Microscopic aspects of magnetism and superconductivity have been studied in the heavy-fermion superconducting alloy systems (U,Th)${\mathrm{Be}}_{13}$ and (U,Th)${\mathrm{Pt}}_3$ using the technique of positive-muon (${\mu }^{+}$) spin rotation and relaxation (μSR). In ${\mathrm{U}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Th}}_{\mathrm{x}}$${\mathrm{Be}}_{13}$, x=0.033, a striking increase of zero-field Kubo-Toyabe relaxation rate ${\sigma }_{\mathrm{KT}}$ is observed below the temperature $T_{c2}$≃0.4 K at which a second phase transition occurs in the superconducting state. This jump is firm evidence for the onset of weak static magnetism below $T_{c2}$. The observed increase of ∼1.5 Oe in the ${\mu }^{+}$ local field corresponds to an effective moment of ${10}^{\mathrm{-}3}$–${10}^{\mathrm{-}2}$ ${\mu }_B$/U atom.

The ${\mu }^{+}$ Knight shift $K_{\mu }$ in the normal states of ${\mathrm{U}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Th}}_{\mathrm{x}}$${\mathrm{Be}}_{13}$, x=0 and 0.033, is proportional to the bulk susceptibility and yields a transferred f-spin-${\mu }^{+}$ hyperfine field of -1.99±0.12 kOe/${\mu }_B$. In the superconducting states of ${\mathrm{U}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Th}}_{\mathrm{x}}$${\mathrm{Be}}_{13}$, x=0, 0.01, and 0.033, a large reduction of the magnitude of $K_{\mu }$ is observed for x=0 but not for x=0.033, and an intermediate reduction is found for x=0.01. This behavior suggests (1) spin-singlet pairing in undoped ${\mathrm{UBe}}_{13}$, and (2) conventional reduction of the spin susceptibility suppression in (U,Th)${\mathrm{Be}}_{13}$ by spin-orbit scattering from Th impurities. In undoped ${\mathrm{UPt}}_3$ small increases of ${\sigma }_{\mathrm{KT}}$ and the transverse-field Gaussian relaxation rate ${\sigma }_G$ below ∼6 K are again evidence for the onset of weak static magnetism similar to that found in (U,Th)${\mathrm{Be}}_{13}$. Recent spin-polarized neutron scattering studies of normal-state ${\mathrm{UPt}}_3$ have observed a commensurate antiferromagnetic (AF) structure with a sublattice magnetization of ∼${10}^{\mathrm{-}2}$ ${\mu }_B$/U atom, in rough agreement with the μSR results. For ${\mathrm{U}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Th}}_{\mathrm{x}}$${\mathrm{Pt}}_3$, x=0.05, zero-field ${\mu }^{+}$ precession frequencies below 6.5 K indicate an AF structure with a considerably larger moment (∼0.6 ${\mu }_B$/U atom). The average ${\mu }^{+}$ Knight shift in the normal state of undoped ${\mathrm{UPt}}_3$ is much smaller than in ${\mathrm{UBe}}_{13}$, which suggests multiple ${\mu }^{+}$ stopping sites with hyperfine couplings of opposite signs.

• Received 7 November 1988

DOI:https://doi.org/10.1103/PhysRevB.39.11345