W. Studer

Muon knight shift in platinum and in β-PdHx (x=0.70, 0.75, 0.86)

Theμ+ Knight shift in platinum has been measured between 20 K and 785 K. It shows a strong temperature dependence and scales with the magnetic bulk susceptibility. A temperature independent contribution of +40 to +60 ppm and a d-electron induced hyperfine field per unpaired d-electron per atom ofBhf,dΩ=−5.03 kG (±8.5%) are obtained. Theμ+ Knight shift in PdH0.70 and PdH0.75 shows no dependence on temperature between 20 K andRT and increases fromKμ ppm forx=0.70 toKμ ppm forx=0.75, in good agreement with proton Knight shift measurements.

POSITIVE MUONS IN ANTIMONY BISMUTH ALLOYS

StroboscopicμSR and TD-μSR techniques were used to measure theμ+ Knight shiftKμ, and relaxation rateλ inSbBi alloys as functions of magnetic fieldH, temperatureT, the angleθ betweenH and the crystallineĉ axis, and the concentration [Bi] of alloyed Bi. In pure Sb and inSbBi (6.5%),Kμ (θ=0) andKμ (θ=π/2) both decrease linearly withT up to about 100 K, but bothKμ and its anisotropy are smaller in the 6.5% alloy, indicating a “dilution” effect. With 15 at % Bi,Kμ is reduced further but itsT-dependence and that ofλ are dramatically altered. At low temperaturesKμ (θ=0) inSbBi(15%) actually becomes negative and the sign of the anisotropy is reversed. In the same sample,λ is proportional toH at both 20 K and 150 K; at 120 Kλ is proportional toKμ ifθ is used as an implicit variable, but at 36 K this is not the case. A consistent phenomenological description is offered.

Muon diffusion in the metal hydrides β-PdHx(x=0.70 and 0.75) and LaNi5H6

We report on zero and transverse fieldμSR measurements in LaNi5H6 and inβ-PdHx (x=0.70 and 0.75) between 16 K and room temperature. Theμ+-depolarization is predominantly caused by the spread in nuclear dipole fields from the protons. Motional averaging is caused by the combined motion of protons and theμ+. The results are quite unexpected and point toμ+-trapping within regions of largely immobile hydrogen configurations or to a highly correlatedμ+-proton diffusion. In LaNi5H6 a linear change of the second moment with temperature between 20 K and 120 K is indicated.

Positive muon Knight shift in graphite and Grafoil

Positive muon Knight shifts and relaxation rates were measured at room temperature in a graphite crystal and in a stack of Grafoil sheets. The Knight shift was ≈ 500 ppm in the single crystal and reduced by 0.702 in Grafoil. Both have the same (large) fractional anisotropy relative to theĉ axis or to the normal to the Grafoil sheets, respectively. The (isotropic) relaxation rates were 0.024(4)μs−1 in the crystal and 0.194(6)μ−1 in the Grafoil. Apparently theμ+ in Grafoil “sees” highly aligned bulk crystalline graphite, and does not reach the surfaces of the sheets.

Detailed investigation of the “DIP” structure in the μ+-relaxation rate in Nb

The depolarization rate of positive muons implanted in a number of nominally pure, cylindrical Nb single crystals (maximal 250 ppm Ta, 100 ppm N + O) was investigated at two temperatures, viz. 14.0 and 36.8 K, in a high transverse field of 7.5 kG with the stroboscopicμSR technique in order to study the nature of the “dip” at 22 K. To determine the sites at which the muon is trapped on both sides of this dip, the full angular dependence of the depolarization rate was measured by rotating a large single crystal around its 〈110〉 cylinder axis in a transverse magnetic field. The resulting curves for both temperatures are quite different, reflecting clearly the different environment in which the muon is trapped above and below 22 K. The trapping site at 36.8 K was identified to be of tetrahedral symmetry, located near a Ta substitutional impurity and possibly associated with an interstitial impurity. Lattice distortions due to these impurities and radial relaxation around the muon,δR/R, were determined. The latter is +6.7(6)% for nearest neighbors and −6(2)% for next nearest neighbors. The 14.0 K angular dependence could not be fitted by considering distorted tetrahedral and octahedral sites and pointlike muons.

Anisotropic muon Knight shift in the HCP single crystals of Cd, Zn and Be

In single crystal samples of Zn, Cd and Be (hcp structure) stroboscopicμSR measurements successfully revealed anisotropies in the muon Knight shift (Kμ). An anisotropic Kμ can provide information on the amount of non s-electrons screening the charge of the muon implanted in these metals as a light hydrogen isotope. In Cd, the anisotropic part depends strongly on the temperature and shows a change in sign at roughly 110 K. In Zn, the anisotropic part below 10 K turns out to comprise 4th order contributions in the direction cosines of the external field. This can be understood on the basis of an anisotropicg-factor of the conduction electrons or spin-orbit coupling, respectively.

Possibility of a Lifshitz phase transition in Cd observed by a singularity in the muon Knight shift

During the past much effort has been devoted to a systematic study of the muon Knight shiftKμ in metallic environments and its implications on the local electronic structure of hydrogen in metals [1]. These measurements in simple metals were essentially all carried out in polycrystalline samples at room temperature. The present measurements in Cd in polycrystalline and single crystal samples cover a temperature range between 20 K and the melting point of this strongly anisotropic metal (hcp crystal structure,c/a ratio 1.89 — idealc/a ratio 1.63). These measurements add qualitatively new and interesting aspects and insights on the screening of a light hydrogen isotope in a metal as well as on certain properties of the host material itself. The outstanding features of the muon Knight shift in Cd are: (i) a strong intrinsic temperature dependence with an increase ofKμ of more than 100% between 20 K and the melting point (T=593 K), (ii) an anomaly at 110 K in the form of a singularity in the isotropic part ofKμ which is interpreted as a band structure effect, (iii) an anisotropic Knight shift contribution fitting the expressionK(T,θ)=Kiso(T)+Kax(T) * (3 · cos2θ−1)/2, where both, the isotropic and the axial contribution ofKμ, are strongly temperature dependent.

Muon Knight shift at a structural defect in zinc crystals

The interaction of a light hydrogen isotope with a structural defect is traced for the first time by means of the temperature dependence of the muon Knight shiftKμ in the hcp metal Zn. A surprising result is the huge and negativeKμ (−520 ppm) at the defect site, probably a multivacancy cluster.

Anomalous Muon Knight Shift Behavior in a Cd Single Crystal

For the positive muon implanted in a metal the precession frequency shift due to hyperfine fields can be measured with high precision. This provides means to obtain information about the local electronic structure of a hydrogen like impurity in any metal in the indefinitely dilute impurity concentration. Ref. 1 gives a summary of the muon Knight shift (KS) investigations in 18 nontransition (simple) metals and some transition metals and discusses the results in the context of the electronic structure of hydrogen in metals.

Positive Muons as Local Probes in Paramagnetic Rare Earth Systems

In recent years a new research method has been developed in solid state physics which is based on the asymmetry of muon decay1. A positive muon at rest decays after a mean lifetime of 2.2 μsec into a positron and two neutrinos, the positron being emitted preferentially in the direction of the muon spin. Hence if spin polarized muons are implanted in a solid, the time evolution of the muon spin polarization can be determined by a measurement of the angular distribution of the positrons. In an external magnetic field transverse to the initial spin direction of the muon one can study the muon spin precession frequency, which is determined by the actual field at the muon, and τ2-relaxation effects. (It is this experimental arrangement from which the most commonly used name “muon spin rotation” [μSR] is derived.) A longitudinal field arrangement allows study of τ1-relaxation effects. The time scale which can be covered by (μSR) is determined by the magnetic field at the muon, the field fluctuations and the muon lifetime. In nonmagnetic substances the time scale ranges from 10−8 sec to 10−5 sec, in magnetic substances it can be extended down to 10−11 sec.