Transcript mSR in Polymers - Instytut Fizyki Jądrowej PAN

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 Muons
Familiar Particles and Muons
Familiar Particles and Muons
A positive muon behaves like an unstable light isotope of hydrogen
Primary International Facilities for mSR
TRIUMF
ISIS
PSI
JPARC
Continuous sources
Pulsed sources
Producing Muons at ISIS
50 m
View of the ISIS Experimental Hall
The mSR Sequence of Events
1)
Pions produced from proton beam striking carbon target
e.g.
2)
Pion decay:
p + p  p + n + p+
p + n  n + n + p+
p+  m++nm (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:
m+  e++ne+nm (lifetime 2.2 ms)
we detect the asymmetric positron emission
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
1)
Bare interstitial m+
2)
Chemically bonded closed shell states, e.g.
Formation of Muon Probe States
m+ (MeV)
Ionisation energy loss
to below 35 keV
Radiolytic e-
m+
Formation of Muon Probe States
Charge exchange
cycle
m+ (MeV)
Ionisation energy loss
to below 35 keV
e- capture
m+
13.5 eV
e- loss
Radiolytic e-
Mu
Formation of Muon Probe States
Charge exchange
cycle
m+ (MeV)
Ionisation energy loss
to below 35 keV
Thermal Mu
PARAMAGNETIC
e- capture
m+
13.5 eV
Mu
e- loss
Radiolytic eThermal m+
DIAMAGNETIC
Formation of Muon Probe States
Charge exchange
cycle
m+ (MeV)
Ionisation energy loss
to below 35 keV
Thermal Mu
PARAMAGNETIC
e- capture
m+
13.5 eV
Mu
e- loss
Chemical
reaction
Radiolytic eThermal m+
DIAMAGNETIC
Mu Radical
PARAMAGNETIC
Formation of Muon Probe States
Charge exchange
cycle
m+ (MeV)
Ionisation energy loss
to below 35 keV
Thermal Mu
PARAMAGNETIC
e- capture
m+
13.5 eV
Mu
e- loss
Delayed Mu
formation
Radiolytic em+
Thermal
DIAMAGNETIC
Ionization/
reaction
Chemical
reaction
Mu Radical
PARAMAGNETIC
Positron Emission and Detection
W(q) = 1+ a cos q
Positron Emission and Detection
W(q) = 1+ a cos q
LF/ZF
Sm
B
F
Positron Emission and Detection
W(q) = 1+ a cos q
LF/ZF
TF
Sm
B
U
Sm
F
B
F
D
Muon Instruments at ISIS
mSRRRR…
• Muon Spin Rotation
• Muon Spin Relaxation
• Muon Spin Resonance
• Muon Spin Repolarisation
Muon Spin Rotation
Energy Levels
Energy Levels
Single frequency wD
wD/2p = 13.55 kHz/G
Energy Levels
Energy Levels
Pair of frequencies
A = w1 + w2
Energy Levels
Energy Levels
Still one pair of
frequencies at high B
A = w1 + w2
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)
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
T<Tg P → D
Level Crossing Resonance
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
14N
14N
m+
quadrupolar mLCR in TTF-TCNQ
T>TCDW
T<TCDW
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 Mu
Quenching 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
Co (S=3/2)
Mohamed Kurmoo, University of Strasbourg
Critical Exponents Measured with mSR
Magnetic order:
Local susceptibility:
Relaxation rate:
M  (TN - T) b
c  (T - TN ) -g
l  | T -TN | -w
Comparison with Established Universality Classes
Scaling relations: a = 2 – 2b – g
n = (2b + g)/d
Dynamic exponent: z = d(2b + w)/(2b + g) = 1.25(6)
h = 2 – g/n
(c.f. z=d/2=1.5 for 3D AF)
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-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 < 2 x 10-4
T-dependent Relaxation from Spinons
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
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
TN (mK)
|J'| (mK)
J (K)
TN/J (10-2)
|J'/J| (10-3)
Experiment
Estimate
<20
7
2.2
<7
110
<0.018
0.006
0.020
<0.06
Sr2CuO3
CuPzN
KCuF3
5.4 K
107
39 K
2K
46
21 K
2200
10.3
406
0.25
1.0
9.6
0.93
4.4
52
DEOCC-TCNQF4 looks like the best example of the
1D Heisenberg Antiferromagnet yet discovered
PRL 96, 247203 (2006)
Molecular Superconductors
Measuring Properties of Type II
Superconductors
H < Hc1 : Meissner state
Surface measurement: l
Abrikosov Vortex Lattice
Hc1 < H < Hc2 : Vortex state
Bulk measurement: l, x
saddles
RMS Width:
Lineshape:
(skewness)
Brms or s
b = (Bave - Bpk) / Brms
cores
minima
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 Diagrams
d8-ETSCN
h8-ETSCN
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
rs across the range of Molecular Superconductors
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
Closer look at Superconducting Parameters vs Conductivity
Note the completely opposite rs - s0 scaling
between molecular and cuprate superconductors
Key:
s0- 1.05
s0- 0.77
1.
k-BETS2GaCl4
2D
2.
TMTSF2ClO4
1D
3.
a-ET2NH4Hg(SCN)4
2D
4.
b-ET2IBr2
2D
5.
l-BETS2GaCl4
2D
6.
k-ET2Cu(NCS)2
2D
7.
K3C60
3D
8.
Rb3C60
3D
1D, 2D & 3D systems
SC properties correlate with highest s direction
s0+ 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 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 rs
Loss of quasiparticle spectral weight is
expected as the Mott-Hubbard transition
is approached
Superfluid Strength vs U/W
Merino and McKenzie PRB61, 7996 (2000)
Powell and McKenzie PRL94, 047004 (2005)
RVB
DMFT
rsZ
Feldbacher et al, PRL93, 136405 (2004)
DMFT
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 Model
Stochastic model describing muon relaxation due to
intermittent hyperfine coupling with a diffusing polaron
The relaxation function takes the form:
Gz (t )  exp(t ) erfc( t )
(Risch-Kehr function)
with the relaxation parameter  following a 1/B law at high field:

w4
0
2we D 2
||
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 ~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 :
1)
Degrading the energy in a cold moderator layer (PSI)
2)
Laser ionization of thermal muonium (RIKEN-RAL)
Surface and Interface Dynamics in Polymers
Surface Layer Model
Substrate
Bulk polymer
Surface layer
Tg 
Tgbulk
1  h0 / h )
1 /n
Supported polystyrene films
(overlaid data from 6 groups using
various different techniques)
Forrest and Dalnoki-Veress,
Adv. Coll. Int. Sci. 94, 167 (2001)
Thin film properties dominated
by higher mobility surface layer
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
PRB 72, R121401 (2005)
Surface Layer Model
Mw = 62,600, Mw/Mn=1.04
Substrate
1 mm thick by 50 mm diameter
copper substrate
Bulk polymer
Surface layer
Film prepared by spin-coating
from a 15% solution of PS in
cyclohexanone
Film thickness of 0.46 mm was
estimated from ellipsometry
Thin film properties dominated
by higher mobility surface layer
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
Model
Fast fluctuation regime:
Indirect coupling to
segmental dynamics:
WLF law for segmental dynamics:
Depth Scan at Tq
Surface Layer Model
d ~ 35 nm at
Tq
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
Substrate
Glassy polymer
Molten layer
T1
Substrate
Glassy polymer
Molten layer
T2
Substrate
Molten layer
T1
T2
T3
T3
Surface melting model: d(T) follows from linear dispersion of surface capillary waves
Herminghaus et al PRL 93, 017801 (2004)
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
mSR
Steve Blundell
Oxford
Molecular Magnets
Mohamed Kurmoo
Strasbourg
Seishi Takagi
Kyushu
Naoki Toyota
Tohoku
Molecular Superconductors
& Takahiko Sasaki
Polymers
Slow Muons
Steve Lee
St. Andrews
Andy Monkman
Durham
Andrew Holmes
Cambridge
Hazel Assender
Oxford
Elvezio Morenzoni
PSI
Introduction to Muon Techniques
For a short review see: S.J. Blundell, Contemp. Phys. 40, 175 (1999)