Muon Spin Spectroscopy Exploiting a novel resonance technique Muons provide a very sensitive A quick introduction to the muon technique probe of the atomic-level Muon spin spectroscopy is less well known than other spin spectroscopic techniques properties of materials. Muon such as NMR and EPR, but it provides researchers with an important tool that can be techniques are available at the used to study a wide range of problems in physics and chemistry. European facilities, enabling unique phenomena to be Muon Positron investigated. implantation Examples of how muon spectroscopy can be used for novel measurements include: Positron Material detector • Probing superconductivity; being studied vortex states, length scales Muons decay with and small spontaneous fields. 2.2µs average lifetime • Studying both static and The muon technique involves implanting applications – for example, in studies of dynamic behaviour in spin-polarised S=½ positive muons into a superconductors (where the vortex lattice material where they act as a local probe. can be probed and characteristic length magnetic systems: from Muons are short-lived particles, decaying scales determined), molecular systems bulk ordered states to more after an average lifetime of 2.2 μs to and chemical reactions, novel battery novel topics such as spin produce positrons. The decay positrons materials and a variety of organic systems. liquids and low dimensional which emerge from a sample after muon In some studies, the positive muon can implantation are detected revealing be thought of as being like a light proton magnetism. information about the muons’ behaviour (muons have a mass of one ninth of • Investigating magnetic inside the material – particularly about the proton mass); implanted muons can how the muon polarisation changed sometimes pick up an electron to form a behaviour at interfaces and within the sample. This, in turn, enables light isotope of hydrogen called muonium surfaces. us to deduce information about the (Mu). By following muon behaviour inside • Characterising hydrogen properties of the material on an atomic a material we can learn about proton and scale, and to probe the system on a hydrogen behaviour. This is important behaviour in semiconductors, unique timescale. in semiconducting materials, proton minerals and hydrogen conductors, hydrogen storage materials storage materials. Neutron scattering and insulating materials. Mossbauer References on the muon technique include: • Measuring ionic diffusion µSR NMR • Muon spin rotation, relaxation and coefficients in battery ac susceptibility resonance: Applications to condensed materials. Remanence matter, A. Yaouanc, P. Dalmas de Réotier, 100 102 104 106 108 1010 1012 Oxford University Press, ISBN 0199596476 • Investigating molecular -1 Fluctuation rate, s (2010). dynamics and electron spin Muons are very sensitive probes of • Spin polarised muons in condensed matter magnetic systems, often able to detect relaxation at a molecular physics, S.J. Blundell, Contemporary Physics effects that are too weak to be seen by level. 40, 175 (1999). other methods; as well as allowing both • Studying reaction kinetics static and dynamic magnetic behaviour to • The positive muon and μSR spectroscopy: powerful tools for investigating the and unusual bonding. be investigated. The penetration depth of low energy muons can be varied by tuning structure and dynamics of free radicals their momentum, allowing behaviour and spin probes in complex systems, This leaflet provides examples I. McKenzie, Annu. Rep. Prog. Chem., Sect. C: of the unique information that at surfaces and interfaces to be probed. Muons also have a wide variety of other Phys. Chem. 109, 65‑112 (2013). can be gained from the muon technique. Example Applications of the Muon as a Magnetic Probe Quantum Magnetism Surfaces & Interfaces μSR is able to map out phase diagrams of low moment Low energy muons can be implanted at different depths systems at very low temperatures and applied fields. allowing surfaces and interfaces to be probed. The extended field and temperature regimes offered by the The energy of muon beams can be tuned allowing them to latest muon spectrometers enable complex phase diagrams be implanted at different depths within materials. Using low and unusual phases to be investigated. A quantum spin energy muons (LEM) enables us to probe magnetic behaviour liquid is one such intriguing state where a system of strongly at surfaces and interfaces as well as within the bulk of interacting magnetic spins avoids a magnetically ordered materials. ground state, even at the lowest temperatures. Measurements Recently this technique has been used of spin liquid systems such as the Mott insulator -(BEDTTTF) χ 2 to study how the Stoner Criterion can be Cu (CN) , have demonstrated no obvious signature for 2 3 overcome to induce room temperature conventional magnetic ordering to 20 mK. ferromagnetism in normally para- or µSR NMR diamagnetic materials. This can be achieved via the interface between QCH w ≈ 0.5 10 Tp W≈0 a metallic thin film (e.g. diamagnetic w ≈ 0 QCM WAFH Cu) and an electron withdrawing C W≈0.3 (ßH ≈ 0.8, ηH ≈ 1) 60 ) 1 2D BEC Δv molecular layer. e (K atur 0.1 LEM μSR measurements on Cu/C QCL WAFL 60 W≈0 (ß ≈ 0.4 η ≈ 0) mper L , L multilayers show that spin-ordered states Te 0.01 Δs w ≈ 1.5 are found at and close to the metal- 0.001 GS H0 H1 molecule interface, which simulations 0.001 0.01 0.1110 indicate are based on a magnetic µ0H (T) hardening of the metal atoms due to electron transfer. The rich phase diagram (left) of χ-(BEDTTTF)2 Cu2(CN)3 is readily explored using muon techniques. Compared to conventional resonance A schematic diagram illustrating how the techniques, muon spectroscopy enables measurements over a greatly LEM measurement in Cu/C60 multilayers was extended field range, reaching to lower fields. performed. F. L. Pratt et al., Nature 471, 612 (2011). F. Al Ma’Mari et al., Nature 524, 69 (2015). Superconductivity Ionic Conductors Muons are a sensitive probe of length scales, symmetry μSR is able to probe intrinsic ion diffusion coefficients and spontaneous fields in superconductors. even in the presence of magnetic ions. Understanding the symmetry of the superconducting state The diffusion of certain ions (e.g. Li+, Na+) past an implanted is critical and muons can determine the nature of the muon alters the local magnetic field at the muon site. This superconducting gap. The optimally doped iron pnictide can allow the intrinsic ionic diffusion rate to be measured superconductor Ba0.65Rb0.35Fe2As2 was investigated under microscopically, even in the presence of magnetic ions. pressure showing the promotion of a nodal gap, most likely The lithium diffusion rate in the battery material Li CoO was d-wave in origin. Also, the onset of spontaneous fields at T is x 2 C measured from μSR experiments by studying the fluctuations a key indicator of time reversal symmetry breaking, as seen in in the local field at the muon site as the Li+ ions diffuse past. LaNiGa , implying triplet pairing. 2 The diffusion rate was found to be in excellent agreement with ab initio calculations despite the presence of magnetic Co ions, which affects the reliability of measurements made by other techniques such as NMR. The nodal d-wave state favoured by the application of pressure to the superconducting phase of Ba0.65Rb0.35Fe2As2 and the onset of spontaneous Li hopping pathways and hopping rates in LixCoO2. fields at CT in LaNiGa2. J. Sugiyama et al., Phys. Rev. Lett. , 147601 (2009). Z. Guguchia et al., Nature Communications 6, 8863 (2015). 103 A. D. Hillier et al., Phys. Rev. Lett. 109, 097001 (2012). Example Applications of the Muon as a Proton Analogue Hydrogen Storage Geophysics The high sensitivity of μSR allows the hydrogen storage μSR is able to probe hydrogen existing irregularly in properties of low density materials to be probed. matter such as in minerals. Graphene is a potential low-density hydrogen storage μSR can be used to understand how water and hydrogen are material. The high sensitivity of μSR measurements allowed stored, even irregularly, within minerals as the muon models the hydrogen storage behaviour of the low-density material, the behaviour of a hydrogen ion. Understanding processes hydrogenated graphene to be investigated. The presence of a in minerals within the Earth is important as these control the muon oscillation signal was observed, usually the fingerprint dynamics and evolution of our planet. Muonium forms when of magnetic order. In this case, however, it was found to arise muons are implanted in the high-pressure silicate mineral from muon-hydrogen nuclear dipolar interactions, providing an stishovite. The very large relaxation rate of the muonium spin insight into the mechanism of hydrogen storage in graphene. polarisation and hyperfine-coupling suggest that the muonium (or hydrogen) does not bind to O or Si but is squeezed into small, anisotropic, interstitial voids, inferring the existence of neutral, atomic hydrogen in the deep mantle. The oscillation in the muon decay asymmetry and the mechanism of muon addition to hydrogenated graphene. M. Riccò et al., Nano Lett., 11(11), 4919‑4922 (2011), The structures of stishovite and quartz and a comparison of their M. Gaboardi et al., J. Mater. Chem. A 2, 1039 (2014). transverse field spectra. N. Funamori et al., Scientific Reports5 , 8437 (2015). Molecular Dynamics Kinetics & Bonding μSR allows the study of intrinsic molecular dynamics Muonium acts as a light hydrogen isotope and can be and electron spin relaxation at a molecular level. used to investigate unusual bonding states. Muonium can add to unsaturated chemical bonds to form The analogous behaviour of muons to light protons makes muoniated radical species. These species provide a unique them an ideal probe of chemical processes including reaction probe for molecular dynamics and electron spin relaxation at a kinetics and bonding interactions.