Muon spin spectroscopy

Muon spin spectroscopy is an experimental technique based on the implantation of spin-polarized muons in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance (ESR or EPR) and, more closely, nuclear magnetic resonance (NMR). Muon spin spectroscopy is an experimental technique based on the implantation of spin-polarized muons in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance (ESR or EPR) and, more closely, nuclear magnetic resonance (NMR). In analogy with the acronyms for these previously established spectroscopies, the muon spin spectroscopy is also known as µSR, which stands for muon spin rotation, or relaxation, or resonance, depending respectively on whether the muon spin motion is predominantly a rotation (more precisely a precession around a still magnetic field), or a relaxation towards an equilibrium direction, or, again, a more complex dynamics dictated by the addition of short radio frequency pulses. The intention of the mnemonic acronym was to draw attention to the analogy with NMR and ESR. More generally speaking, the abbreviation covers any study of the interactions of the muon's magnetic moment with its surroundings when implanted into any kind of matter. µSR is an atomic, molecular and condensed matter experimental technique that exploits nuclear detection methods. Although particles are used as a probe, it is not a diffraction technique. Its two main features are the local nature of the muon probe, due to the short effective range of its interactions with matter, and the characteristic time-window (10−13 – 10−5 s) of the dynamical processes in atomic, molecular and condensed media that can be investigated by this technique. The closest parallel to µSR is 'pulsed NMR', in which one observes time-dependent transverse nuclear polarization or the so-called 'free induction decay' of the nuclear polarization. However, a key difference is that in µSR one uses a specifically implanted spin (the muon's) and does not rely on internal nuclear spins. In addition, and due to the specificity of the muon, the µSR technique does not require any radio-frequency technique to align the probing spin. On the other hand, a clear distinction between the µSR technique and those involving neutrons or X-rays is that scattering is not involved. Neutron diffraction techniques, for example, use the change in energy and/or momentum of a scattered neutron to deduce the sample properties. In contrast, the implanted muons are not diffracted but remain in a sample until they decay. Only a careful analysis of the decay product (i.e. a positron) provides information about the interaction between the implanted muon and its environment in the sample. As with many of the other nuclear methods, µSR relies on discoveries and developments made in the field of particle physics. Following the discovery of the muon by Seth Neddermeyer and Carl D. Anderson in 1936, pioneer experiments on its properties were performed with cosmic rays. Indeed, with one muon hitting each square centimeter of the earth's surface every minute, the muons constitute the foremost constituent of cosmic rays arriving at ground level. However, µSR experiments require muon fluxes of the order of 10 4 − 10 7 {displaystyle 10^{4}-10^{7}} muons per second and square centimeter. Such fluxes can only be obtained in high-energy particle accelerators which have been developed during the last 50 years. The collision of an accelerated proton beam (typical energy 600 MeV) with the nuclei of a production target produces positive pions ( π + {displaystyle pi ^{+}} ) via the possible reactions: From the subsequent weak decay of the pions ( MEAN lifetime τ π + {displaystyle au _{pi ^{+}}} = 26.03 ns) positive muons ( μ + {displaystyle mu ^{+}} ) are formed via the two body decay: Parity violation in the weak interactions implies that only left-handed neutrinos exist, with their spin antiparallel to their linear momentum (likewise only right-handed anti-neutrino are found in nature). Since the pion is spinless both the neutrino and the μ + {displaystyle mu ^{+}} are ejected with spin antiparallel to their momentum in the pion rest frame. This is the key to provide spin-polarised muon beams. According to the value of the pion momentum different types of μ + {displaystyle mu ^{+}} -beams are available for µSR measurements. The first type of muon beam is formed by the pions escaping the production target at high energies. They are collected over a certain solid angle by quadrupole magnets and directed on to a decay section consisting of a long superconducting solenoid with a field of several Tesla. If the pion momentum is not too high, a large fraction of the pions will have decayed before they reach the end of the solenoid.