Physica B 289}290 (2000) 620}624
Muons in sulphur Ivan D. Reid *, Stephen F.J. Cox Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland ISIS Facility, Rutherford Appleton Lab, Chilton OX11 0QX, UK
Abstract Longitudinal-"eld repolarisation measurements of positive muons in sulphur suggest the existence of two paramagnetic muon species, consistent with a molecular radical and interstitial muonium. Avoided level-crossing measurements reveal a very weak signal at low temperatures ((100 K), ascribed to the *M"1 resonance of a radical with a hyper"ne constant of 233$5 MHz. We report further lSR experiments in sulphur, which attempt to shed light on the dynamics of muon charge states in this material. Above 200 K, transverse-"eld (TF) measurements show two diamagnetic signals, one of small amplitude and low relaxation j, the other with high j and a T-dependent amplitude. From 200 to 300 K the amplitude of the `fasta component increases rapidly, suggesting that the species it represents is formed in a thermally activated process from a paramagnetic precursor. Its relaxation follows a similar trend, but further investigation shows that j for this component falls above 300 K while the amplitude remains essentially constant up to the b-phase transition. The amplitude drops in the b-phase and the fast relaxation disappears in the melt, where most of the polarisation is found in a slowly relaxing signal. While no TF radical signals have been found at any temperature, very recent low-"eld measurements at low temperatures show features consistent with an extremely quickly relaxing prompt muonium fraction, a possible precursor for the `fasta diamagnetic component. 2000 Elsevier Science B.V. All rights reserved. Keywords: Muon; Muonium; Muoniated radicals
1. Introduction The success of lSR techniques in modelling hydrogen centres in semiconductors with positive muons has led to recent interest in the behaviour of muons in other low-band-gap materials such as sulphur which, surprisingly, has not been very intensively studied by lSR over the years. Early studies on l> depolarisation [1,2] gave low values for residual polarisation in sulphur, leading to its repu-
* Corresponding author. Tel.: #41-56-310-3200; fax: #4156-310-3294. E-mail address:
[email protected] (I.D. Reid).
tation as a good depolarising material; investigations with a natural tetragonal single crystal also revealed no coherent lSR signals [3]. Later reports [4,5] indicated high values (&30 ls\) for the relaxation j of transverse-"eld (TF) l> signals in sulphur. Modern repolarisation measurements in longitudinal "elds [6] suggest that there are two paramagnetic muon species in sulphur, consistent with a molecular radical and interstitial muonium. Subsequent avoided-level-crossing (ALC) measurements at PSI [7,8] revealed a very weak signal at low temperatures ((100 K) which was ascribed to a *M"1 resonance of a radical with a hyper"ne constant of 233$5 MHz. Room-temperature TF
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experiments failed to detect either muonium or radical signatures. However, they did show two diamagnetic lSR signals, one of low amplitude and slow relaxation, the other with higher amplitude and very fast relaxation [7].
process from some paramagnetic precursor. The relaxation of this component also rises with temperature over this range, consistent with its depolarisation in another thermally activated process. Fourier transforms of the experimental data in this regime revealed no sign of radical signals.
2. Experimental results
2.2. High xeld, high temperature
We have now extended the TF experiments to study the temperature dependence of the diamagnetic signals, and also to search for radical and muonium signals. The results described here are of a preliminary nature, as they were obtained on an ad hoc basis to provide guidance for a subsequent rigorous investigation into the charge states of muons in sulphur.
Subsequently, experiments were performed at 2 kG TF in the decay-muon spectrometer GPD, using the LN -#ow `chemistrya cryostat at temper atures between 200 and 400 K. The sample was sulphur powder sealed in a thin-walled glass bulb. Below 300 K, the behaviour of the diamagnetic signals was consistent with that observed earlier. However, at higher temperatures it was evident that while the amplitudes of both components remained essentially constant, the relaxation of the `fasta component fell with increasing temperature, a feature that in retrospect was also seen in the 320 K data obtained in GPS. Ironically, the maximum relaxation (50}60 ls\) occurs around 300 K, where most of the early investigations were performed. It should also be noted that essentially the full muon polarisation is recovered in the diamagnetic signals from 300 K upwards, so it is not expected that any muonium or radical signals can be observed in this region. The `fasta component amplitude remains constant up to the b-phase transition at 368 K, with a slight drop in the b-phase, but it falls drastically in the melt ('392 K), where most of the polarisation is found instead in the slowly relaxing signal. Fig. 2 summarises the observed temperature dependence of the amplitude and relaxation for the `fasta component in both GPS and GPD spectrometers. Also shown is the result of quenching the sample as rapidly as possible from 400 to 200 K which illustrates, together with data taken when cooling more slowly, that the relatively slow thermal rearrangement of the sulphur structure has a noticeable e!ect on the lSR results.
2.1. High xeld, low temperature First, experiments were carried out using the surface-muon GPS spectrometer at PSI, using high purity sulphur powder, in the temperature range 20}320 K at 3 kG TF. Again, two diamagnetic signals were seen, with the `fasta component decreasing in amplitude and relaxation at lower temperatures. Indeed, between 200 and 300 K the amplitude of the `fasta component follows an Arrhenius behaviour (Fig. 1), suggesting that the species it represents is formed in a thermally activated
2.3. Zero xeld, low temperature Fig. 1. Arrhenius plot of the amplitude and relaxation j of the `fasta diamagnetic l> signal observed in the GPS spectrometer in sulphur above 200 K. The dashed line is a guide to the eye.
Since the anisotropic components of radical hyper"ne tensors may be observed in zero-"eld (ZF)
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Fig. 3 shows a representative "t. In all cases an extremely quickly relaxing Mu component was seen at early times, with j in the range + 60}75 ls\, albeit with no obvious temperature dependence. Unfortunately, a mains power outage at a critical stage prevented the extension of these measurements to higher temperatures; however, the results are consistent with a signi"cant, quickly depolarised, prompt muonium fraction.
3. Discussion It is obvious that the behaviour of positive muons in sulphur is complex, further complicated by the involved thermal behaviour of sulphur itself. However, several conclusions may be drawn:
Fig. 2. Combined results for the amplitude and relaxation of the `fasta diamagnetic l> component in sulphur in both the GPD and GPS spectrometers. The point labelled `quencheda was taken after cooling rapidly from 400 to 200 K.
experiments [9,10], several ZF experiments were carried out below room temperature in the GPD spectrometer, using sulphur #akes in an aluminium sample container in the LHe-#ow Janis cryostat. However, no spontaneous oscillations were seen. 2.4. Low xeld, low temperature We have recently been able to carry out low-"eld (8 G) TF experiments on high-purity (99.998%) sulphur #akes in the GPS spectrometer between 5 and 133 K, in an attempt to detect signals from muonium precession. The histograms covered 10 ls (8192 channels at 1.25 ns resolution) and the data were "tted to a model consisting of a nonrelaxing muon signal and a relaxing muonium signal, with all four histograms "tted simultaneously.
E Radical signatures are seen only in longitudinal "elds } repolarisation or ALC measurements. This implies that radical formation is not a prompt process. Unfortunately, only a *M"1 ALC resonance can be seen in natural sulphur, and then only at low temperatures where molecular motion is slow enough for the hyper"ne asymmetry to be observable; at these temperatures it appears that the radical yield is reduced. E A small fraction (&10%) of muons thermalise in a diamagnetic environment and thereafter remain unreactive. E The remainder of the muons thermalise in a paramagnetic environment, which low-"eld measurements strongly suggest to be muonium. In high "elds this component is unobservable, leading to an increasing `missing fractiona as the temperature is reduced below 300 K. E This prompt muonium fraction presumably provides the precursor to the radical state, but a temperature-dependent proportion also reacts in a thermally activated process to form a further diamagnetic state (or, conceivably, a radical with a very low hyper"ne coupling) such that the diamagnetic yield appears close to 100% in TF spectra above &300 K. E The diamagnetic product undergoes further strong depolarisation, which is very likely due to delayed encounter with or capture of radiolytic electrons since the nuclear magnetism in sulphur
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Fig. 3. TF lSR asymmetries in sulphur at 8 G and 50 K. The solid lines are a simultaneous "t to all four GPS histograms of a model representing a non-relaxing l> signal and a relaxing Mu signal. j "60$6 ls\. +
is too weak to account for the observed damping rates. While this appears to be a thermally activated process at low temperatures, it is evident that at higher temperatures some dynamic process comes into play, suggestive of motional narrowing. E The absence of depolarisation in the liquid phase suggests that the depolarisation involves the S rings, which tend to open into chains in the melt. The exact details of the processes involved are still the subject of some debate. We suggest above that the rapid depolarisation of the diamagnetic component is recombination with electrons from the thermalisation track, which di!use more rapidly at higher temperatures. Another possibility is that the secondary diamagnetic state is a MuSQ radical and that depolarisation occurs via interaction with the unpaired electron, moderated through the hopping of the muon and/or the unpaired electron around the ring, or even between rings. The fact that depolarisation does not occur in the melt tends to rule out the diamagnetic species' being SQ }S Mu.
4. Conclusions Preliminary investigations of the behaviour of positive muons implanted into sulphur show a complex pattern of conversions between charge states, most of which have yet to be de"nitively identi"ed. However, a broad picture of the interactions has emerged and will serve as a guide for further lSR experiments in this material. As well as continuing conventional methods of investigation, it may also prove useful to employ more novel methods to unravel the complicated processes at work: E RF or pulsed techniques may be able further to characterise the states formed some time after implantation, by maintaining longitudinal polarisation until the "nal states have formed. E Since sulphur is photoconductive, experiments under illumination may help to determine the ro( le played by other charge carriers in the various interconversions. In this endeavour it may be necessary to utilise low-energy l> to ensure that the regions of muon thermalisation and illumination coincide.
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E The use of applied electric "elds on the sample may elucidate the e!ect of the l> ionisation track on the initial states of the muons (see, e.g. Ref. [11]). E Because of the high relaxation rates observed for the various fractions, it may be advantageous to use a very-high time-resolution spectrometer [12] to investigate the prompt muon states, both in low "elds and in zero "eld. E If possible, ALC experiments should be carried out with S-enriched samples, to characterise radical species by observation of *M"0 resonances.
References [1] [2] [3] [4]
[5] [6] [7] [8] [9]
Acknowledgements We wish to thank the Paul Scherrer Institute for the use of the lSR Facility instruments, and Drs. D. Herlach, A. Amato and U. Zimmermann for providing access to the spectrometers. We also thank Dr. U.A. Jayasooriya and Mr. G. Hopkins for assistance with the zero-"eld experiments.
[10]
[11] [12]
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