The Positive Muon as a Condensed Matter Probe

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The Positive Muon as a Condensed Matter Probe

• Francis Pratt
• ISIS Facility,
• Rutherford Appleton Laboratory, UK

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• Introduction
• The muon and its properties
• The range of mSR 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

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Familiar Particles and Muons
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Familiar Particles and Muons
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Familiar Particles and Muons
A positive muon behaves like an unstable light
isotope of hydrogen
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Primary International Facilities for mSR
ISIS
PSI
TRIUMF
JPARC
Continuous sources
Pulsed sources
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Producing Muons at ISIS
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View of the ISIS Experimental Hall
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The mSR Sequence of Events

• 1) Pions produced from proton beam striking
  carbon target
• e.g. p p ? p n p
• p n ? n n p
• Pion decay p ? mnm (lifetime 26 ns)
• the muons are 100 spin polarised
• 3) Muon implantation into sample of interest
• Muons experience their local environment
• spin precession and relaxation
• Muon decay m ? enenm (lifetime 2.2 ms)
• we detect the asymmetric positron emission

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Nature of the Muon Probe States
Paramagnetic states Muonium (Mu me) 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
• Bare interstitial m
• Chemically bonded closed shell states, e.g.

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Formation of Muon Probe States
Ionisation energy loss to below 35 keV
m (MeV)
m
Radiolytic e-
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Formation of Muon Probe States
Charge exchange cycle
e- capture
Ionisation energy loss to below 35 keV
m (MeV)
m 13.5 eV Mu
e- loss
Radiolytic e-
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Formation of Muon Probe States
Charge exchange cycle
Thermal Mu PARAMAGNETIC
e- capture
Ionisation energy loss to below 35 keV
m (MeV)
m 13.5 eV Mu
e- loss
Radiolytic e-
Thermal m DIAMAGNETIC
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Formation of Muon Probe States
Charge exchange cycle
Thermal Mu PARAMAGNETIC
e- capture
Ionisation energy loss to below 35 keV
m (MeV)
m 13.5 eV Mu
e- loss
Chemical reaction
Radiolytic e-
Thermal m DIAMAGNETIC
Mu Radical PARAMAGNETIC
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Formation of Muon Probe States
Charge exchange cycle
Thermal Mu PARAMAGNETIC
e- capture
Ionisation energy loss to below 35 keV
m (MeV)
m 13.5 eV Mu
e- loss
Chemical reaction
Delayed Mu formation
Radiolytic e-
Ionization/ reaction
Thermal m DIAMAGNETIC
Mu Radical PARAMAGNETIC
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Positron Emission and Detection
W(q) 1 a cos q
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Positron Emission and Detection
W(q) 1 a cos q
LF/ZF
Sm
B
F
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Positron Emission and Detection
W(q) 1 a cos q
LF/ZF
TF
U
Sm
Sm
B
F
B
F
D
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Muon Instruments at ISIS
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mSRRRR

• Muon Spin Rotation
• Muon Spin Relaxation
• Muon Spin Resonance
• Muon Spin Repolarisation

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Muon Spin Rotation
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Energy Levels
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Energy Levels
Single frequency wD wD/2p 13.55 kHz/G
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Energy Levels
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Energy Levels
Pair of frequencies A w1 w2
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Energy Levels
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Energy Levels
Still one pair of frequencies at high B A w1
w2
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TF Muon Spin Rotation Spectoscopy of Muoniated
Molecular Radicals
2kG TF
TTF
Singly occupied molecular orbital of muoniated
radical
Magn. Res. Chem. 38, S27 (2000)
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Muon Spin Relaxation
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RF Resonance

• B swept to match a level splitting with the RF
  frequency
• also
• 90 pulse techniques
• Spin echoes
• Spin Decoupling

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Paramagnetic/Diamagnetic State Conversion
measured with RF
Polybutadiene above and below the Glass Transition
TgtTg D ? P
TltTg
TltTg P ? D
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Level Crossing Resonance
Resonances classified in terms of M me mm
mp DM 1 muon spin flip B0 Am / 2gm
(needs anisotropy) DM 0 muon-proton spin
flip-flop B0 (Am- Ak ) / 2(gm- gk) (to
first order)
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Quadrupolar Level Crossing Resonance
14N
m
Quadrupolar splitting depends on electric field
gradient at the nucleus
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Repolarisation of Mu

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

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Repolarisation of Mu
Quenching of the superhyperfine coupling to
nuclear spins Sensitive to total number of spins
e.g. protonation/deprotonation studies
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Molecular Magnetism
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Critical Fluctuations in a Co Glycerolate Layered
Magnet
Co (S3/2)
Mohamed Kurmoo, University of Strasbourg
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Critical Exponents Measured with mSR
Relaxation rate l ? T -TN -w
Local susceptibility c ? (T - TN ) -g
Magnetic order M ? (TN - T) b
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Comparison with Established Universality Classes
Scaling relations a 2 2b g n (2b
g)/d h 2 g/n
Dynamic exponent z d(2b w)/(2b g)
1.25(6) (c.f. zd/21.5 for 3D AF)
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Quantum Critical Fluctuations in a Highly Ideal
Heisenberg Antiferromagnetic Chain
Structure of DEOCC-TCNQF4 viewed along the chain
axis
Molecular radical providing the S1/2 Heisenberg
spins
Cyanine dye molecule providing the bulky
diamagnetic spacers
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Just How Ideal is DEOCC-TCNQF4?
Zero field muon spin relaxation for DEOCC-TCNQF4
at 20 mK and 1 K.
Comparison of DEOCC-TCNQF4 with other benchmark
1DHAF magnets.
J 110 K but no LRMO down to 20 mK ! i.e. TN / J
lt 2 x 10-4
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T-dependent Relaxation from Spinons
T dependent mSR relaxation rate l at 3 mT with
contributions from qp/a and q0.
The 1DHAF spin excitation spectrum contributing
to l.
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Anisotropic Spin Diffusion
The B dependence of l 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.
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Summary of 1DHAF Magnetic Parameters
TN (mK) J' (mK) J (K) TN/J
(10-2) J'/J (10-3) Experiment
lt20 2.2 110 lt0.018 0.020 Estimate
7 lt7 0.006 lt0.06 Sr
2CuO3 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
PRL 96, 247203 (2006)
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Molecular Superconductors
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Measuring Properties of Type II Superconductors
H lt Hc1 Meissner state Surface measurement l
Abrikosov Vortex Lattice
Hc1 lt H lt Hc2 Vortex state Bulk measurement l,
x
saddles
cores
RMS Width Brms or s Lineshape
b (Bave - Bpk) / Brms (skewness)
minima
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Muon Spin Rotation Spectrum
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Melting/Decoupling of the Vortex Lattice in the
Organic Superconductor ET2Cu(SCN)2
3D Flux Lattice
Decoupled 2D Layers
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Overall Vortex Phase Diagrams
d8-ETSCN
h8-ETSCN
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Scaling Properties in the Electrodynamic Response
of Molecular Superconductors

• Famous Uemura Plot for cuprates and other
  superconductors
• Tc ? s (mSR relaxation rate)
• Equivalently
• Tc ? ns/m
• Tc ? rs (superfluid strength)
• Tc ? 1/l2 (l is penetration depth)

What about molecular superconductors?
n/m is small and doesnt vary much, so they
should sit in one small region of the plot
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rs across the range of Molecular Superconductors
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Uemura Plot for the Molecular Superconductors
Molecular systems have their own empirical
scaling law Tc follows 1/l3 rather than 1/l2 ?
Tc ? (ns/mb) 3/2
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Closer look at Superconducting Parameters vs
Conductivity
Note the completely opposite rs - s0 scaling
between molecular and cuprate superconductors

• Key
• k-BETS2GaCl4
• TMTSF2ClO4
• a-ET2NH4Hg(SCN)4
• b-ET2IBr2
• l-BETS2GaCl4
• k-ET2Cu(NCS)2
• K3C60
• Rb3C60

s0- 1.05
s0- 0.77
s0 0.75
PRL 94, 097006 (2005)
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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 s0
  and decreases Tc and rs , following the trends
  expected from the scaling curves

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Dynamical Mean-Field Theory for Calculating
effect of U/W on rs
Loss of quasiparticle spectral weight is expected
as the Mott-Hubbard transition is approached
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Superfluid Strength vs U/W
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Dynamical Processes in Polymers
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Conducting Polymers
Muon both generates a polaron and probes its
motion, e.g. for PPV
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Diffusion and the Risch-Kehr Model
Stochastic model describing muon relaxation due
to intermittent hyperfine coupling with a
diffusing polaron
The relaxation function takes the form
(Risch-Kehr function)
with the relaxation parameter G following a 1/B
law at high field
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Polyaniline
Data are well fitted by the Risch-Kehr function
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Polyaniline
1/B law predicted by RK model is seen for G at
higher B Cutoff at low B reflects interchain
hopping
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Polyaniline
Effect of ring librational modes at higher
temperatures
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Two types of PPV polymer with different side
chains
Similar on-chain behaviour
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Interchain Diffusion Rate D?
Inter-chain behaviour highly dependent on
sidegroups
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Slow Muons

• Normal (4 MeV) muons penetrate 1-2 mm
• 10-15 stopping width, so thinnest sample is
  100mm,
• (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
• Degrading the energy in a cold moderator layer
  (PSI)
• Laser ionization of thermal muonium (RIKEN-RAL)

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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)
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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
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Polystyrene Film Sample used for LEM Study
PRB 72, R121401 (2005)
Surface Layer Model
Mw 62,600, Mw/Mn1.04 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 mm was
estimated from ellipsometry
Substrate
Bulk polymer
Surface layer
Thin film properties dominated by higher mobility
surface layer
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Measured ZF Relaxation in PS
Surface Layer Model
Substrate
Bulk polymer
Surface layer
Thin film properties dominated by higher mobility
surface layer
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Measured Relaxation in the Bulk Polymer
Model
Fast fluctuation regime
WLF law for segmental dynamics
Indirect coupling to segmental dynamics
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Depth Scan at Tq
Surface Layer Model
Substrate
Bulk polymer
Surface layer
Thin film properties dominated by higher mobility
surface layer
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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)
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Size of the Surface Dynamical Region
T1
T2
T3
Surface melting model d(T) follows from linear
dispersion of surface capillary
waves Herminghaus et al PRL 93, 017801 (2004)
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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

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Acknowledgements
mSR 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 H
azel Assender Oxford Slow Muons Elvezio
Morenzoni PSI
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Introduction to Muon Techniques
For a short review see S.J. Blundell, Contemp.
Phys. 40, 175 (1999)
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Muon Probe States in DEOCC-TCNQF4
The muon thermalises as m or as muonium (Mu).
m will combine with a TCNQF4- to form a
muoniated radical state with hyperfine parameters
A and D (below). A and D can be independently
measured using muonium level-crossing-resonance
(LCR) spectroscopy of neutral TCNQF4 (right).
m
Mu
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Anisotropic spin diffusion parameters derived
from the B dependence of l
The interchain diffusion rate and anisotropy
(inset).
The on-chain spin diffusion rate.
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Homes Plot bringing in Conductivity just above
Tc

• Key
• k-BETS2GaCl4
• TMTSF2ClO4
• a-ET2NH4Hg(SCN)4
• b-ET2IBr2
• l-BETS2GaCl4
• k-ET2Cu(NCS)2
• K3C60
• Rb3C60

Homes scaling law rs ? s0Tc doesnt apply to
molecular superconductors
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RK Relaxation in DB-PPV
DB-PPV
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Intrachain Mobility

• Taking d7Å
• and the Einstein relation
• m eD/kBT
• gives m 0.05 cm2V-1s-1 at 300 K for both PPV
  samples
• This is comparable with local mobility values
  measured in pulse radiolysis time-resolved
  microwave measurements
• e.g. me 0.5 cm2V-1s-1 at 300 K
• Other techniques, e.g. time of flight, give
  mobility values several orders of magnitude
  smaller

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Depth Resolution Fluorescence Labelling
Ellison and Torkelson Nature Materials 2,695
(2003)
Surface Layer Model
Substrate
Bulk polymer
Surface layer
Thin film properties dominated by higher mobility
surface layer
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Muoniated Radicals in PS
A 500 MHz D 10-15 MHz
TF
LF
Physica B 326,34 (2003)
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Coupling to Polymer Dynamics
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Depth Resolution Implanted Positrons
Jean et al PRB 56, R8459 (1997)
Surface Layer Model
Substrate
Bulk polymer
Surface layer
Thin film properties dominated by higher mobility
surface layer