Muon perpendicular

When relaxation is allowed, the global minimum shifts to the bond-center site (Claxton et al., 1986 Estle et al., 1987 Briddon et al., 1988). This is in agreement with the experimental observation that anomalous muonium is the most stable state for muons in diamond (Holzschuh et al., 1982). An expansion of the bond length by 42% is necessary. The bond center was found to be more stable than the interstitial muonium by s 1.9 eV. Displacements of the muon along directions perpendicular to the bond cost little energy (Estle et al., 1987). 

The technique of muon spin rotation involves applying a magnetic field perpendicular to the direction of the incoming beam of muons (transverse to their spin) and monitoring the resulting precession signal via the emission of positrons that are emitted preferentially in the direction of the muon spin at the moment of its radioactive decay. For the bare muons this is simply the Larmor frequency but for muonium several frequencies are observed. In the case of a small h q)erfine constant, one can easily reach the so-called Paschen-Back regime in moderate fields and then a triplet of lines is seen in a Fourier transform of the raw data. 

When speaking of Muon Spin Rotation one emphasizes the measurement of coherent Larmor precession of the ensemble of muon spins in the magnetic field present at the site of the muons embedded in the sample. The spin rotation firequency is a direct measure of the magnitude of this field. To produce a precessional motion the field must have a component perpendicular to direction of the muon spin. Usually, this can be achieved by applying an external magnetic field in this direction, and Muon Spin Rotation is often synonymous with transverse field [aSR. 

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... 

The muon spin relaxation rates Ay and Ax, observed in ZF measmements with muons implanted with initial spin polarization parallel and perpendicular to the c-axis, are given by... 

Fig. 30. Critical spin fluctuations in Gd ftom ZF- iSR measurements. Left Anisotropy of ftie relaxation rate A just above the Curie point. After Hartmann et al. (1990a). Right Comparison of the temperature dependence of the relaxation rate measured in perpendicular geometry with the prediction of mode-coiq>ling ftieory for two muon stopping sites. The rates of 1989 were re-analyzed, changing slightly their absolute values (compared to those plotted in the left-hand panel). Tq and 7) mark the points where dipolar and uniaxial anisotropies start to play a significant role. After Hennebeiger et al. (1997).

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.

A linear relation between the field at the muon site, corrected for the (calculated) Lorentz field Rl nd the magnitude of the c-component of the R magnetic moment could be established for the full series (fig. 90) of R2pei4B compounds. Large corrections are quite apparent for the cases (Er, Tm) where the moments are oriented perpendicular to the c-axis. 

Fig. 130. Left ZF xSR spectrum of Ceo87Lao, 3Ri2Si2 together with the theoretical depolarization fimetion based on incommensurate sinusoidally modulated spin wave magnetic order (see text for details). From Yamamoto et al. (1997). Right Temperature dependence of the mean field seen by muons in magnetic Ce(R% jsRho ] 5)2 12 A single crystal oriented with the c-axis perpendicular to the muon beam was used. From Murayama et al.

Fig. 4.1 Illustration of the variable which denotes the component of the muon momentum perpendicular to the jet direction...

Figure 12.28 ZF- jSR time spectra observed in the P-phase crystai ofp-NPNN with initiai muon spin polarization perpendicular to the b-axis. 

Figure 15.25 shows the result for the initial muon spin polarization perpendicular to the Z -axis. When the muon spin is polarized parallel to the Z>-axis, the amplitude of the oscillating signal becomes very small (about 20% of that of the perpendicular orientation) [30]. This suggests tiiat the spin orientation in different domains is not aligned randomly and is most likely along the b-axis. Recent FM resonance experiments by... 

Figure 15.25. ZF-pSR time spectra observed in / -phase crystals of p-NPNN with the initial muon spin polarization perpendicular to the Z)-axis. (Reprinted with permission from ref 31)...

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