2.2.4 Counter/muon spin geometries

In general, there are two types of spin relaxation defined: the T₁ and the T₂ relaxation [34]. In $\mu$SR measurements, the meaning of these two spin relaxation becomes intuitive, because the muon spin is polarized at t=0.

  

Figure 14: (a) Longitudinal field (LF) and Zero field (ZF) $\mu$SR. (b) Weak transverse field (wTF) $\mu$SR. (c) high transverse field (hTF) $\mu$SR.

The T₁ relaxation is defined as the relaxation of the spin component parallel to the external magnetic field [34]. In order to measure the T₁ relaxation with $\mu$SR, one uses the configuration shown in Fig.14a, because the muon spin is parallel to the beam axis by default (see Fig.6).

With the same counter configuration (Fig.14b), it is also possible to measure T₂ relaxation, which is the relaxation of the spin components perpendicular to the external field [34]. In this counter geometry, there is a certain upper limit for the transverse field $H_{\rm TF}$ ($\sim$200 G for surface muons), because the muon trajectory curves in the magnetic field, and in the worst case, it misses the sample. For T₂ relaxation measurements in higher fields, the `Left-Right' (or `Up-Down') configuration has to be employed (Fig.14c). The measurement with this configuration requires a good DC-separator on the beamline, which is capable of rotating the muon spin perpendicular to the beam (see inset of Fig.10).

One benefit to the $\mu$SR method is that measurements in zero magnetic field are possible. This condition yields the highest sensitivity to small internal magnetic fields. To understand the spin relaxation in the zero-field, the spin relaxation theories developed for the Nuclear Magnetic Resonance (NMR) method become inadequate, because those theories assume the existence of an external magnetic field. The next chapter introduces spin relaxation theories which are applicable to this zero-field condition.