High Time Resolution Muon Spectroscopy Exploiting a novel magnetic resonance technique Muons provide a very sensitive A quick introduction to the muon technique probe of the atomic-level properties of materials. High Muon spin resonance spectroscopy is and chemical reactions, novel battery Field muon techniques are less well known than other spin- materials and a variety of organic spectroscopic techniques such as NMR systems. In some studies, the positive being developed by the and EPR, but it provides researchers muon can be thought of as being like a European facilities; the high with an important tool that can be used light proton (muons have a mass of one time resolution available at the to study a wide range of problems in ninth of the proton mass). Implanted physics and chemistry. muons will sometimes pick up an SµS enables unique electron to form a light isotope of The muon technique involves implanting phenomena to be investigated. hydrogen called muonium (Mu). By spin-polarised positive muons into a following muon behaviour inside a material. Muons are short-lived particles, Examples of how high time material we can learn about proton and decaying after an average lifetime of hydrogen behaviour. This is important in resolution muon spectroscopy 2.2µs to produce positrons. The decay semiconducting materials, proton can be used for novel positrons which emerge from a sample conductors and hydrogen storage after muon implantation are detected measurements include: materials and insulating materials. revealing information about the muons' • Probing superconductivity; behaviour inside the material – vortex states and length particularly about how the muon polarisation changed within the sample. References on the muon technique include: scales This, in turn, enables us to deduce • Muon spin rotation, relaxation and resonance: Applications to condensed • Studying magnetic systems information about the atomic-level properties of the material. matter A Yaouanc, P Dalmas de Réotier, such as spin liquids and low Oxford University Press (2010), ISBN 0199596476 dimensional magnetism Muons are very sensitive probes of magnetic systems, often detecting • Spin polarised muons in condensed matter • Characterising hydrogen effects that are too weak to be seen by physics S J Blundell, Contemporary Physics, other methods. They also have a wide 40 (1999) 175 impurities in semiconductors variety of other applications – for • The Muon Method in Science, V.P. Smilga, • Investigating quantum example, in studies of superconductors, Yu.M. Belousov, Nova Science Publishers magnetic materials, molecular systems (1994) ISBN 9781560721611 fluctuations in high spin molecules. Muon Positron implantation The muon technique – implantation of positive, spin-polarised muons into a sample, followed by detection of positrons emitted when the muons decay. Positron Material detector being studied Muons decay with 2.2µs average lifetime High resolution muon Example Applications of High Resolution Muon Spectroscopy in Condensed Matter Physics spectroscopy: the basic idea Superconductivity Once implanted inside a material, muons interact with their The vortex state induced in a type-II superconductor when a local atomic environment. In some cases this interaction can strong magnetic field is applied can be studied using muons. be strong, and fast timing resolution is required to follow the The technique probes the magnetic field on a length scale much evolution of the muon spin polarization. For example, in shorter than the inter vortex distance, enabling information magnetic systems, large internal fields give rise to fast about the internal vortex structure and interactions to be precession frequencies, while broad internal field distributions obtained. will lead to a rapid decay of the muon polarisation. In chemical systems, the measurement of detailed spectroscopic information requires large probing fields which, in turn, give rise to energy level splittings of the order of hundreds of y t i megahertz. s n 0.1 e Field distribution t n The beam structure of the SµS, located at PSI, Switzerland is I (with model fit) of a vortex ideally suited to these types of measurement. Here, muons are lattice formed in SrFe Co As at 1.6K and implanted into the sample one by one, enabling accurate 1.75 0.25 2 an external field of 10mT. measurement of the time interval between the arrival of the 0 Adapted from R. Khasanov et. al. muon and the detection of the decay positron. With careful Phys. Rev. Lett. 103, 067010 (2009). instrument design and advanced detector technologies, time 8.0 10.0 12.0 14.0 Magnetic field (mT) resolutions better than 80ps are possible. This is illustrated by the transverse field experiment, where fast sad muon precession is measured in a large external magnetic field applied perpendicular to the initial muon spin polarisation. In this case a 9.5T field was applied to muons stopped in a silver plate and a precession frequency of ~1.3 GHz is measured. The decay of the muon response and the corresponding shape of the y t Fourier transform reflect the microscopic field distribution i s n sensed by the muon. e t n I min min H <B> sad max µ+ 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 Magnetic field (mT) Positron Muons are now routinely used to determine characteristic length detector scales, such as the magnetic penetration depth and coherence Muon detector length, and the muon technique enables vortex lattice topology Sample + to be investigated. Muons are also playing a key role in the e search for experimental evidence for exotic vortex states. For example, a change in the spatial field distribution around the vortex cores has been predicted for clean superconductors at low temperatures and at fields close to the upper critical field. 35 Spectrometers capable of extended temperature and field 0.4 measurements promise to bring a new insight to these studies. 30 n 0.2 o i t a BCS model GL limit of BCS s 0 i 25 r T 0 T Tc a l y o t -0.2 i P ) s ) ) ) n 20 1 1 B B e ( -0.4 ( t - - c c n v v I B B ( ( 15 12345 / / 0 ) ) ) Time (ns) ) 0 B B ( ( - - B B 10 ( ( -1 Y Y 5 XX Models for conventional (left) and exotic (right) vortex states can be 0 1286 1288 1290 1292 1294 investigated using muon techniques. Frequency (MHz) A. Maisuradze et al., arXiu:1303.0209v1 (2013). Precise measurement of the time interval between muon arrival and decay (top) enables high resolution spectra to be recorded. ion Muon Spectroscopy in Condensed Matter Physics Probing Spin Liquids Semiconductors and Oxides The quantum spin-liquid phase is an intriguing state where the Muonium, a bound µ+e- system, can be considered as a light usual magnetically ordered ground state is avoided even at the hydrogen isotope, and is frequently used to obtain information lowest temperatures for a system of strongly interacting about isolated hydrogen in semiconducting systems. High magnetic spins. Spin liquid systems such as the Mott insulator transverse field muon spin rotation measurements enable high χ -(BEDTTTF)2Cu2(CN)3 display a complex phase diagram that can resolution spectroscopy of the different electronic states this best be investigated using the extended field and temperature hydrogen-like isotope can take, with the hyperfine coupling regimes offered by the latest muon spectrometers. Existing providing information about the local environment. Spin measurements have demonstrated no obvious signature for dynamics and state transitions can also be probed by conventional magnetic ordering to 20mK. investigating the field dependence of polarised muonium at different temperatures. µSR NMR 2.0 QC H w ≈ 0.5 10 Tp W≈0 w ≈ 0 E C WAF H QC M B W≈0.3 2 D (ß H ≈ 0.8 , ηH ≈ 1) 1.5 ) 1 Δ K v ( O e r y u t + t i µ s a 0.1 r n 1.0 e WAF QC L L e Zn t p 5 n W≈0 (ß ≈ 0.4 η ≈ 0) . I m L , L 1 e T ≈ 0.01 w Δs 0.5 0.001 GS H0 H1 0.001 0.01 0.1 1 10 µ0H (T) 0 402 403 404 405 406 407 408 χ Frequency (MHz) The rich phase diagram (left) of the Mott insulator -(BEDTTTF)2 (right, grey + C and yellow = S) Cu2(CN)3 is readily explored using muon techniques. Compared to conventional resonance techniques, muon spectroscopy Spectroscopy of a Mu(H) centre formed in ZnO (inset). Line intensities enables measurement over a greatly extended field range. reflect electron polarization. F. L. Pratt et al., Nature 471, 612 (2011). Adapted from K. Shimomura et al., PSI Annual Report 2005. Low Dimensional Magnetism High Spin Molecules Low dimensional quantum spin systems are remarkable for their Molecular clusters containing as few as 10 to 100 atoms might diverse and fascinating physical behaviour, and the muon be used as magnetic memory units, potentially offering greatly technique provides an ideal probe of their properties. For increased storage density. These systems are high spin example, quantum phase transitions between gapped and molecules, comprising a small network of magnetic ions such gapless phases of two-leg spin-ladder systems such as that the net spin of the cluster is large (e.g. 10, 27/2 or 39/2). (Hpip)2CuBr4 can be driven using a large external magnetic field. Unfortunately, molecular spin relaxation rates currently limit the The Luttinger Liquid regime, where the spectrum is gapless with application of these systems, and high field muon spectroscopy no finite order parameter, can also be investigated from the provides an ideal method for determining the quantum high-temperature classical regime through a crossover. fluctuations and tunnelling driving this spin relaxation. 0 0.5 1.0 1.5 2.0 2.5 2 Cm/T [mJ/gK ] 5 50 4.5 (Hpip) 2CuBr 4 B||a 4.0 ) c l ) 3.5 o 0 K ( m / e 3.0 a J r k u ( t y a 2.5 r g r e e p 2.0 n m E -50 e T 1.5 1.0 QC 0.5 QD LL B B -100 0 c s 0246810 0246810 12 14 Field (T) Magnetic field (T) Energy levels for Mn12-acetate16 (S=10) (grey = C, white = H, red = O and Phase diagram of the spin-ladder (Hpip)2CuBr (inset).