Muon spin relaxation parallel

Muon Spin Relaxation refers to the observation of incoherent motions of the muon spins which result in a loss of polarization with time. This will occur if the magnetic field sensed by the ensemble of implanted muons is broadly distributed. If the local field each muon sees in addition fluctuates randomly during a muon s life we observe what is called dynamic depolarization , but also a stationary distributed field causes depolarization by phase incoherence ( static depolarization ). These two cases must be clearly distinguished. The situation corresponds to the two relaxation times Ty (spin-lattice) and Ti (spin-spin) in NMR. Muon Spin Relaxation measurements can be carried out without observing spin rotation and thus are possible in zero applied field or with a longitudinally applied field (i.e., a field applied parallel to the muon spin direction at the moment of implantation). Longitudinal field measurements are the most appropriate way to obtain a clear distinction between static and dynamic muon spin depolarization. Muon Spin Relaxation hence mostly refers to zero or longitudinal field (iSR. 

We shall discuss the information contained in fp below. Gfit) is the transverse muon spin relaxation function as indicated by the index x (the z-axis is commonly fixed parallel to the muon spin). 

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. 108. Muon-spin relaxation in CeNiSn at very low temperatures. Left Temperature dependence of relaxation rate in ZF and various TF for a single-crystalline sample with the a-axis parallel to the p-beam. Right TF = 1 kG data for the a-axis (squares) and the c-axis parallel to the p-beam (circles). Also shown are corresponding data for polycrystalline CeNiSn (triangles) and LaajsCeogsNiSn (diamonds). The lines are guides to the eye (but see text). From Kalvius et al. (1994, 1995c).

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. 166. piSR data on single-crystalline Ce,Nij. Left Measurements above Top Temperature dependence of the ZF-relaxation rate for two orientations. Bottom Angular dependence of the muon spin precession frequencies (two signals are seen) at 20 K in a transverse field of 6 kG. The marks refer to crystalline orientations parallel to the applied field. Right Measurements below T, . Top ZF spectra at 1.8K for c 5 and c (inset). The fits are explained in text. Bottom Temperature dependence of the spontaneous muon spin precession frequency. (Bottom left Schenck et al. 2001 all others Kralzer et al. 2001.)... 

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