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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).

Acronym

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.

How it works

The time scale on which the spin motion may be exploited is that of the muon decay, i.e. a few mean lifetimes, each roughly 2.2 µs (2.2 millionths of a second). Both the production of muon beams with nearly perfect alignment of the spin to the beam direction (what was referred to above as spin polarization and caused by the spontaneous symmetry breaking), and the ability to detect the muon spin direction at the instant of the muon decay rely on the violation of parity, which takes place whenever weak forces are at play.

In short this means that certain elementary events happen only when including clockwise (or only when including counterclockwise) rotations. For instance, the positive muon decays into a positron plus two neutrinos and the positron is preferentially emitted in the direction of the muon spin. Therefore it would most often see the spin as a counterclockwise rotation while flying away from the decay point.

Spin alignment allows the production of a muon beam with an aligned magnetic moment. Muons are injected into the material under investigation as short-lived spies [1] sending information from the interior back out to the experimental apparatus. These muons are able to send a message from inside the crystal about the local magnetic field in their surroundings. After some time (mean lifetime 2.2 µs) these spies decay and emit positrons. A beam of aligned muons produces asymmetric positron radiation. The asymmetry of positron radiation contains information about the direction of local magnetic field in the moment of muon decay. Taking into consideration the initial direction of muon magnetic moment and the time interval between the moment of injection and moment of muon decay we can calculate the precession frequency (how rapidly the muon's magnetic moment rotates). The frequency of magnetic moment precession depends on the local magnetic field. Larmor precession is appeared with z-direction magnetic field and only decay in 2.2 µs. But when x-direction magnetic field is applied in muon, the rate of decay is enhanced by gaussian with depolarization rate.

Since 1987 this method was used to measure internal magnetic fields inside high-temperature superconductors. High-temperature superconductors are Type II superconductors, in which the local magnetic fields inside the superconductor depend on the superconducting carrier density—one of the significant parameters of any superconductor (see for example the Bardeen–Cooper–Shrieffer theory of superconductors).

Applications

Muon Spin Rotation and Relaxation are mostly performed with positive muons. They are well suited to the study of magnetic fields at the atomic scale inside matter, such as those produced by various kinds of magnetism and/or superconductivity encountered in compounds occurring in nature or artificially produced by modern material science.

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. The dependence of ns on temperature and magnetic field directly indicates the symmetry of the superconducting gap. 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.

Other important fields of application of µSR exploit the fact that positive muons capture electrons to form muonium atoms which behave chemically as light isotopes of the hydrogen atom. This allows investigation of the largest known "isotope effect" in some of the simplest types of chemical reactions, as well as the early stages of formation of radicals in organic chemicals. Muonium is also studied as an analogue of hydrogen in semiconductors, where hydrogen is one of the most ubiquitous impurities.

Facilities

µSR requires a particle accelerator for the production of a muon beam. This is presently achieved at few large scale facilities in the world: the CMMS[2] continuous source at TRIUMF in Vancouver, Canada; the LMU continuous source at the Paul Scherrer Institut (PSI) in Villigen, Switzerland; the ISIS and RIKEN-RAL pulsed sources at the Rutherford Appleton Laboratory in Chilton, United Kingdom; and the J-PARC facility in Tokai, Japan, where a new pulsed source is being built to replace that at KEK in Tsukuba, Japan. Muon beams are also available at the Laboratory of Nuclear Problems, Joint Institute for Nuclear Research (JINR) in Dubna, Russia. The International Society for µSR Spectroscopy (ISMS) exists to promote the worldwide advancement of µSR. Membership in the society is open free of charge to all individuals in academia, government laboratories and industry who have an interest in the society's goals.