Although the interstitial hydrogen atom would seem to be one of the simplest defect centres in any lattice, its solid state chemistry is in fact unknown in many materials, not least amongst the elements. In semiconductors, the realization that hydrogen can profoundly influence electronic properties even as a trace impurity has prompted its study by all available means-but still only in the functionally important or potentially important materials-for the elements, Si, Ge and diamond. Even here, it was not studies of hydrogen itself but of its pseudo-isotope, muonium, that first provided the much needed microscopic pictures of crystallographic site and local electronic structure-now comprehensively confirmed by ab initio computation and such data as exists for monatomic, interstitial hydrogen centres in Si. Muonium can be formed in a variety of neutral paramagnetic states when positive muons are implanted into non-metals. The simple trapped atom is commonly only metastable. It coexists with or reacts to give defect centres with the unpaired electron in somewhat more extended orbitals. Indications of complete delocalization into effective mass states are discussed for B, α-Sn, Bi and even Ge, but otherwise all the muonium centres seen in the elemental semiconductors are deep and relatively compact. These are revealed, distinguished and characterized by μSR spectroscopy-muon spin rotation and resonance informing on sites and spin-density distributions, muon spin relaxation on motional dynamics and charge-state transitions. This Report documents the progress of μSR studies for all the semiconductors and semimetals of the p-block elements, Groups III-VI of the Periodic Table. The striking spectra and originally unanticipated results for Group IV are for the most part well known but deserve summarizing and updating; the sheer diversity of muonium states found is still remarkable, especially in carbon allotropes. The interplay of crystallographic site and charge state in Si and Ge at high temperatures, or under illumination, reflects the capture and loss of charge carriers that should model the electrical activity of monatomic hydrogen but still challenges theoretical descriptions. Spin-flip scattering of conduction electrons by the paramagnetic centres is revealed in heavily doped n-type material, as well as some modification of the local electronic structures. The corresponding spectroscopy for the solid elements of Groups III, V and VI is rather less well known and is reviewed here for the first time; a good deal of previously unpublished data is also included. Theoretical expectations and computational modelling are sparse, here. Recent results for B suggest a relatively shallow centre with molecular character; P and As show deeper quasi-atomic states, but still with substantial overlap of spin density onto surrounding host atoms. Particular attention is paid to the chalcogens. Muonium centres in Te show charge-state transitions already around room temperature; the identification of those in S and Se has been complicated by unusual spin dynamics of a different character, here attributed to spin-orbit coupling and interstitial reorientation. In the metals and semimetals, muonium is not formed as a paramagnetic centre. Here the implanted muons mimic interstital protons and interest shifts to a variety of other topics, including aspects of charge screening (α-Sn, Sb, Bi), site preference and quantum mobility (Al, β-Sn, Pb). The post-transition metals receive only a brief mention, by way of contrast with the nonmetals. Systematic studies of local susceptibility via measurements of muon Knight shifts extends in favourable cases to revealing the elusive high-field Condon domains (Al, Sn, Pb, Bi). Some new information is available on the superconducting phases. Appendices include a derivation of the spin Hamiltonian for paramagnetic muonium centres or molecular radicals having varying admixtures of orbital angular momentum, including the extreme case of orbital degeneracy, and examine the consequences of significant spin-orbit coupling for μSR spectroscopy and muon spin relaxation. This is the framework for the tentative assignments made here for the muonium defect centres formed in sulphur and selenium, namely diatomic species resembling the chalcogen monohydrides. Equally, it provides guidelines for eventual solid-state detection of OMu-the elusive muoniated hydroxyl radical.

https://iopscience.iop.org/article/10.1088/0034-4885/72/11/116501/pdf

Muonium as a model for interstitial hydrogen in the semiconducting and semimetallic elements

The authors have studied magnetic fluctuations in the paramagnetic phase of rare-earth-aluminium intermetallics of the type (RE)Al2 by the method of transverse-field muon spin rotation ( mu SR). In the case with strong 4f exchange they could observe a strong increase in the damping of the mu SR signal on approaching the Curie point Tc. One important contribution to the increased damping rate is the slowing down of magnetic fluctuations attributed to the formation of paramagnetic spin correlations which are observed to persist far above Tc. The crystallographic site for the mu + is discussed as well as the hyperfine field induced at this site due to interstitial electron polarisation.

/pdf/a-mu-sr-study-of-paramagnetic-fluctuations-in-rare-earth-ulsv0s0z8q.pdf

A mu SR study of paramagnetic fluctuations in rare-earth-aluminium intermetallics

Chapter 2 - Quantum Tunneling Diffusion in Solids*

Some recent result of muon spin relaxation measurements in rare earth metals and intermetallic compounds are reviewed. Special emphasis is put on measurements that relate to the properties of correlated regions of spins existing relatively far above the ordering temperature in the rare earth ions. As far as comparable data from paramagnetic neutron scattering exist, they will be discussed in the same framework. For each temperature the correlated regions (or short-lived magnetic clusters) are characterized by their size, possible anisotropy with respect to the crystalline axes and their lifetime. The actual form of the interaction between the rare earth spins themselves and with the crystal fields determine the temperature dependence of these properties; a strong dipole interaction can, for instance, be expected to change the critical behaviour nearTc. Much of the time will be devoted to experiments on Gd-metal where there are experimental indications that several interesting phenomena occur: (1) a strong effect of a cross-over from a non-conserved dynamics (dipolar) regime to a conserved (exchange dominated) regime some 10 K aboveTc, (2) an anisotropy of the magnetic clusters with respect to the hexagonalc-axis, and (3), a persistence of spin correlations far aboveTc. Some attempts to correlate the rare earth spin relaxation times measured in this region with cluster lifetimes deduced from neutron scattering will be reviewed, as well as a model for understanding these lifetimes in terms of temperature dependent cluster wall motion, which is determined by exchange and magnetic anisotropy parameters. Effects of possible quantum correlations originating from the “spin system+bath” interaction will be mentioned.

Rare earth paramagnetism, as studied by μSR

Publisher Summary This chapter discusses the results on magnetic materials obtained by a single technique— namely, muon spin rotation (μSR) spectroscopy. The magnetic properties of certain materials as collected by different methods and techniques are focused in the chapter. The application of μSR-spectroscopy has added to the understanding of established magnetic phenomena. However, when using positive muons (μ + ) μSR spectroscopy has shown the potential to uncover new and unexpected magnetic features owing to its high sensitivity to small magnetic fields and spatially inhomogeneous properties. Thus μSR-spectroscopy is most powerful in the field of small moment magnetism and in all instances when magnetic order is of a random or short range nature and where neutron scattering will fail. The μSR-spectroscopy also works in the case of broad lines and short relaxation rates. The local probe aspect of μSR and its sensitivity to inhomogeneous features has brought the real nature of solids into light that are never perfect in lattice structure, stoichiometry, and morphology; and hence also magnetic properties do not show up in an ideal manner. To perform μSR measurements, positive muons have to be implanted into the material of interest.

Chapter 2 Magnetic materials studied by muon spin rotation spectroscopy

The muon spin relaxation rateΛ (T) in an orientated polycrystalline sample of erbium constructed of large monocrystals has been measured for temperatures 20 <T<300 K. It has been shown that theΛ (T) for erbium is bounded from above asT → TN, whereTN=84.4 K is the Neel temperature. This fact may be explained by assuming that atT=TN erbium undergoes a weak phase-transition of the first order.

The MSR-investigation of antiferromagnetic phase transitions in erbium

A muon spin relaxation rate in a super-pure sample of bismuth has been measured. The experimental data and the theory of coherent diffusion in crystalline lattices with shifted levels are compared.

V. I. Selivanov

Papers

The MSR-investigation of antiferromagnetic phase transitions in erbium

Quantum diffusion of muons in bismuth