Muons spin polarization

The techniques of u.SR and p-LCR are based on the fact that parity is violated in weak interactions. Consequently, when a positive muon is created from stationary pion decay its spin is directed opposite to its momentum. This makes it possible to form a beam of low energy (4 MeV) positive muons with nearly 100% spin polarization at high intensity particle accelerators such as TRIUMF in Canada, the PSI in Switzerland, LAMPF and BNL in the USA, KEK in Japan, and RAL in England. Furthermore the direction of position emission from muon decay is positively correlated with the muon spin polarization direction at the time of decay. This allows the time evolution of the muon spin polarization vector in a sample to be monitored with a sensitivity unparalleled in conventional magnetic resonance. For example, only about 101 7 muon decay events are necessary to obtain a reasonable signal. Another important point is that //.SR is conventionally done such that only one muon is in the sample at a time, and for p,LCR, even with the highest available incident muon rates, the 2.2 fis mean lifetime of the muon implies that only a few muons are present at a given time. Consequently, muonium centers are inherently isolated from one another. 

Fig. 1. Schematic for /zSR and fiLCR experiments. For pSR the muon spin polarization vector starts off in the x direction (open arrow). It then precesses about an effective field (the vector sum of the external field and the internal hyperfine field), which is normally approximately the z direction. The muons are detected in the M counter, and positrons from muon decay are detected in the L or R counters. For pLCR, the muon spin polarization is initially along the external field or t axis (solid arrow). The positron rates in the F and B counters are measured as a function of external field. A sharp decrease in the asymmetry of the F and B counting rates signifies a level crossing.

In general, the amplitudes and phases of the two radical precession frequencies differ. To observe radicals at all, muon spin polarization must be transferred from muoniun to the radical. The degree of transfer depends on reaction rates and precession frequencies, which in turn depend on the magnetic field. This field of study is still in its infancy, however, so the reader is referred elsewhere for some preliminary results.29... 

Basically, p.SR is the measurement of the temporal development of the spatial orientation of the spins of muons which have been implanted in the material of interest with all spins initially fixed in one direction (complete muon spin polarization). The three names covered by the acronym p,SR, namely muon spin rotation, relaxation or resonance, refer loosely to different means of observation. 

The group at KEK (Nagamine et al. 1995, Miyake et al. 1995, 1997) produces ultra-slow muons by first generating thermal muonium at the surface of a hot tungsten target placed in the pulsed primary proton beam. They then resonantly ionize the muonium by synchronously pulsed intense light from an UV laser. The resulting thermal p" are electrostatically collected and form the pulsed ultra-slow muon beam with about 50% of muon spin polarization preserved. The p spin is adjusted perpendicular to the beam axis. Test spectra have been obtained for a lOnm Au sample. Intensity is still very low. 

Transverse field (TF) means that the apphed field is oriented perpendicular to the initial muon spin polarization. As mentioned, this does not necessarily mean that the field is oriented perpendicular to the muon beam. With a surface beam, it may be oriented along the beam momentum when the muon spin has previously been turned by a spin rotator (see sect. 2.5). We restrict this discussion (except for some short remarks) to the strong-field limit, that is to say, we assume that the local quantization axis for muon spin and its surroundings is determined by the externally applied field alone. Then only the secular term in the Zeeman interaction of the local moments with Bapp need to be considered (details can be found, for example in Schenck 1985, chapter 2.3.1). Sensing a transverse field, the muon spin will precess in the plane perpendicular to the field axis, which generates the asymmetry spectrum... 

Fig. 35. Temperature dependence of signal amplitude and relaxation rate measured in ZF on a single crystal of erbium oriented with its c-axis parallel and perpendicular to the muon beam (muon spin polarization). Squares and circles refer to two different run sequences. After Wappling et al. (1993).

Fig. 83, Temperature dependence of the pSR relaxation rate in NdRhjSij. Left A single e>q>onentially relaxing signal is seen for the c-axis parallel to muon spin polarization. The rate below the Neel temperature is fitted to a two-magnon process. Right Critical behavior of the paramagnetic relaxation rate for the c-axis perpendicular to the muon spin polarization (longitudinal spin fluctuations). The insert shows a fit to a critical power law.

Fig. 86. Temperature dependences of the spontaneous muon spin precession iiequency (in the ferromagnetic state) and the muon spin relaxation rate (both in the ferromagnetic and paramagnetic states) in EuO. The data were analyzed with an exponential decay of muon spin polarization throughout. After Hartmann et al. (1996).

Fig. 150. ZF- J,SR spectrum of UPdjAls at 80 mK, fitted to an exponential decay of muon spin polarization. The negative initial polarization is an artifact of measurement geometry. The inset shows the unit cell with prominent interstitial sites. The muon occupies the b site. From Amato et al. (1992b).

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