Muons provide a very sensitiveprobe of the atomic-levelproperties of materials. HighField muon techniques arebeing developed by theEuropean facilities; the hightime resolution available at theSµS enables uniquephenomena to be investigated.

Examples of how high timeresolution muon spectroscopycan be used for novelmeasurements include:

• Probing superconductivity;vortex states and lengthscales

• Studying magnetic systemssuch as spin liquids and lowdimensional magnetism

• Characterising hydrogenimpurities in semiconductors

• Investigating quantumfluctuations in high spinmolecules.

High Time Resolution Muon SpectroscopyExploiting 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 detectedrevealing information about the muons'behaviour inside the material –particularly about how the muonpolarisation changed within the sample.This, in turn, 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,magnetic materials, molecular systems

and chemical reactions, novel batterymaterials and a variety of organicsystems. In some studies, the positivemuon can be thought of as being like alight proton (muons have a mass of oneninth of the proton mass). Implantedmuons will sometimes pick up anelectron to form a light isotope ofhydrogen called muonium (Mu). Byfollowing muon behaviour inside amaterial we can learn about proton andhydrogen behaviour. This is important insemiconducting materials, protonconductors and hydrogen storagematerials and insulating materials.

References on the muon technique include:

• Muon spin rotation, relaxation andresonance: Applications to condensedmatter A Yaouanc, P Dalmas de Réotier,Oxford University Press (2010), ISBN 0199596476

• Spin polarised muons in condensed matterphysics S J Blundell, Contemporary Physics,4400 (1999) 175

• The Muon Method in Science, V.P. Smilga,Yu.M. Belousov, Nova Science Publishers(1994) ISBN 9781560721611

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

Once implanted inside a material, muons interact with theirlocal atomic environment. In some cases this interaction canbe strong, and fast timing resolution is required to follow theevolution of the muon spin polarization. For example, inmagnetic systems, large internal fields give rise to fastprecession frequencies, while broad internal field distributionswill lead to a rapid decay of the muon polarisation. Inchemical systems, the measurement of detailed spectroscopicinformation requires large probing fields which, in turn, giverise to energy level splittings of the order of hundreds ofmegahertz.

The beam structure of the SµS, located at PSI, Switzerland isideally suited to these types of measurement. Here, muons areimplanted into the sample one by one, enabling accuratemeasurement of the time interval between the arrival of themuon and the detection of the decay positron. With carefulinstrument design and advanced detector technologies, timeresolutions better than 80ps are possible.

This is illustrated by the transverse field experiment, where fastmuon precession is measured in a large external magnetic fieldapplied perpendicular to the initial muon spin polarisation. Inthis case a 9.5T field was applied to muons stopped in a silverplate and a precession frequency of ~1.3 GHz is measured. Thedecay of the muon response and the corresponding shape of theFourier transform reflect the microscopic field distributionsensed by the muon.

High resolution muonspectroscopy: the basic idea

Example Applications of High Resolution Muon Spectroscopy in Condensed Matter Physics

H

Muondetector

µ+

Sample

e

Positrondetector

+

01286 1288 1290 1292

1 2 3 4 5

1294

5

10

15

20-0.4

-0.2

0

0.2

0.4

25

30

35

Frequency (MHz)

Time (ns)

Pola

risa

tion

Inte

nsit

y

Precise measurement of the time interval between muon arrival and decay(top) enables high resolution spectra to be recorded.

SuperconductivityThe vortex state induced in a type-II superconductor when astrong magnetic field is applied can be studied using muons.The technique probes the magnetic field on a length scale muchshorter than the inter vortex distance, enabling informationabout the internal vortex structure and interactions to beobtained.

Muons are now routinely used to determine characteristic lengthscales, such as the magnetic penetration depth and coherencelength, and the muon technique enables vortex lattice topologyto be investigated. Muons are also playing a key role in thesearch for experimental evidence for exotic vortex states. Forexample, a change in the spatial field distribution around thevortex cores has been predicted for clean superconductors atlow temperatures and at fields close to the upper critical field.Spectrometers capable of extended temperature and fieldmeasurements promise to bring a new insight to these studies.

Models for conventional (left) and exotic (right) vortex states can beinvestigated using muon techniques.

A. Maisuradze et al., arXiu:1303.0209v1 (2013).

8.0 10.0Magnetic field (mT)

12.0 14.0

0

0.1

Inte

nsit

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8.0 10.0Magnetic field (mT)

12.0 14.0 16.0 18.0 20.0 22.0

Inte

nsit

y

sad

maxsad

min

min<B>

Field distribution (with model fit) of a vortexlattice formed inSrFe1.75Co0.25As2 at 1.6K andan external field of 10mT.

Adapted from R. Khasanov et. al.Phys. Rev. Lett. 103, 067010 (2009).

X XYY

(B-(

B))/

(Bvc

-(B)

)

(B-(

B))/

(Bvc

-(B)

)

BCS modelT 0

GL limit of BCS

-1

1

0

1

0

T Tc

ion Muon Spectroscopy in Condensed Matter Physics

Probing Spin Liquids The quantum spin-liquid phase is an intriguing state where theusual magnetically ordered ground state is avoided even at thelowest temperatures for a system of strongly interactingmagnetic spins. Spin liquid systems such as the Mott insulator χ-(BEDTTTF)2Cu2(CN)3 display a complex phase diagram that canbest be investigated using the extended field and temperatureregimes offered by the latest muon spectrometers. Existingmeasurements have demonstrated no obvious signature forconventional magnetic ordering to 20mK.

The rich phase diagram (left) of the Mott insulator χ-(BEDTTTF)2 (right, grey+ C and yellow = S) Cu2(CN)3 is readily explored using muon techniques.Compared to conventional resonance techniques, muon spectroscopyenables measurement over a greatly extended field range.

F. L. Pratt et al., Nature 471, 612 (2011).

Low Dimensional Magnetism Low dimensional quantum spin systems are remarkable for theirdiverse and fascinating physical behaviour, and the muontechnique provides an ideal probe of their properties. Forexample, quantum phase transitions between gapped andgapless phases of two-leg spin-ladder systems such as(Hpip)2CuBr4 can be driven using a large external magnetic field.The Luttinger Liquid regime, where the spectrum is gapless withno finite order parameter, can also be investigated from thehigh-temperature classical regime through a crossover.

Phase diagram of the spin-ladder (Hpip)2CuBr (inset). Transitions betweenthe quantum disordered (QD), quantum critical (QC) and Luttinger-Liquid(LL) phases can readily be explored using muon techniques.

Adapted from Ch. Rüegg et al, Phys Rev Lett 101 247202 (2008).

Semiconductors and OxidesMuonium, a bound µ+e- system, can be considered as a lighthydrogen isotope, and is frequently used to obtain informationabout isolated hydrogen in semiconducting systems. Hightransverse field muon spin rotation measurements enable highresolution spectroscopy of the different electronic states thishydrogen-like isotope can take, with the hyperfine couplingproviding information about the local environment. Spindynamics and state transitions can also be probed byinvestigating the field dependence of polarised muonium atdifferent temperatures.

Spectroscopy of a Mu(H) centre formed in ZnO (inset). Line intensitiesreflect electron polarization.

Adapted from K. Shimomura et al., PSI Annual Report 2005.

High Spin Molecules Molecular clusters containing as few as 10 to 100 atoms mightbe used as magnetic memory units, potentially offering greatlyincreased storage density. These systems are high spinmolecules, comprising a small network of magnetic ions suchthat the net spin of the cluster is large (e.g. 10, 27/2 or 39/2).Unfortunately, molecular spin relaxation rates currently limit theapplication of these systems, and high field muon spectroscopyprovides an ideal method for determining the quantumfluctuations and tunnelling driving this spin relaxation.

Energy levels for Mn12-acetate16 (S=10) (grey = C, white = H, red = O andpurple = Mn). Fluctuations and tunneling rates can be probed using muontechniques.

G. Chaboussant et al., Phys. Rev. B70, 104422 (2004).

0.001 0.01µ0H (T)0.1 1 10

1

10

0.1

0.01

0.001

Tem

pera

ture

(K)

QCHW≈0

QCMW≈0.3

QCL WAFL(ßL ≈ 0.4, ηL ≈ 0)

WAFH(ßH ≈ 0.8, ηH ≈ 1)

W≈0

GS

w ≈ 0.5

w ≈ 0

w ≈

1.5

2 D B E C

H0 H1

Δs

Δv

Tp

µSR NMR

404403402 405Frequency (MHz)

406 407 408

0

0.5

2.0

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1.0

Inte

nsit

y µ+

Zn

O

0 2Magnetic field (T)

4 6 8 10 12 140

2.0

3.0

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3.5

4.0

4.5

5

0.5

1.0

1.5

0 2.0 2.50.5 1.0 1.5

Tem

pera

ture

(K)

QD

QC

c

a

LL

(Hpip)2CuBr4 B||a

Cm/T [mJ/gK2]

Bc Bs 0 2Field (T)4 6 8 10

-100

-50

0

50

Ener

gy (k

J/m

ol)

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.

Contacts:

PSI FacilityProf. Elvezio Morenzoni,elvezio.morenzoni@psi.ch

Tel: +41 (0)56 310 4666Web: lmu.web.psi.ch

Paul Scherrer InstitutLaboratory for Muon-Spin SpectroscopyCH-5232 Villigen PSISwitzerland

ISIS FacilityDr Adrian Hillier,adrian.hillier@stfc.ac.uk

Tel: +44 (0)1235 446001Web:www.isis.stfc.ac.uk/groups/muons

STFC Rutherford Appleton LaboratoryHarwell OxfordDidcot OX11 0QXUK

Facilities for Muon Spectroscopy

AAbboovvee: High field muon spectrometer at ISIS, UK.

LLeefftt: The new instrument for high field muonspectroscopy at PSI. The 9.5 T magnet is on theright side. On the left is the dilution refrigeratorwith the gas handling system visible, which cancool samples to temperatures below 20 mK.

July

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