Muon Spin Rotation/Relaxation/Resonance

Muon Spin µSR Rotation/Relaxation/Resonance (µµµSR) Unlike the electron, the muon is an magnetic moment is 3.18 times larger Understanding the fundamental unstable particle, living for only about than a proton. Thus when implanted in physical properties of matter at a two millionths of a second. Muons matter this feature makes them an microscopic level enables the extension carry a positive (µ+) or negative (µ-) extremely sensitive microscopic probe of existing technologies and leads to the charge, and spontaneously decay into a of magnetism. development of reliable new materials positron (or an electron) and a neutrino- for tomorrow’s applications. For these anti-neutrino pair as follows: reasons, scientists are interested in The Birth of µµµSR studying microscopic structures and µ e ++ ++→ νν processes in a wide range of materials. e µ he acronym µSR was coined in Only through experimental verification e −− ++→ ννµ T can one establish physical laws e µ 1974 to grace the cover of the first issue describing their inner workings. Since of the µSR Newsletter, in which the we cannot see such small-scale Muon following definition and explanation phenomena directly with our eyes, we were given: must rely on experimental methods that can probe deep inside materials for us. µµµSR stands for Muon Spin Relaxation, Rotation, Resonance, Research or The µSR technique is one such method. what have you. The intention of the It makes use of a short-lived subatomic mnemonic acronym is to draw particle called a muon, whose spin and attention to the analogy with NMR and charge are exquisitely sensitive local ESR, the range of whose applications magnetic and electronic probes of is well known. Any study of the matter. µSR’s place amongst those interactions of the muon spin by virtue experimental techniques that utilize a of the asymmetric decay is considered probe magnetic moment to investigate Proton µµµSR, but this definition is not intended matter is distinguishable by its extreme to exclude any peripherally related sensitivity to magnetism and its unique phenomena, especially if relevant to time window for dynamical processes. the use of the muon's magnetic Researchers generally use the µSR moment as a delicate probe of matter. technique to tackle fundamental problems in condensed matter physics and chemistry that one cannot The story of µSR began with an Solid-state physicists and investigate by other means. American revolution in theoretical chemists generally think of physics. T.D. Lee and C.N. the muon as a light Yang, co-winners of the What Are Muons? proton. Nobel Prize in 1957, predicted that any High up in the earth’s process governed n 1937, the muon was discovered as I atmosphere, muons are by the weak secondary radiation from cosmic rays. naturally created by the nuclear With a mass about 200 times that of an interaction of cosmic rays electron (or 9 times less than that of a with gas molecules. Here proton) the muon appeared to be simply on earth we can produce a heavier version of the electron. The muons using a particle mere existence of the muon was so accelerator. Muons are completely unexpected at the time that charged spin-½ particles its discovery prompted the following that can couple to their remark: local environment via µµµSR is a collection of methods that uses the their spin. The muon’s muon spin to look at structural and dynamical “Who ordered that?” −−− I.I. Rabi −−− processes in the bulk of a material on an atomic scale. 1 µSR interaction might not have a while minimizing multiple scattering of higher momentum (approximately 50- corresponding "mirror image" process the proton beam. The charged pions 100 MeV/c), a larger momentum spread of equal probability. Prior to their that are produced live for only about 26 (and therefore lower stopping density) suggestion it was firmly believed by the billionths of a second and then decay and much larger phase space (and physics community that if a reaction into a muon and muon neutrino (anti- therefore lower luminosity). While the were viewed in a mirror, the mirror neutrino): two latter features are less desirable, image was a priori just as likely to backward muons are the only means of occur as the original process a + + studying samples contained in a thick +→ νµπ u principle known as parity symmetry. target vessel. Such vessels are used in − − +→ νµπ µ studies of gases or liquids and studies Although parity "violation" was first of high-pressure effects. observed in kaon decay, credit for its experimental discovery is usually given High Carbon or Why Does µµµSR Work? to C.S. Wu et al. who confirmed its Energy Neutrino 60 Proton Beryllium existence in the β-decay of Co. Nuclei However, at almost the same time experiments were performed at the The µSR technique is made Nevis cyclotron of Columbia possible by the unique properties of the University by R.L. Garwin, L.M. Pion pion and muon decays: Lederman and M. Weinrich, and at the Chicago cyclotron by J.I. Friedman and First, thanks to maximal parity V.L. Telegdi, which showed a dramatic violation in the weak interaction decay of pions, surface muons are perfectly effect in the decay of pions to muons Muon and the subsequent decay of muons to spin polarized opposite to their electrons, neutrinos and anti-neutrinos. Muon beams are made here on momenta, so when a muon is The Nevis group suggested in their earth using high-energy protons transported down the beam line to stop landmark paper that non-conservation to produce short-lived pions. in the sample being studied, it arrives of parity in muon decay might furnish a nearly 100% spin polarized. This is a sensitive general-purpose probe of significant improvement on other matter. The history of µSR began with magnetic resonance probes such as + that experiment. In the modern µSR Most positive muon (µ ) beams at a nuclear magnetic resonance (NMR) and method, the lifetime experience of the µSR facility are generated from pions electron spin resonance (ESR) methods muon in matter is passed on to us by decaying at rest in the surface layer of that must rely upon thermal equilibrium way of its decay into a positron the primary production target hence spin polarization in a magnetic field (electron), which we can easily detect. the common name, surface muons. The so that sufficient polarization is often muon is emitted isotropically from the achieved only at low temperatures pion with momentum pµ = 29.8 MeV/c and/or in strong magnetic fields. Making Muons and kinetic energy 4.119 MeV (in the rest frame of the π+). Unfortunately, Second, when the muon decays it emits this mode is not available for negative a fast decay positron (electron) Although muons are produced in a muons (µ-) because a negative pion preferentially along the direction of its variety of high-energy processes and stopping in the production target almost spin due to the parity violating decay. elementary particle decays, µSR always undergoes nuclear capture from From a single decay positron we cannot requires low energy muons that will low-lying orbitals of pionic atoms be certain which direction the muon stop in the samples being studied. Low- before it has a chance to decay. This spin is pointing in the sample. energy muons are available in the problem is overcome by allowing the However, by measuring the anisotropic required intensities only from ordinary pions to decay in flight within a long distribution of the decay positrons from two-body pion decay. Thus, before superconducting solenoid. The muons a bunch of muons deposited at the same making a source of muons, one must that are emitted opposite to the conditions, one can determine the make pions. Pions are produced in direction of the pion momentum are statistical average direction of the spin sufficient numbers from collisions of called backward muons, which can be polarization of the muon ensemble. The high-energy protons (>500 MeV) with selectively extracted by a bending time evolution of the muon spin the nuclei of an intermediate target. A magnet. While this method can also be polarization depends sensitively on the light element such as carbon or used for µ+SR, for µ-SR there is no spatial distribution and dynamical beryllium is used for the primary target alternative. Compared to surface muon fluctuations of the muons’ magnetic in order to maximize pion production, beams, backward muon beams have environment. 2 µSR a=1/3 µ+ a=1 + Parity-violating collinear decay of a pion πππ at rest Angular distribution of the positrons from the + into a muon µµµ and a muonic neutrino νννµµµ. muon decay: W(E,θθθ) = 1 + a(E)cos(θθθ). When all positron energies E are sampled with equal probability the asymmetry parameter has the µµµSR Facilities value a = 1/3 (red curve). Pulsed beam facilities direct intense allows detection of muon decay events The muon beams currently available bunched proton pulses produced from a beyond 10 muon lifetimes providing for µSR are distinguishable by their time synchrotron or linac onto the muon greater sensitivity to the form of the structure: production target. The pulse structure of muon relaxation function. A pulsed the primary surface muon beam reflects muon source is also ideally suited for Continuous Wave (CW) facilities deliver the pulse structure of the proton beam, resonance studies, since an RF field a nearly continuous source of protons but with the pulses further smeared out and/or light illumination can be that are used to produce muons that by the pion lifetime. A general synchronized with the muon pulses.

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