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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 m SR techniques Molecular Magnetism Critical behaviour in a layered magnet Spin fluctuations in a highly ideal 1DHAF

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The positive muon as a condensed matter probe

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 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




Familiar particles and muons2
Familiar Particles and Muons

A positive muon behaves like an unstable light isotope of hydrogen


Primary international facilities for m sr
Primary International Facilities for mSR

ISIS

PSI

TRIUMF

JPARC

Continuous sources

Pulsed sources




The m sr sequence of events
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+ m++nm (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+ e++ne+nm (lifetime 2.2 ms)

    we detect the asymmetric positron emission


Nature of the muon probe states
Nature of the Muon Probe States

  • Paramagnetic states

    • Muonium (Mu = m+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

    • Bare interstitial m+

    • Chemically bonded closed shell states, e.g.


Formation of Muon Probe States

Ionisation energy loss to below 35 keV

m+ (MeV)

m+

Radiolytic e-


Formation of Muon Probe States

Charge exchange cycle

e- capture

Ionisation energy loss to below 35 keV

m+ (MeV)

m+13.5 eVMu

e- loss

Radiolytic e-


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 eVMu

e- loss

Radiolytic e-

Thermal m+

DIAMAGNETIC


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 eVMu

e- loss

Chemical reaction

Radiolytic e-

Thermal m+

DIAMAGNETIC

Mu Radical

PARAMAGNETIC


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 eVMu

e- loss

Chemical reaction

Delayed Mu formation

Radiolytic e-

Ionization/ reaction

Thermal m+

DIAMAGNETIC

Mu Radical

PARAMAGNETIC



Positron emission and detection1
Positron Emission and Detection

W(q) = 1+ a cos q

LF/ZF

Sm

B

F


Positron emission and detection2
Positron Emission and Detection

W(q) = 1+ a cos q

LF/ZF

TF

U

Sm

Sm

B

F

B

F

D



M srrrr
mSRRRR…

  • Muon Spin Rotation

  • Muon Spin Relaxation

  • Muon Spin Resonance

  • Muon Spin Repolarisation




Energy levels1
Energy Levels

Single frequency wD

wD/2p = 13.55 kHz/G



Energy levels3
Energy Levels

Pair of frequencies

A = w1 + w2



Energy levels5
Energy Levels

Still one pair of frequencies at high B

A = w1 + w2


Tf muon spin rotation spectoscopy of muoniated molecular radicals
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)



Rf resonance
RF Resonance Radicals

  • 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
Paramagnetic/Diamagnetic State Conversion measured with RF Radicals

Polybutadiene above and below the Glass Transition

T>Tg D → P

T<Tg

T<Tg P → D


Level crossing resonance
Level Crossing Resonance Radicals

DM=1 mLCR

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)


Quadrupolar level crossing resonance
Quadrupolar Level Crossing Resonance Radicals

14N quadrupolar mLCR in TTF-TCNQ

T>TCDW

T<TCDW

14N

m+

Quadrupolar splitting depends on electric field gradient at the nucleus


Repolarisation of mu
Repolarisation of Mu Radicals

  • Progressive quenching of the muon spin from its dipolar and hyperfine couplings

  • Useful for orientationally disordered systems with residual anisotropy


Repolarisation of mu1
Repolarisation of Mu Radicals

Quenching of the superhyperfine coupling to nuclear spins

Sensitive to total number of spins

e.g. protonation/deprotonation studies



Critical Fluctuations in a Co Glycerolate Layered Magnet Radicals

Co (S=3/2)

Mohamed Kurmoo, University of Strasbourg


Critical Exponents Measured with RadicalsmSR

Local susceptibility:

c (T - TN ) -g

Relaxation rate:

l | T -TN | -w

Magnetic order:

M  (TN - T) b


Comparison with Established Universality Classes Radicals

Scaling relations: a = 2 – 2b – gn = (2b + g)/d h = 2 – g/n

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


Quantum critical fluctuations in a highly ideal heisenberg antiferromagnetic chain
Quantum Critical Fluctuations in a Highly Ideal Heisenberg Antiferromagnetic Chain

Structure of DEOCC-TCNQF4 viewed along the chain axis

Molecular radical providing the S=1/2 Heisenberg spins

Cyanine dye molecule providing the bulky diamagnetic spacers


Just How Ideal is DEOCC-TCNQF Antiferromagnetic Chain4?

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 < 2 x 10-4


T-dependent Relaxation from Spinons Antiferromagnetic Chain

T dependent mSR relaxation rate l at 3 mT with contributions from q=p/a and q=0.

The 1DHAF spin excitation spectrum contributing to l.


Anisotropic Spin Diffusion Antiferromagnetic Chain

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.


Summary of 1DHAF Magnetic Parameters Antiferromagnetic Chain

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

PRL 96, 247203 (2006)


Molecular superconductors
Molecular Superconductors Antiferromagnetic Chain


Measuring properties of type ii superconductors
Measuring Properties of Type II Superconductors Antiferromagnetic Chain

H < Hc1 : Meissner state

Surface measurement: l

Abrikosov Vortex Lattice

Hc1 < H < Hc2 : Vortex state

Bulk measurement: l, x

saddles

RMS Width: Brms or s

Lineshape: b = (Bave - Bpk) / Brms

(skewness)

cores

minima


Muon spin rotation spectrum
Muon Spin Rotation Spectrum Antiferromagnetic Chain


Melting decoupling of the vortex lattice in the organic superconductor et 2 cu scn 2
Melting/Decoupling of the Vortex Lattice in the Organic Superconductor ET2Cu(SCN)2

3D Flux Lattice

Decoupled 2D Layers


Overall vortex phase diagrams
Overall Vortex Phase Diagrams Superconductor ET

d8-ETSCN

h8-ETSCN


Scaling properties in the electrodynamic response of molecular superconductors
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 doesn’t vary much, so they should sit in one small region of the plot


R s across the range of molecular superconductors
r Molecular Superconductorss across the range of Molecular Superconductors


Uemura plot for the molecular superconductors
Uemura Plot for the Molecular Superconductors Molecular Superconductors

Molecular systems have their own empirical scaling law:

Tc follows 1/l3 rather than 1/l2

⇒ Tc (ns/mb) 3/2


2D Molecular Superconductors

1D

2D

2D

2D

2D

3D

3D

1D, 2D & 3D systems

SC properties correlate with highest s direction

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)


Is there a single controlling parameter
Is there a single controlling parameter? Molecular Superconductors

  • 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


Dynamical mean field theory for calculating effect of u w on r s
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


Superfluid strength vs u w
Superfluid Strength vs U/W

Merino and McKenzie PRB61, 7996 (2000)

Powell and McKenzie PRL94, 047004 (2005)

DMFT

RVB

rsZ

Experimental picture

Feldbacher et al, PRL93, 136405 (2004)

DMFT



Conducting polymers
Conducting Polymers

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


Diffusion and the risch kehr model
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:


Polyaniline
Polyaniline

Data are well fitted by the Risch-Kehr function


Polyaniline1
Polyaniline

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

Cutoff at low B reflects interchain hopping


Polyaniline2
Polyaniline

Effect of ring librational modes at higher temperatures



Interchain diffusion rate d
Interchain Diffusion Rate D

Inter-chain behaviour highly dependent on sidegroups


Slow muons
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)


Surface and interface dynamics in polymers
Surface and Interface Dynamics in Polymers

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer

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

Forrest and Dalnoki-Veress,

Adv. Coll. Int. Sci. 94, 167 (2001)


Calculated range for muons in polystyrene using trim sp
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
Polystyrene Film Sample used for LEM Study

PRB 72, R121401 (2005)

Surface Layer Model

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 mm was estimated from ellipsometry

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer


Measured zf relaxation in ps
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
Measured Relaxation in the Bulk Polymer

Model

Fast fluctuation regime:

WLF law for segmental dynamics:

Indirect coupling to segmental dynamics:


Depth scan at t q
Depth Scan at T q

d ~ 35 nm at Tq

Surface Layer Model

Substrate

Bulk polymer

Surface layer

Thin film properties dominated by higher mobility surface layer


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
Size of the Surface Dynamical Region

Substrate

Glassy polymer

Molten layer

Substrate

Glassy polymer

Molten layer

Substrate

Molten layer

T1

T2

T3

T1

T2

T3

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

Herminghaus et al PRL 93, 017801 (2004)


Summary
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
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

Hazel Assender Oxford

Slow Muons Elvezio Morenzoni PSI


Introduction to muon techniques

Introduction to Muon Techniques

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


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