Muon Level Crossing Resonance Spectroscopy An application of a novel magnetic resonance technique

Muons provide a valuable A quick introduction to the muon technique probe of the atomic-level properties of materials. Muon spin resonance spectroscopy is (muons have a mass of one ninth of the Unique information can be less well known than other spin- proton mass). Implanted muons will spectroscopic techniques such as NMR sometimes pick up an electron to form a obtained using the technique and EPR, but it provides researchers light isotope of hydrogen called of Level Crossing Resonance with an important tool that can be used muonium (Mu). By following muon (LCR). to study a wide range of problems in behaviour inside a material we can learn physics and chemistry. about proton and hydrogen behaviour. This is important in semiconducting The muon technique involves implanting LCR can be used to: materials, proton conductors and spin-polarised positive muons into a hydrogen storage materials. • determine free radical material. Muons are short-lived particles, decaying after an average lifetime of structures by measurement 2.2µs to produce positrons. The decay of muon hyperfine coupling positrons which emerge from a sample constants after muon implantation are detected, References on the muon technique include: revealing information about the muons' behaviour inside the material – • Spin polarised muons in condensed matter • investigate the reactions, physics S J Blundell, Contemporary Physics, particularly about how the muon 40 (1999) 175 molecular dynamics and polarisation changed within the sample. local environment of free This, in turn, this enables us to deduce • Implanted muon studies in condensed information about the atomic-level matter science S F J Cox, J. Phys. C: Sol. radicals Stat. Phys., 20 (1987) 3187 properties of the material. • study spin dynamics in • Muon Spectroscopy U A Jayasooriya and Muons are very sensitive probes of R Grinter, Encyclopedia of Applied Physics magnetic systems magnetic systems, often detecting (2009) effects that are too weak to be seen by • determine muon sites, for • Muon spin rotation, relaxation and other methods. They also have a wide resonance: Applications to condensed example in semiconductors variety of other applications – for matter A Yaouanc, P Dalmas de Réotier, example, in studies of superconductors, Oxford University Press (2010), This leaflet provides examples molecular systems and chemical ISBN 0199596476 reactions, novel battery materials and a of how the LCR technique can • Using polarized muons as ultrasensitive variety of organic systems. In some spin labels in free radical chemistry be used. studies, the positive muon can be I McKenzie and E Roduner, thought of as being like a light proton Naturwissenschaften, 96 (2009) 873

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 What can LCR tell us about free radicals? Muon LCR: the basic idea

Once implanted inside a material, muons interact with Structure their local atomic environment. This interaction can be particularly strong when an energy level in the muon Mu 1.5 The structure of a free system matches one within the environment. The radical can be inferred 3.3 1.4 muons and their surroundings are then put on from the muon and % Unpaired ‘speaking terms’, and this can strongly affect the 30 nuclear hyperfine spin density 14 muons’ behaviour. couplings. Such resonances – called level crossing resonances, 2.0 13 13 C60Mu radical. The C 5.4 LCR, (or, sometimes, ‘avoided level crossing hyperfine couplings can be resonances’) – between the muons and their determined from the positions of the resonances. environment can be produced by changing the applied They indicate that the magnetic field in a muon experiment. The resonances unpaired electron is can be detected by observing the muon polarisation – significantly delocalised they are seen as a dip in the polarisation as the applied around the fullerene sphere. field is changed. Observation of such resonances gives P W Percival et al., Chem. Phys. Lett. 245 (1995) 90 us additional information about the muons’ atomic 1.10 1.20 1.30 1.40 environment. Field (T) (a) Molecular dynamics

The resonance lineshape 7 nucleus provides information + H 1 µ d about molecular 1 dynamics in the solid 6 state. 2 4 The lineshape indicates that Mu norbornenyl radicals 5 3 rotate around an axis parallel to C3-C5. E = E H µ nucl M Ricco et al., Phys. Lett. A 183 K 129 (1988) 390; E Roduner et al., Chem. Soc. Rev. 22 (1993) 337 1.50 1.52 1.54 1.56 (b) Field (T) A A µ nuc Reaction rates + – µ e nucleus Radical reaction rates can be measured from ortho- para- meta-PEA-Mu OH OH OH the broadening of resonances, are a CH 2 CH 2 CH 2 H2C H2C H2C function of reactant Mu s l

concentration. e

H v

Mu e l

y g r

H e n Reaction of cyclohexadienyl E radicals with paramagnetic H Mu 2+ Ni . 0 mM H Dilger et al, Physica B 374-375 (2006) 317 1 mM B 0 Field (B)

2 mM Level crossing resonances occur when muons are put 'on speaking terms' with their surroundings. This might be directly with neighbouring nuclei via dipole-dipole coupling as in (a), or 3 mM via hyperfine coupling with an unpaired electron – as found in radical systems – as in (b). 5 mM

1.90 1.95 2.00 2.05 2.10 2.15 Field (T) Example applications of LCR LCR as a probe of soft matter Muon sites in semiconductors LCR can be used to determine the local environment and In semiconducting materials muons are frequently used as light dynamics of co-surfactants present in low concentrations in proton isotopes to model hydrogen behaviour, as hydrogen soft matter structures such as lamellar phases. In the example itself can be very difficult to study directly. here, phenylethanol co-surfactants are spin labeled by the LCR has been used to determine the lattice site of diamagnetic addition of muonium. muons (µ+) in p-type GaAs. Ga and As are quadrupolar nuclei R Scheuermann et al., Langmuir 29 (2004) 2652; A Martyniak et al., Phys. (I>1/2), and so level crossing resonances occur at fields for Chem. Chem. Phys. 8 (2006) 4723 which the muon Zeeman energy matches the combined Zeeman and quadrupolar energy of a nucleus. The positions of the resonances allow both the distances and angles of the High temperature Lα phase muon with respect to neighbouring nuclei and crystal directions to be found. • ∆1 resonances – – • Resonance field indicative of Paramagnetic muonium species (Mu) are also present in GaAs, and LCR can again be used As OH non-polar environment. + to determine its precise lattice location. µ+ + H C 2 Ga CH Co-surfactants reside in the bilayer 2 + H with the hydroxy group near the Right: Quadrupolar resonances of µ Mu with As nuclei for two different field 0.005 interface. The5 cosurfactants are directions in GaAs, together with the (a) 0 rapidly rotating around an axis. muon site. B E Schultz et al., Phys. Rev. Lett. 95 (2005) 086404 -0.005 B||<100> 75 As 75 As (–) (54.7°) 75 As (+) (54.7°) 0.004 0 Below: Bond-centred muonium B||<111> resonances in GaAs. R F Kiefl et al., 0 Phys. Rev. B 58 (1987) 1780 N 75 As Δ1 Δ0 o -0.004 r m 0.66 0.68 0.70 0.72 0.74 -5 a

0.4 0.8 1.2 1.6 2.0 l i

s Field (T)

5 75°C e (b) d

69 Ga (–) (90°) 69 Ga (+) (90°) L 5 C

(a) R (b)

69 (–) 69 (+)

s Ga (90°) Ga (90°) A i s g y m n

m 75 (–) 75 (+) As (54.7°) As (54.7°) a e 0 65°C l t r y

d 0 i f f e r e n c

e 69 (–)

Ga (35.3°) ( 55°C / 1

0 69 (–) 0 -5 Ga (35.3°) 0

) 2.9 3.0 3.1 3.2 3.3 Field (T) -5 0.4 0.8 1.2 1.6 2.0 2.9 3.0 3.1 3.2 3.3 A s

y Field (T) Field (T) 45°C m m e t r y

d

35°C i

Magneticf systems f e r e

Muonn level crossings in magnetic systems have been used c e

(

to study/ spin dynamics in the single-ion magnet 25°C 1 0 0

LiY1-x0 HoxF4. The enhancement of the spin lattice relaxation at the) crossing in a magnetic system is due to a direct exchange of energy between the electronic and probe reservoirs, which results in a cross relaxation. The position, 1.8 2.0 2.2 shape and relative intensity of the peaks in the measured Field (T) spin lattice relaxation provide important information about the spin Hamiltonian of the system and the details of its Low temperature Lβ phase interaction with the spin probe and its environment.

Magnetic field • No ∆1 resonances – 0.88 H C OH dependence of the muon T = 1.8 K • Resonance field indicative of 2 CH 2 spin relaxation rate in – aqueous environment. H LiY0.998 Ho0.002F4 Mu 0.84 Co-surfactants are expelled from the ++ M J Graf, et al., Phys. Rev. bilayer and reside in the aqueous Lett. 99 (2007) 267203 layer. 0.80

0.76 20 40 60 80 Field (mT)

Facilities for Muon Spectroscopy

Europe is fortunate in having two muon sources that are complementary. The beam structure of the SµS, located at the PSI in Switzerland, makes it ideally suited for applications where high timing resolution is essential, such as following fast muon precession or rapid spin depolarisation. In contrast, the pulsed muon beam operated by the STFC in the UK, allows low background time differential data to be captured at high data rates. It also enables the effect of beam synchronous stimuli (such as Radio Frequency or laser radiation) to be investigated. Together, these facilities provide beams of muons for a wide variety of atomic-level studies in condensed matter, molecular, chemical, biological, geological and engineering materials. Further details of the various instruments and sample environment equipment can be found on the facility web sites.

Above: High field muon spectrometer at PSI, Switzerland.

Left: High field muon spectrometer at ISIS, UK At both facilities a number of spectrometers are available with specialist sample environment equipment to enable a broad range of condensed matter and molecular studies on solid, liquid and gaseous samples. Temperature studies can extend from millikelvin temperatures to 1500 K and solid-sample pressures up to 2.5 GPa can be applied. Both facilities have recently completed major instrument upgrades to provide high magnetic fields; at ISIS fields of 5 T parallel to the muon spin are possible, while PSI provides a 9.5 T spectrometer optimised for spin rotation Contacts: measurements. ISIS Facility Dr Adrian Hillier, Using the Facilities [email protected] Tel: +44 (0)1235 446001 Both facilities welcome experiment proposals from scientists of all disciplines. Calls Web: www.isis.stfc.ac.uk/groups/muons for proposals occur twice a year: deadlines at ISIS are 16 April and 16 October, while at PSI deadlines are 10 December and 11 June. Proposals can be made using the STFC online systems available through the respective web pages – typically a two-page Rutherford Appleton Laboratory science case is required. Harwell Oxford Didcot OX11 0QX Members of both groups are available to give advice on all aspects of muon science UK and running muon experiments. They can be contacted to discuss ideas for experiments, for technical and practical information on the muon instruments and to offer advice on draft proposals. PSI Facility Dr Elvezio Morenzoni, [email protected] Tel: +41 (0)56 310 4666 Web: lmu.web.psi.ch Paul Scherrer Institut Laboratory for Muon-Spin Spectroscopy CH-5232 Villigen PSI Switzerland