What is µSR?
Introduction to µSR --> here
The acronyn "µSR" was first defined and explained in the inaugural issue of the µSR Newsletter in 1974:
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µSR stands for Muon Spin Relaxation, Rotation, Resonance, Research or what have you. The intention of the mnemonic acronym is to draw attention to the analogy with NMR and ESR, the range of whose applications is well known. Any study of the interactions of the muon spin by virtue of the asymmetric decay is considered µSR, but this definition is not intended to exclude any peripherally related phenomena, especially if relevant to the use of the muon's magnetic moment as a delicate probe of matter. |
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As will be discussed in detail in the section on µSR Techniques, there are many ways in which the muon can be used for such purposes; but an introduction may be best served by an example that illustrates one of the simplest methods: weak transverse magnetic field (wTF)-µ+SR:
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In time-differential (TD) wTF-µ+SR at a continuous beam facility, a positive muon (µ+) with its spin antiparallel to its momentum passes through a thin muon counter, starting a high resolution time digitizer ("clock"). The muon immediately stops in a sample located in a magnetic field transverse to its initial spin direction, which causes its spin to precess at the muon Larmor frequency [math]\displaystyle{ \omega_\mu }[/math]. Some time later (on average the muon lifetime, [math]\displaystyle{ \tau_\mu }[/math] = 2.197 µs) the muon decays, emitting a high energy (up to about 52 MeV) positron (e+) which passes through another counter, generating a pulse which stops the clock. The time interval is digitized and the corresponding bin of a time histogram is incremented, after which the process can begin again as soon as another muon arrives. This is repeated around a million times (not difficult for such a short [math]\displaystyle{ \tau_\mu }[/math]) to form the typical histogram (time spectrum) shown above. |
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Beneath the "raw" time histogram N(t) is shown the corresponding "asymmetry" spectrum A(t) extracted by removing any time-independent background and dividing out the exponential decay of the muon. These functions have the form
[math]\displaystyle{ N(t) = N_0 \{BG + e^{-t/\tau_\mu} [1 + A(t)]\} }[/math]
where typically
[math]\displaystyle{ A(t) = A_0 G_{xx}(t) \cos(\omega_\mu t + \phi) }[/math].
Here N0 is a normalization factor, BG is a fraction of time-independent background, A0 is the empirical initial asymmetry of muon decay (sensitive to the muon's spin polarization as well as various systematic parameters to be discussed later), Gxx(t) is a transverse spin relaxation function (technically an autocorrelation function) describing the envelope of the sinusoidal oscillations, and [math]\displaystyle{ \phi }[/math] is the initial phase of the precession. The muon Larmor frequency is proportional to the magnetic field B at the muon's site:
[math]\displaystyle{ \omega_\mu = \gamma_\mu }[/math]B
where [math]\displaystyle{ \gamma_\mu/2\pi }[/math] = 135.5 MHz/T is the muon magnetogyric ratio.
