W. F. Lankford

The depolarization and diffusion of μ+ in chromium

Precession of polarized positive muons is used to probe internal magnetic fields in a polycrystalline sample of high purity chromium. A depolarization, or damping in time, of the precession oscillation is observed in the antiferromagnetic states between 77 K and 312 K. The results are used to obtain the temperature dependence of the muon diffusion rates, with the assumption that the local fields are of dipolar origin.

The localization and thermal diffusion of positive muons in niobium

The depolarization rate for spin polarized μ+ particles implanted into a high purity niobium crystal was studied as a function of temperature. The results were analyzed in terms of nuclear dipolar field inhomogeneity due to the host93Nb, and the local field averaging effect of the muons motion. An analysis is presented in terms of the structure of the muon wavefunction and parameters characterizing the muon diffusion.

Static magnetic ordering of CeCu2.1Si2 found by muon spin relaxation

Abstract Zero- and longitudinal-field muon spin relaxation measurements on a poly-crystal sample of a heavy-fermion superconductor CeCu2.1Si2 ( Tc = 0.7 K) have revealed an onset of static magnetic ordering below T ∼ 0.8 K. The line shapes of the observed spectra in zero field indicate a wide distribution of static random local fields at muon sites, suggesting that the ordering is either spin glass or incommensurate spin-density-wave state. The observed width of the random local field at T = 0.05 K corresponds to a small averaged static moment of the order of 0.1μB per formula unit.

Sites and diffusion for muons and hydrogen in titanium hydrides

Low temperature sites for muons implanted in TiHx have been found to be a mixture of interstitial and substitutional sites, with substitutional occupancy determined by the probability that a muon in an interstitial site will have a vacant nearest neighbor substitutional site. As with ZrHx, activation from the interstitial site is observed below 300 K. From the depolarization rate in the substitutional site, the muon likely displaces the neighboring H atoms by about 0.1 A. Diffusion for the substitutional muons occurs above room temperature with an activation of about 0.38 eV, which is less than the 0.505 eV for hydrogen vacancy motion observed by NMR. To explain this the muon transition rate to a vacancy must be less than that of hydrogen.

On the study of defects in metals with positive muons

The technique of positive muon spin depolarization is reviewed, and its sensitivity to the presence of defects in metals is discussed. Results are presented of an experimental survey on copper, aluminum, indium and beryllium. There are indications of μ+ trapping at defects in neutron-irradiated and deformed copper, in indium near its melting point, and in beryllium. The results are discussed in the context of muon diffusion.

Muon Diffusion in Nb-H Systems

We have studied the muon diffusion in various Nb−HX systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ+ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.

Muon spin rotation in iron and its dilute alloys

Muon spin rotation measurements are reported for iron and its dilute alloys. The average local field seen by the muon diffusing among interstitial sites is corrected for the Lorentz cavity field to extract the average hyperfine field. The rate of change of hyperfine field with solute concentration at room temperature is given for iron alloyed with N, Al, Si, Ge, Ti, V, Cr, Mn, Co, Ni, Mo, and W. The origin of strain sensitivity of the average local field is discussed using results on the effects of applied fields on polycrystalline and single crystal samples.

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu2.1Si2, the relaxation rate of muon spins increases rapidly with decreasing temperature below TC. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5TC, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift Kμ in the normal (or paramagnetic) state of various heavy-fermion systems. Kμ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu2Si2, UPt3 and CeAl3, while more complicated signals are measured in CePb3 and CeB6. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.

Superconductivity and magnetic ordering in YBa2(Cu1−x Fe x )3O7

Transverse-and zero-field μSR measurements have been made for YBa2(Cu1−xFex)3O7 withx=0.04, 0.08 and 0.12. The temperature range studied was from approximately 7.5 K to 100 K. The onset of magnetic ordering commences at about 7.5 K forx=0.04, 10 K forx=0.08 and 20 K forx=0.12. The Gaussian depolarization parameter, σ ofGx(t) = exp(−σ2t2/2), is depressed by a factor of about 0.6 forx=0.04, but for thex=0.08 sample σ is depressed by a factor of 10 and increasing suppression is seen as the temperature is lowered below 45 K. This decrease in σ is interpreted in terms of decreasing electronic mean free paths.

Muon hyperfine fields in iron and its dilute alloys

Abstract The temperature dependence (240 to 633 K) of the interstitial magnetic field, B μ , as determined by the rotation of the spin of the μ + , has been measured for dilute polycrystalline iron alloys with Mo, Ti and Nb additions. In all cases the behaviours differ from one another and from the Fe(A1) alloys previously studied. B μ , which is negative with respect to the magnetization, is increased in magnitude by A1 and Mo, and decreased greatly by Ti. The addition of Nb creates a two- phase alloy from which we can assess the role of heterogeneity and/or strain on B μ in iron. If the temperature dependence of the hyperfine field B hf extracted from B μ for Fe(Mo) alloys is interpreted on the model previously used to discuss the Fe(A1) data, we would conclude that the muon is attracted to the Mo atom while repelled by the A1 atoms as the temperature decreases. Measurements giving room temperature values of B μ for iron alloys with Mn, Cr, V and W taken after annealing above the recrystallization temperature are also reported.