Muons provide a valuable probe of the atomic-level properties of materials. Unique information can be obtained using the technique of Level Crossing Resonance (LCR). LCR can be used to: • determine free radical structures by measurement of muon hyperfine coupling constants • investigate the reactions, molecular dynamics and local environment of free radicals • study spin dynamics in magnetic systems • determine muon sites, for example in semiconductors This leaflet provides examples of how the LCR technique can be used. Muon Level Crossing Resonance Spectroscopy An application of a novel magnetic resonance technique Muon spin resonance spectroscopy is less well known than other spin- spectroscopic techniques such as NMR and EPR, but it provides researchers with an important tool that can be used to study a wide range of problems in physics and chemistry. The muon technique involves implanting spin-polarised positive muons into a material. Muons are short-lived particles, decaying after an average lifetime of 2.2μs to produce positrons. The decay positrons which emerge from a sample after muon implantation are detected, revealing information about the muons' behaviour inside the material – particularly about how the muon polarisation changed within the sample. This, in turn, this enables us to deduce information about the atomic-level properties of the material. Muons are very sensitive probes of magnetic systems, often detecting effects that are too weak to be seen by other methods. They also have a wide variety of other applications – for example, in studies of superconductors, molecular systems and chemical reactions, novel battery materials and a variety of organic systems. In some studies, the positive muon can be thought of as being like a light proton (muons have a mass of one ninth of the proton mass). Implanted muons will sometimes pick up an electron to form a light isotope of hydrogen called muonium (Mu). By following muon behaviour inside a material we can learn about proton and hydrogen behaviour. This is important in semiconducting materials, proton conductors and hydrogen storage materials. References on the muon technique include: • Spin polarised muons in condensed matter physics S J Blundell, Contemporary Physics, 40 (1999) 175 • Implanted muon studies in condensed matter science S F J Cox, J. Phys. C: Sol. Stat. Phys., 20 (1987) 3187 • Muon Spectroscopy U A Jayasooriya and R Grinter, Encyclopedia of Applied Physics (2009) • Muon spin rotation, relaxation and resonance: Applications to condensed matter A Yaouanc, P Dalmas de Réotier, Oxford University Press (2010), ISBN 0199596476 • Using polarized muons as ultrasensitive spin labels in free radical chemistry I McKenzie and E Roduner, Naturwissenschaften, 96 (2009) 873 The muon technique – implantation of positive, spin-polarised muons into a sample, followed by detection of positrons emitted when the muons decay. Muon implantation Material being studied Muons decay with 2.2μs average lifetime Positron Positron detector A quick introduction to the muon technique
Transcript
Muons provide a valuableprobe of the atomic-levelproperties of materials. Unique information can beobtained using the techniqueof Level Crossing Resonance(LCR).
LCR can be used to:
• determine free radicalstructures by measurementof muon hyperfine couplingconstants
• investigate the reactions,molecular dynamics andlocal environment of freeradicals
• study spin dynamics inmagnetic systems
• determine muon sites, forexample in semiconductors
This leaflet provides examplesof how the LCR technique canbe used.
Muon Level Crossing Resonance SpectroscopyAn application of a novel magnetic resonance technique
Muon spin resonance spectroscopy isless well known than other spin-spectroscopic techniques such as NMRand EPR, but it provides researcherswith an important tool that can be usedto study a wide range of problems inphysics and chemistry.
The muon technique involves implantingspin-polarised positive muons into amaterial. Muons are short-lived particles,decaying after an average lifetime of2.2µs to produce positrons. The decaypositrons which emerge from a sampleafter muon implantation are detected,revealing information about the muons'behaviour inside the material –particularly about how the muonpolarisation changed within the sample.This, in turn, this enables us to deduceinformation about the atomic-levelproperties of the material.
Muons are very sensitive probes ofmagnetic systems, often detectingeffects that are too weak to be seen byother methods. They also have a widevariety of other applications – forexample, in studies of superconductors,molecular systems and chemicalreactions, novel battery materials and avariety of organic systems. In somestudies, the positive muon can bethought of as being like a light proton
(muons have a mass of one ninth of theproton mass). Implanted muons willsometimes pick up an electron to form alight isotope of hydrogen calledmuonium (Mu). By following muonbehaviour inside a material we can learnabout proton and hydrogen behaviour.This is important in semiconductingmaterials, proton conductors andhydrogen storage materials.
References on the muon technique include:
• Spin polarised muons in condensed matterphysics S J Blundell, Contemporary Physics,4400 (1999) 175
• Implanted muon studies in condensedmatter science S F J Cox, J. Phys. C: Sol.Stat. Phys., 2200 (1987) 3187
• Muon Spectroscopy U A Jayasooriya andR Grinter, Encyclopedia of Applied Physics(2009)
• Muon spin rotation, relaxation andresonance: Applications to condensedmatter A Yaouanc, P Dalmas de Réotier,Oxford University Press (2010), ISBN 0199596476
• Using polarized muons as ultrasensitivespin labels in free radical chemistryI McKenzie and E Roduner,Naturwissenschaften, 9966 (2009) 873
The muon technique – implantation of positive,spin-polarised muons into a sample,
followed by detection of positrons emitted when the muons decay.
Muonimplantation
Materialbeing studied
Muons decay with 2.2µs average lifetime
Positron
Positrondetector
A quick introduction to the muon technique
Field (T)1.90
5 mM
3 mM
2 mM
1 mM
0 mM
1.95 2.00
OH
Mu
MuH
H MuH
CH2H2C
2.05 2.10 2.15
OH
CH2H2C
OHortho- para- meta-PEA-Mu
CH2H2C
Muon LCR: the basic ideaOnce implanted inside a material, muons interact withtheir local atomic environment. This interaction can beparticularly strong when an energy level in the muonsystem matches one within the environment. Themuons and their surroundings are then put on‘speaking terms’, and this can strongly affect themuons’ behaviour.
Such resonances – called level crossing resonances,LCR, (or, sometimes, ‘avoided level crossingresonances’) – between the muons and theirenvironment can be produced by changing the appliedmagnetic field in a muon experiment. The resonancescan be detected by observing the muon polarisation –they are seen as a dip in the polarisation as the appliedfield is changed. Observation of such resonances givesus additional information about the muons’ atomicenvironment.
Level crossing resonances occur when muons are put 'onspeaking terms' with their surroundings. This might be directlywith neighbouring nuclei via dipole-dipole coupling as in (a), orvia hyperfine coupling with an unpaired electron – as found inradical systems – as in (b).
Structure
The structure of a freeradical can be inferredfrom the muon andnuclear hyperfinecouplings.
13C60Mu radical. The 13Chyperfine couplings can bedetermined from thepositions of the resonances.They indicate that theunpaired electron issignificantly delocalisedaround the fullerene sphere.
P W Percival et al., Chem.Phys. Lett. 224455 (1995) 90
Molecular dynamics
The resonance lineshapeprovides informationabout moleculardynamics in the solidstate.
The lineshape indicates thatnorbornenyl radicals rotate around an axisparallel to C3-C5.
M Ricco et al., Phys. Lett. A112299 (1988) 390; E Roduner etal., Chem. Soc. Rev. 22(1993) 337
Reaction rates
Radical reaction ratescan be measured fromthe broadening ofresonances, are afunction of reactantconcentration.
Reaction of cyclohexadienylradicals with paramagneticNi2+.
H Dilger et al, Physica B 337744--337755 (2006) 317
Ener
gy le
vels
Field (B)
nucleus
µ+
µ+
e–
nucleus
Hd
Aµ
Anuc
B0
Eµ
= Enucl
(b)
(a)
What can LCR tell us about free radicals?
Field (T)
1.10 1.20 1.30 1.40
1.5
1.43.3
30
Mu
14
5.42.0
% Unpaired spin density
Field (T)1.521.50 1.54 1.56
183 KH
Mu
3
2
1
1
7
6
5
4
Muon sites in semiconductorsIn semiconducting materials muons are frequently used as lightproton isotopes to model hydrogen behaviour, as hydrogenitself can be very difficult to study directly.
LCR has been used to determine the lattice site of diamagneticmuons (µ+) in p-type GaAs. Ga and As are quadrupolar nuclei(I>1/2), and so level crossing resonances occur at fields forwhich the muon Zeeman energy matches the combinedZeeman and quadrupolar energy of a nucleus. The positions ofthe resonances allow both the distances and angles of themuon with respect to neighbouring nuclei and crystaldirections to be found.
Paramagnetic muonium species (Mu) are alsopresent in GaAs, and LCR can again be usedto determine its precise lattice location.
RRiigghhtt:: Quadrupolar resonances of µ+
with As nuclei for two different fielddirections in GaAs, together with themuon site. B E Schultz et al., Phys.Rev. Lett. 9955 (2005) 086404
BBeellooww:: Bond-centred muoniumresonances in GaAs. R F Kiefl et al.,Phys. Rev. B 5588 (1987) 1780
Magnetic systemsMuon level crossings in magnetic systems have been usedto study spin dynamics in the single-ion magnet LiY1-xHoxF4. The enhancement of the spin lattice relaxationat the crossing in a magnetic system is due to a directexchange of energy between the electronic and probereservoirs, which results in a cross relaxation. The position,shape and relative intensity of the peaks in the measuredspin lattice relaxation provide important information aboutthe spin Hamiltonian of the system and the details of itsinteraction with the spin probe and its environment.
Magnetic fielddependence of the muonspin relaxation rate inLiY0.998Ho0.002F4
M J Graf, et al., Phys. Rev.Lett. 9999 (2007) 267203
Field (T)0.66
B||<111>
-0.004
0
0.004
Nor
mal
ised
LC
R si
gnal 0.005
0
-0.005
0.68 0.70 0.72 0.74
75As
B||<100> 75As
As
Gaµ+
Field (T)
Asy
mm
etry
dif
fere
nce
(/10
00)
5(a)
(b)
0
-50.8
75As(–)(54.7°) 75As(+)(54.7°)
69Ga(+)(90°)
69Ga(–)(35.3°)
69Ga(–)(90°)
0.4 1.2 1.6 2.0
5
0
-53.02.9 3.1 3.2 3.3
Field (T)Field (T)
Asy
mm
etry
dif
fere
nce
(/10
00)
5(a) (b)
0
-50.8
75As(–)(54.7°) 75As(+)(54.7°)
69Ga(+)(90°)
69Ga(–)(35.3°)
69Ga(–)(90°)
0.4 1.2 1.6 2.0 3.02.9 3.1 3.2 3.3
T = 1.8 K
Field (mT)
0.88
0.84
0.80
0.7620 40 60 80
75°C
Δ1 Δ0
65°C
55°C
45°C
35°C
25°C
2.22.0
Field (T)
1.8
HCH2
H2C
OH
Mu
––
++
H
CH2
H2C OH
Mu
–
–
+ +
Example applications of LCR
LCR as a probe of soft matterLCR can be used to determine the local environment anddynamics of co-surfactants present in low concentrations insoft matter structures such as lamellar phases. In the examplehere, phenylethanol co-surfactants are spin labeled by theaddition of muonium.
R Scheuermann et al., Langmuir 2299 (2004) 2652; A Martyniak et al., Phys.Chem. Chem. Phys. 88 (2006) 4723
High temperature Lα phase
• ∆1 resonances
• Resonance field indicative ofnon-polar environment.
Co-surfactants reside in the bilayerwith the hydroxy group near theinterface. The cosurfactants arerapidly rotating around an axis.
Low temperature Lβ phase
• No ∆1 resonances
• Resonance field indicative ofaqueous environment.
Co-surfactants are expelled from thebilayer and reside in the aqueouslayer.
Europe is fortunate in having two muon sources that are complementary. Thebeam structure of the SµS, located at the PSI in Switzerland, makes it ideallysuited for applications where high timing resolution is essential, such as followingfast muon precession or rapid spin depolarisation. In contrast, the pulsed muonbeam operated by the STFC in the UK, allows low background time differentialdata to be captured at high data rates. It also enables the effect of beamsynchronous stimuli (such as Radio Frequency or laser radiation) to beinvestigated. Together, these facilities provide beams of muons for a wide varietyof atomic-level studies in condensed matter, molecular, chemical, biological,geological and engineering materials. Further details of the various instrumentsand sample environment equipment can be found on the facility web sites.
At both facilities a number of spectrometers are available with specialist sampleenvironment equipment to enable a broad range of condensed matter and molecularstudies on solid, liquid and gaseous samples. Temperature studies can extend frommillikelvin temperatures to 1500 K and solid-sample pressures up to 2.5 GPa can beapplied. Both facilities have recently completed major instrument upgrades toprovide high magnetic fields; at ISIS fields of 5 T parallel to the muon spin arepossible, while PSI provides a 9.5 T spectrometer optimised for spin rotationmeasurements.
Using the FacilitiesBoth facilities welcome experiment proposals from scientists of all disciplines. Callsfor proposals occur twice a year: deadlines at ISIS are 16 April and 16 October, whileat PSI deadlines are 10 December and 11 June. Proposals can be made using theonline systems available through the respective web pages – typically a two-pagescience case is required.
Members of both groups are available to give advice on all aspects of muon scienceand running muon experiments. They can be contacted to discuss ideas forexperiments, for technical and practical information on the muon instruments and tooffer advice on draft proposals.
