Muon spin relaxation technique

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

The experimental situation is inconclusive and sometimes even the same experimental techniques used by different groups give contrary results. Especially for the compounds k-(ET)2Cu(NCS)2 and K-(ET)2Cu[N(CN)2]Br many different techniques have been employed to measure A(T). Evidence for non BCS-like behavior has been obtained by complex ac susceptibility [220], radio-frequency penetration depth [221], muon spin relaxation (//SR) [222], and microwave surface impedance measurements [223]. In contrast, results consistent with conventional BCS theory, sometimes revealing a tendency towards strong coupling, are reported for measurements of the //SR [224], microwave surface impedance [225, 226], and dc magnetization [227]. 

A relatively new technique which is being increasingly applied to the study of magnetic materials is that of muon spin rotation [jliSR also known as muon spin relaxation or resonance (Schenck 1985)]. In the most common arrangement a beam of spin polarized muons ju,+ (say) is directed towards and stopped in a target. The anisotropy in the ju, - e decay rate (e.g., from a comparison of the rate in backward and forward directions) is monitored as a function of elapsed muon lifetime for a large number of stopped muons. The basic equation on which the technique is based is... 

More recently, longitudinal muon spin relaxation was used to measure rate constants for the reactions of organic radicals with molecular oxygen and with NO in the gas phase [32, 46]. The reactions are important in combustion processes and for the degradation of organic pollutants in the atmosphere. Accurate determinations by conventional techniques have often proved to be non-trivial, so that the muon technique appears to be a very valuable addition to the tool box of experimental methods. 

Since the discovery of slow relaxation in lanthanide complexes [11], lanthanides [184, 185] and, more recently, actinides [12, 186] have become very popular in molecular magnetism. Most of the analysis of the magnetic properties of these complexes involved powder d.c. and a.c. susceptibility and magnetization measurements [187, 188]. Other techniques used for the investigation of lanthanide-containing MNMs have included single crystal susceptibihty [189], Mossbauer spectroscopy [190], muon spin relaxation [191], and magnetic circular dichroism spectroscopy [192]. 

The term pSR was originally used for muon spin rotation , but muon spin science has now developed into a variety of techniques and is not limited to the rotation technique. It is fortunate, however, that most of the other techniques (muon spin relaxation, muon spin repolarization, and muon spin resonance) have the same abbreviated form pSR. Thus pSR is sometimes used to describe all these techniques collectively. When it is necessary to specify these different techniques, pS Rotation , pS Resonance , etc. will be used. 

In the present section we focus on the various chemical and physical properties of the equiatomic YbTX compounds especially the physical properties, which have been intensively investigated in the last two decades. Besides detailed magnetic susceptibility and electrical resistivity measurements, various other techniques have been used to get deeper insight into the peculiar properties of these intermetallics " Sn and °Yb Mdssbauer spectroscopy, specific-heat data, thermopower measurements, solid-state NMR, photoemission studies, neutron dif action, muon spin relaxation, and a variety of high-pressure experiments. The diverse data are summarized in the following subsections. 

The activation parameters for the ring rotation in ferrocene have been estimated in the literature using NMR [23] and QENS [24]. Activation energies of 5.4 0.5 and 4.4 0.5 kJ mol, and an attempt frequency of 3.16 x 10 and 1.25 x 10 s respectively were reported. Close agreement between these independently estimated values and those obtained from muon spin relaxation is evidence that the same dynamic process is measured in all three techniques. 

Another new microscopic technique which can determine in principle S(q,t) in spin glasses is the measurement of muon spin relaxation (juSR). Here the q dependenees are not tunable as in the NSE method (eq. 70) but are broadly averaged over all q. The window of relaxation times seen by ptSR spans the 10 " s to 10 s regime, and henee partly overlaps with that of the neutron techniques (10 s to 10 s). 

In this chapter we do not describe the theory potentially applicable to single-crystal neutron data because it is the subject of Handbook chapters by Norman and Koelling and by Liu (Vol. 17, chs. 110 and 111, respectively). Scattering overlaps with and complements two other techniques sensitive to microscopic magnetic correlations. The techniques are nuclear resonance (NMR) and muon spin relaxation (p SR) spectroscopies whose applications to heavy-fermion materials are reviewed by Nakamura et al. (1988) (NMR) and Barth et al. (1988) and Schenck (1992) (p SR). Finally, there have by now been nearly countless general reviews of experiments and theory on heavy-fermion systems, many of which have appeared in this Handbook series (Vol. 10, chs. 63 and 70, Vol. 14, chs. 94, 96 and 97, Vol. 15, ch, 98, Vol. 16, chs. 105 and 106, Vol. 17, clis. 110 and 111 and this volume, chs. 130, 132 and 133). For a recent pedagogical introduction, the reader can consult the book by Hewson (1993). 

In comparisons of muons with protons and of muonium with hydrogen atoms, pronounced quantum effects occur whenever dynamics are involved. In this way, muons have been utilized to probe a large variety of properties and materials insulators, semiconductors, metals, superconductors, insulators, gases, liquids, crystalline and amorphous solids, static and dynamic magnetic properties of all kinds, electron mobility, quantum diffusion, chemical reactivity and molecular structure and dynamics. The term adopted for the broad field of muon spin spectroscopy techniques, fiSR, emphasizes the analogy with other types of magnetic resonance for example EPR. juS represents muon spin , and R in a more general sense stands simultaneously for rotation , relaxation and resonance . 

The relaxation effects as probed via the Mossbauer hyperfine interaction can be investigated by other methods which can be regarded as complementary to Mossbauer spectroscopy. The techniques of perturbed angular correlation of gamma rays (PAC) and positive muon spin rotation (pSR) spectroscopy will be briefly discussed here. A more detailed review can be found in Dattagupta (1981). 

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