The Positive Muon as a Condensed Matter Probe

Francis Pratt

ISIS Facility,

Rutherford Appleton Laboratory, UK

• Introduction

The muon and its properties

The range of SR techniques

• Molecular Magnetism

Critical behaviour in a layered magnet

Spin fluctuations in a highly ideal 1DHAF

• Molecular Superconductors

Stability of the vortex lattice

Universal scaling of the electrodynamic response

• Dynamical Processes in Polymers

Charge mobility in polymers

Polymer surface dynamics

Familiar Particles and Muons

Familiar Particles and Muons

Familiar Particles and Muons

A positive muon behaves like an unstable light isotope of hydrogen

Primary International Facilities for SR

ISIS

JPARCPSITRIUMF

Continuous sources Pulsed sources

Producing Muons at ISIS

50 m

View of the ISIS Experimental Hall

The SR Sequence of Events1) Pions produced from proton beam striking carbon target

e.g. p + p p + n + +

p + n n + n + +

2) Pion decay: + ++(lifetime 26 ns)

the muons are 100% spin polarised

3) Muon implantation into sample of interest

4) Muons experience their local environment:

spin precession and relaxation

5) Muon decay: + e++e+ (lifetime 2.2 s)we detect the asymmetric positron

emission

Nature of the Muon Probe States

Paramagnetic states

Muonium (Mu = +e); the muon analogue of the neutral hydrogen atom

… highly reactive in many molecular systems, leading to the formation of molecular radicals, e.g.

Diamagnetic states

1) Bare interstitial +

2) Chemically bonded closed shell states, e.g.

Formation of Muon Probe States

+ (MeV)

Radiolytic e-

Ionisation energy loss to below 35 keV

+

Formation of Muon Probe States

+ (MeV)

Radiolytic e-

Ionisation energy loss to below 35 keV

+ 13.5 eV Mu

e- capture

e- loss

Charge exchange cycle

Formation of Muon Probe States

+ (MeV)

Radiolytic e-

Ionisation energy loss to below 35 keV

+ 13.5 eV Mu

e- capture

e- loss

Thermal +

DIAMAGNETIC

Thermal MuPARAMAGNETIC

Charge exchange cycle

Formation of Muon Probe States

+ (MeV)

Radiolytic e-

Ionisation energy loss to below 35 keV

+ 13.5 eV Mu

e- capture

e- loss

Thermal +

DIAMAGNETIC

Thermal MuPARAMAGNETIC

Mu RadicalPARAMAGNETIC

Chemical reaction

Charge exchange cycle

Formation of Muon Probe States

+ (MeV)

Radiolytic e-

Ionisation energy loss to below 35 keV

+ 13.5 eV Mu

e- capture

e- loss

Thermal +

DIAMAGNETIC

Thermal MuPARAMAGNETIC

Mu RadicalPARAMAGNETIC

Chemical reaction

Delayed Mu formation

Charge exchange cycle

Ionization/ reaction

Positron Emission and DetectionW() = 1+ a cos

Positron Emission and DetectionW() = 1+ a cos

S

B F

LF/ZF

Positron Emission and DetectionW() = 1+ a cos

S

B F

LF/ZF

S

B F

TFU

D

Muon Instruments at ISIS

SRRRR…

• Muon Spin Rotation

• Muon Spin Relaxation

• Muon Spin Resonance

• Muon Spin Repolarisation

Muon Spin Rotation

Energy Levels

Energy Levels

Single frequency D

D/2 = 13.55 kHz/G

Energy Levels

Energy Levels

Pair of frequencies

A = 1 + 2

Energy Levels

Energy Levels

Still one pair of frequencies at high B

A = 1 + 2

TF Muon Spin Rotation Spectoscopy of Muoniated Molecular Radicals

TTF

2kG TF

Magn. Res. Chem. 38, S27 (2000)

Singly occupied molecular orbital of muoniated radical

Muon Spin Relaxation

RF Resonance

• B swept to match a level splitting with the RF frequency

also

• 90⁰ pulse techniques

• Spin echoes

• Spin Decoupling

Paramagnetic/Diamagnetic State Conversion measured with RF

Polybutadiene above and below the Glass Transition

T>Tg D → P

T<Tg P → D

T<Tg

Level Crossing Resonance

Resonances classified in terms of

M = me + m + mp

M = 1 muon spin flip:

B0 = A / 2(needs anisotropy)

M = 0 muon-proton spin flip-flop:

B0 = (AAk ) / 2(k(to first order)

M=1 LCR

Quadrupolar Level Crossing Resonance

14N quadrupolar LCR in TTF-TCNQ

T>TCDW

T<TCDW

14N +

Quadrupolar splitting depends on electric field gradient at the nucleus

Repolarisation of Mu• Progressive quenching of the muon spin from its dipolar and hyperfine couplings• Useful for orientationally disordered systems with residual anisotropy

Repolarisation of MuQuenching of the superhyperfine coupling to nuclear spins

Sensitive to total number of spins

e.g. protonation/deprotonation studies

Molecular Magnetism

Critical Fluctuations in a Co Glycerolate Layered Magnet

Mohamed Kurmoo, University of Strasbourg

Co (S=3/2)

Critical Exponents Measured with SR

Magnetic order:

M (TN - T)

Relaxation rate:

| T -TN | -w

Local susceptibility:

(T - TN )

Comparison with Established Universality Classes

Scaling relations: = 2 – 2 – = (2 + )/d = 2 – /

Dynamic exponent: z = d(2 + w)/(2 + ) = 1.25(6) (c.f. z=d/2=1.5 for 3D AF)

Quantum Critical Fluctuations in a Highly Ideal Heisenberg Antiferromagnetic Chain

Molecular radical providing the S=1/2 Heisenberg spins

Cyanine dye molecule providing the bulky diamagnetic spacers

Structure of DEOCC-TCNQF4 viewed along the chain axis

J = 110 K but no LRMO down to 20 mK !

i.e. TN / J < 2 x 10-4

Zero field muon spin relaxation for DEOCC-TCNQF4 at 20 mK and 1 K.

Comparison of DEOCC-TCNQF4 with other benchmark 1DHAF magnets.

Just How Ideal is DEOCC-TCNQF4?

T dependent SR relaxation rate at 3 mT

with contributions from q=/a and q=0.The 1DHAF spin excitation

spectrum contributing to .

T-dependent Relaxation from Spinons

Anisotropic Spin Diffusion

The B dependence of at 1 K. The

dotted line illustrates the behaviour

expected for ballistic spin transport.

The solid line is a fit to an

anisotropic spin diffusion model.

The form of the spin correlation function

S(t) that is consistent with the data.

Crossover between 1D and 3D diffusion

takes place for time scales longer than

~10 ns.

TN (mK) |J'| (mK) J (K) TN/J (10-2) |J'/J| (10-3)

Experiment <20 2.2 110 <0.018 0.020

Estimate 7 <7 0.006 <0.06

Sr2CuO3 5.4 K 2 K 2200 0.25 0.93

CuPzN 107 46 10.3 1.0 4.4

KCuF3 39 K 21 K 406 9.6 52

DEOCC-TCNQF4 looks like the best example of the

1D Heisenberg Antiferromagnet yet discovered

Summary of 1DHAF Magnetic Parameters

PRL 96, 247203 (2006)

Molecular Superconductors

Measuring Properties of Type II Superconductors

H < Hc1 : Meissner state

Surface measurement:

Hc1 < H < Hc2 : Vortex state

Bulk measurement:

coresminima

saddles

RMS Width: Brms or

Lineshape: = (Bave - Bpk) / Brms

(skewness)

Abrikosov Vortex Lattice

Muon Spin Rotation Spectrum

Melting/Decoupling of the Vortex Lattice in the Organic Superconductor ET2Cu(SCN)2

3D Flux Lattice

Decoupled 2D Layers

Overall Vortex Phase Diagramsd8-ETSCN

h8-ETSCN

Scaling Properties in the Electrodynamic Response of Molecular Superconductors

Famous ‘Uemura Plot’ for cuprates and other superconductors

Tc (SR relaxation rate)

Equivalently:Tc ns/m* Tc s (superfluid strength)Tc 1/2 ( is penetration depth)

What about molecular superconductors?

n/m* is small and doesn’t vary much, so they should sit in one small region of the plot

s across the range of Molecular Superconductors

Uemura Plot for the Molecular Superconductors

Molecular systems have their own empirical scaling law:

Tc follows 1/3 rather than 1/2

⇒ Tc (ns/mb) 3/2

Key:

1. -BETS2GaCl4

2. TMTSF2ClO4

3. -ET2NH4Hg(SCN)4

4. -ET2IBr2

5. -BETS2GaCl4

6. -ET2Cu(NCS)2

7. K3C60

8. Rb3C60

Closer look at Superconducting Parameters vs Conductivity

2D

1D

2D

2D

2D

2D

3D

3D

1D, 2D & 3D systems

SC properties correlate with highest direction

Note the completely opposite s - 0 scaling between molecular and cuprate superconductors

0- 1.05

0- 0.77

0+ 0.75

PRL 94, 097006 (2005)

Is there a single controlling parameter?

• The simplicity of the scaling suggests a single dominant

control parameter

• U/W is a likely candidate for molecular systems, which

are generally rather close to a Mott insulator phase

• Real pressure as well as ‘chemical pressure’ can be

used to tune U/W

• Increasing pressure decreases U/W, increases 0 and

decreases Tc and s , following the trends expected from

the scaling curves

Dynamical Mean-Field Theory for Calculating effect of U/W on s

Loss of quasiparticle spectral weight is expected as the Mott-Hubbard transition is approached

Superfluid Strength vs U/W

Powell and McKenzie PRL94, 047004 (2005)

RVB

Feldbacher et al, PRL93, 136405 (2004)

DMFT

Merino and McKenzie PRB61, 7996 (2000)

DMFT

sZ

Experimental picture

Dynamical Processes in Polymers

Conducting Polymers

Muon both generates a polaron and probes its motion, e.g. for PPV:

Diffusion and the Risch-Kehr ModelStochastic model describing muon relaxation due to intermittent hyperfine coupling with a diffusing polaron

)erfc()exp()( tttzG

The relaxation function takes the form:

2||

2

40De

with the relaxation parameter following a 1/B law at high field:

(Risch-Kehr function)

Polyaniline

Data are well fitted by the Risch-Kehr function

Polyaniline

1/B law predicted by RK model is seen for at higher B

Cutoff at low B reflects interchain hopping

Polyaniline

Effect of ring librational modes at higher temperatures

Two types of PPV polymer with different side chains

Similar on-chain behaviour

Interchain Diffusion Rate D

Inter-chain behaviour highly dependent on sidegroups

Slow Muons

Normal (4 MeV) muons penetrate ~1-2 mm

10-15% stopping width, so thinnest sample is ~100m,

(a bit less with flypast mode)

For studying nanoscale structures and phenomena need muons with energies in the region of keV rather than MeV

Two methods for producing slow muons :

1) Degrading the energy in a cold moderator layer (PSI)

2) Laser ionization of thermal muonium (RIKEN-RAL)

Surface and Interface Dynamics in Polymers

Supported polystyrene films (overlaid data from 6 groups using various different techniques)

Forrest and Dalnoki-Veress, Adv. Coll. Int. Sci. 94, 167 (2001)

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

/10 /1 hh

TT

bulkg

g

Calculated Range for Muons in Polystyrene using TRIM.SP

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

Polystyrene Film Sample used for LEM Study

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

Mw = 62,600, Mw/Mn=1.04

1 mm thick by 50 mm diameter copper substrate

Film prepared by spin-coating from a 15% solution of PS in cyclohexanone

Film thickness of 0.46 m was estimated from ellipsometry

PRB 72, R121401 (2005)

Measured ZF Relaxation in PS

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

Measured Relaxation in the Bulk Polymer

Fast fluctuation regime:

Indirect coupling to segmental dynamics:

WLF law for segmental dynamics:

Model

Depth Scan at Tq

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

d ~ 35 nm at Tq

Size of the Surface Dynamical Region

Surface melting model: d(T) follows from linear dispersion of surface capillary waves

Herminghaus et al PRL 93, 017801 (2004)

Size of the Surface Dynamical Region

Surface melting model: d(T) follows from linear dispersion of surface capillary waves

Herminghaus et al PRL 93, 017801 (2004)

Glassy polymer

Molten layer

Substrate

Glassy polymer

Molten layer

Substrate

Molten layer

Substrate

T1

T2

T3

T1 T2 T3

Summary

•Flexible local magnetic probe

•Magnetism, superconductivity and various dynamical phenomena

•Also applications in semiconductors and using the muon as a hydrogen analogue

•Single crystal samples not essential

•Overlap and complementarity with other techniques such as neutron scattering

Acknowledgements

SR Steve Blundell Oxford

Molecular Magnets Mohamed Kurmoo Strasbourg

Seishi Takagi Kyushu

Molecular Superconductors Naoki Toyota Tohoku

& Takahiko Sasaki

Steve Lee St. Andrews

Polymers Andy Monkman Durham

Andrew Holmes Cambridge

Hazel Assender Oxford

Slow Muons Elvezio Morenzoni PSI

Introduction to Muon Techniques

For a short review see: S.J. Blundell, Contemp. Phys. 40, 175 (1999)