Quasparticle Spin Susceptibility in Heavy-Fermion Superconductors: An NMR Study Compared with Specific Heat Results

Abstract

Quasi-particle spin susceptibility (χ qp ) for various heavy-fermion (HF) superconductors are discussed on the basis of the experimental results of NMR Knight shift (K), NMR relaxation rate (1/T1), and electronic specific heat (γ el ) within the framework of the Fermi liquid model for a Kramers doublet crystal electric field (CEF) ground state. χγ is calculated from the enhanced Sommerfeld coefficient γ el , and χT 1 from the quasi-particle Korringa relation T1T (KT 1 ) 2 = const. via the relation of χT 1 = (NAµB/A hf )KT 1 where A hf is the hyperfine coupling constant, NA the Abogadoro's number and µB the Bohr magneton. For the even-parity (spin-singlet) superconductors CeCu2Si2, CeCoIn5 and UPd2Al3, the fractional decrease in the Knight shift, δK obs = K obs (Tc) − K obs (T → 0), below the superconducting transition temperature (Tc) is due to the decrease of the spin susceptibility of heavy quasi-particle estimated consistently from χγ and χT 1 . This result allows us to conclude that the heavy quasi-particles form the spin-singlet Cooper pairs in CeCu2Si2, CeCoIn5 and UPd2Al3. On the other hand, no reduction in the Knight shift is observed in UPt3 and UNi2Al3, nevertheless the estimated values of χγ and χT 1 are large enough to be probed experimentally. The odd-parity superconductivity is therefore concluded in these compounds. The NMR Knight shift result provides a convincing way to classify the HF superconductors into either even-or odd-parity pairing.

Spin Dynamics in UBe13:9Be-NMR Studies

“…In the heavy fermion system, since θ is almost comparable to the Kondo temperature T K , the Kondo temperature is roughly obtained as T K ≈ 35 K. On the other hand, the temperature dependence of [13]. Actually the enhancement factor from the non-interacting Korringa product, [14,15], at 2 K is obtained to be ≈ 2, indicating the existence of antiferromagnetic spin fluctuations at a finite q. For the two-channel quadrupole Kondo mechanism with the non magnetic Γ 3 CEF ground state, the magnetic response at low temperatures in the Γ 3 CEF ground state arises from the Van Vleck type magnetic excitations [5,6].…”

Evaluation of Spin-Triplet Superconductivity in Sr2RuO4

“…12,13) Recent progress in the studies of ferromagnetic heavy-fermion superconductors such as UGe 2 , 14) URhGe, 15) and UIr, 16) and in particular UCoGe, 17) motivates researchers to seek for obtaining direct evidence for spin-triplet pairing. Among the organic superconductors, possible spintriplet pairing in quasi-one-dimensional superconductors (TMTSF) 2 X (X ¼ ClO 4 and PF 6 ) has been considered.…”

Odd parity and line nodes in nonsymmorphic superconductors

“…In contrast, this restriction does not exist for an even parity order parameter. There are, though, several heavy fermion superconductors where Knight shift data indicate that the Cooper pair spins are in a triplet state, yet thermodynamic measurements imply the existence of a line of nodes [5].The aim of the present paper is to investigate the generality of Blount's arguments. Specifically, we show that in crystals with a twofold screw axis, line nodes are possible whenever the Fermi surface intersects the Brillouin zone face perpendicular to this axis, even in the presence of spin-orbit interactions.…”

“…Again, the Knight shift suggests a spin triplet state [5], while measurements of the NMR relaxation rate find a power law consistent with the presence of a line of nodes [20]. UBe 13 has the nonsymmorphic space group F m3c that has twofold screw axes perpendicular to the square faces of the face centered cubic zone.…”