Muon spin rotation

Muons are unstable spin-1/2 particles with charge ±e which have a mass m_μ = 206.7 me. Their half-life is τ_μ = 2.2 μs. The positive muon is quite useful as a probe of magnetic solids because it occupies an interstitial site where it experiences the local magnetic field. Negative muons are like heavy electrons and they bind closely to atomic nuclei, which is useful for cold fusion. Muon beams are produced in accelerators, where high-energy protons collide with a target producing pions, which decay into muons 26 ns later:
π ⁺ → μ⁺ + ν_μ.
Remarkably, the muons produced are fully spin polarized; this is because the pion has no spin and the muon neutrino ν_μ has its spin antiparallel to its momentum and so the muon also has its spin antiparallel to its momentum. The muons are created with energy in the MeV range, but they are rapidly thermalized on entering a solid specimen without loss of spin polarization. The final resting place of the muon in the sample is an interstitial site far from the track of radiation damage produced in the early stages of thermalization. After a time t there is a probability proportional to 1 − ^e−t/τμ that the muon will have decayed into a positron and two neutrinos:
μ⁺ → e⁺ + ν_e + ¯ν_μ.
The positron emerges in a direction related to the spin direction of the parent muon. If a magnetic field is applied in the perpendicular direction, the muon precesses around this field at its Larmor frequency of 135 MHz T⁻¹ before decaying to emit the positron.
There might only be a single muon in the sample at a given instant, but by averaging over many events, curves showing the intensity oscillations of the positron flux in fixed detectors can be recorded and the precession frequency of the muon is determined. The muon precesses equally well around the internal magnetic field present at its interstitial site and the main use of muon spin rotation (μSR) in solids is to study these local fields, which are in the range 10⁻⁴–1 T. The spin depolarization of the muon can be used to probe spin dynamics both above and below the Curie temperature of a ferromagnet.