

Abstract

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