Muon spin spectroscopy
Muon spin spectroscopy is an atomic, molecular and condensed matter experimental technique that exploits nuclear detection methods.
The acronym stands for muon spin rotation, relaxation, or resonance, depending respectively on whether the muon spin motion is predominantly a rotation (more precisely a precession around a still magnetic field), a relaxation towards an equilibrium direction, or a more complex dynamic dictated by the addition of short radio frequency pulses.
Its two most notable features are its ability to study local environments, due to the short effective range of muon interactions with matter, and the characteristic time-window (10−13 – 10−5 s) of the dynamical processes in atomic, molecular and condensed media.
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.
The collision of an accelerated proton beam (typical energy 600 MeV) with the nuclei of a production target produces positive pions (
) 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).
High-energy muon beams are formed by the pions escaping the production target at high energies.
They are collected over a certain solid angle by quadrupole magnets and directed onto a decay section consisting of a long superconducting solenoid with a field of several tesla.
In these beams, muons arise from pions decaying at rest inside but near the surface of the production target.
Such muons are 100% polarized, ideally monochromatic, and have a very low momentum of 29.8 MeV/c (corresponding to a kinetic energy of 4.1 MeV).
It was christened with the acronym μSOL (muon separator on-line) and initially employed LiF as the moderating solid.
In 1987, the slow μ+ production rate was increased 100-fold using thin-film rare-gas solid moderators, producing a usable flux of low-energy positive muons.
[4] This production technique was subsequently adopted by PSI for their low-energy positive muon beam facility.
In addition to the above-mentioned classification based on energy, muon beams are also divided according to the time structure of the particle accelerator, i.e. continuous or pulsed.
The main advantage is that the time resolution is solely determined by the detector construction and the read-out electronics.
There are two main limitations for this type of source, however: (i) unrejected charged particles accidentally hitting the detectors produce non-negligible random background counts; this compromises measurements after a few muon lifetimes, when the random background exceeds the true decay events; and (ii) the requirement to detect muons one at a time sets a maximum event rate.
Furthermore, detectors are active only after the incoming muon pulse, strongly reducing the accidental background counts.
On one side it is very fast (much faster than 100 ps), which is much shorter than a typical μSR time window (up to 20 μs), and on the other side, all the processes involved during the deceleration are Coulombic (ionization of atoms, electron scattering, electron capture) in origin and do not interact with the muon spin, so that the muon is thermalized without any significant loss of polarization.
The positive muons usually adopt interstitial sites of the crystallographic lattice, markedly distinguished by their electronic (charge) state.
For example, in most metallic samples, which are Pauli paramagnets, the muon's positive charge is collectively screened by a cloud of conduction electrons.
In insulators or semiconductors a collective screening cannot take place and the muon will usually pick up one electron and form a so-called muonium (Mu=μ++e−), which has similar size (Bohr radius), reduced mass, and ionization energy to the hydrogen atom.
is measured over a statistical ensemble of implanted muons and it depends on further experimental parameters, such as the beam spin polarization
In this case the asymmetry shows up as an imbalance between the positron counts in two equivalent detectors placed in front and behind the sample, along the beam axis.
Another simple type of μSR experiment is when implanted all muon spins precess coherently around the external magnetic field of modulus
Mrad(sT)−1, the frequency spectrum obtained by means of this experimental arrangement provides a direct measure of the internal magnetic field intensity distribution.
A more general case is when the initial muon spin direction (coinciding with the detector axis) forms an angle
The London penetration depth is one of the most important parameters characterizing a superconductor because its inverse square provides a measure of the density ns of Cooper pairs.
Muon spin spectroscopy provides a way to measure the penetration depth, and so has been used to study high-temperature cuprate superconductors since their discovery in 1986.
