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Muon studies of spin dynamics in polyaniline
ELSEVIER
Synthetic
Metals 84 (1997)
943-944
Muon studies of spin dynamics in polyaniline F.L. Pratt’~2, K. Ishida’, K. Nagamine’,
P.A. Pattenden’, Th. JestSid?, K.H. Chow’,
S.J.Blundel12, W. Hayes’and A.P. Monkman
‘Muon
Science Laboratory The Institute of Physical and Chemical Research (RIKEN), Rutherford Appleton Laboratoy, Chilton, Didcot OX1 1 OQX, U.K. 2 Department of Physics, University of Oxford, Clarendon Laboratoty, Parkr Road, Oxford OXI 3PU, U.K. ’ Department of Physics, University of Durham, South Road, Durham DHI 3LE, U.K.
Abstract
The muon is a valuable probe of spin excitations in polymers, as the muon implantation process itself generates a test excitation We report here studies on undoped whose dynamical properties can be studied via the evolution of the muon spin polarisation. polyaniline in its emeraldine base form (PANI:EB). Characteristic field dependences and cutoff frequencies for the muon spin relaxation are observed which are related to the spin diffusion. One-dimensional diffusion is seen at low temperatures and at short probe times. The on chain diffusion is observed to have a weak metallic temperature dependence whereas the interchain diffusion is strongly activated and phenyl ring rotations are seen to have an important effect on the diffusion processes. Keywords: Polyaniline
and derivatives
1. Introduction
Fundamental to the understanding of conducting polymer systems are the nature and properties of their charge and spin excitations which are strongly coupled to the underlying molecular structure of the polymer. The muon is a particularly sensitive probe of such soliton and polaron excitations as the muon implantation process itself can generate an excitation whose dynamical properties can be studied via the evolution of This was first demonstrated in the muon spin polarisation. polacetylene [I] and subsequent studies were reported for a range of conducting polymers [2-41. In previous studies the muon spin relaxation was fitted to an exponential ;ecay function which does not describe the relaxation so well over a wide time range. Risch and Kehr [5] recently derived a relaxation function that more properly describes the 1D diffusion of the spin defect; their longitudinal muon spin relaxation function in finite fields has the form: G(t)
= #(rf>
for
AT >> 1
(1)
where
where co, is the electronic Larmor frequency, w0 is the muonelectron hyperfine coupling and D,l is the one dimensional diffusion rate. When D,, is large compared to 0: / ds, relaxation parameter shows a I/B field dependence
the
which is independent of the spin flip rate and depends sensitively on the diffusion rate D,,. At low fields there will be a cutoff to the I/B field dependence at B, which may be due to a number of factors. There may be a crossover to a 3D diffusion regime when w, becomes smaller than the interchain ditision rate D, ; a crossover to a slow fluctuation regime will also occur if 0; / Jw becomes larger than D,, and also coupling to nuclear dipolar fields can become important in the region below IOG.
4(x) = exp(x) erfc(&) 2. Experimental
erfc signifies the complementary error function, ;i the electron spin flip rate, T the experimental timescale and r is a relaxation parameter. This reiaxation function goes as t?” at long times rather than decaying exponentially. r is given by 0379-6779/97/$17.00 0 1997 Else&r Science S.A. Ail rights reserved PII 80379-6779(96)04222-l
Results
We have carried out muon spin relaxation measurements in longitudinal and transverse applied fields for samples of PANI:EB at the RAL and PSI muon facilities using positive
FL. Pratt et al. /Synthetic
944
surface muons for times up to 32 ps, fields up to 6 kG and temperatures down to 6 K. We find that the measured relaxation can be well described using Eqn. 1 over a wide range of experimental conditions. The data are fitted with only two parameters; the field dependent initial amplitude and the field and temperature dependent relaxation parameter r. Some results for PANI:EB are shown in Fig. 1.
Metals
84 (1997)
943-944
derive the diffusion rate from the measured relaxation parameter via Eqn. 3, a value for the hyperfine coupling o. was required. We estimated this as w. = 27~ x 150 MHz from the longitudinal decoupling field of the initial muon asymmetry; the corresponding diffusion rate is shown in Fig. 3.
e 10”
2
-
e .-E v) 2 B 5x1013 t 10
30
100 Temperature
1000
100 Magnetic
Field
Fig. 3 The temperature dependence of the polaron diffusion rate D/i derived from the 1 kG data of Fig. 2 using the value ~0 = 2n x 150 MHz.
(G)
Fig. 1. Relaxation parameter r versus field for PANI:EB at 6K and 300K. The lines show the regions where I- obeys the l/B law. It can be seen in Fig. 1 that at 6 K the l/B regime of Eqn. 3 holds down to below 10 G whereas at 300 K the I/B regime only holds down to 300 G or so. This suggests that the interchain diffusion rate increases by around two orders of magnitude between 6 K and 300 K where it reaches a value of -1.6~10’~ rad/s. Since at 500 G and above the I/B field dependence is obeyed over a wide range of temperature, a field of 1 kG was chosen for a more detailed study of the temperature dependence of the relaxation. This is shown in Fig. 2. 5
G 1 c b s
” 4-
E 3. e I2
*a
, _
.
c 2.&? j,:
.
The difision rate shows a weak metallic temperature coefficient at low temperatures which becomes rather stronger above 150 K. Between 150 K and 200 K the diffusion rate is inversely proportional to temperature which is suggestive of phonon limited metallic transport. The temperature dependence of the diffusion parameters are summarised in Table 1. In contrast to Dll, the interchain diffusion D, increases sharply above 150 K, suggesting that ring rotation assists interchain transport but hinders intrachain motion. It is interesting to note that our values for D,, at 300 K and for the temperature dependence of D, are quite similar to an earlier ESR study of spin dynamics in metallic emeraldine salt PAN1 [S] but the temperature dependence of D,i is rather different in the undoped material studied here. Table 1 Estimated values for D/i and D, ( assuming D, = Bcl yeye) in units of rad/s at several temperatures, together with the estimated anisotropy Q/D,.
.
6K
K
150 K
300K
1.7x1014 <2x10* >lx106
1.1x10’4 4.4x109
7.4x1013 5.4x109
2.5~10~
1.4x104
50
. .
l
:
. l *
1.8x10’4 <2x108 >lx106
Dll DA W’,
10
300 (K)
30
100 Temperature
300
References
(K)
Fig. 2 Temperature dependence ot the relaxation parameter r for PANI:EB at 1 kG. From Fig. 2 it can be seen that there is a rapid increase in the relaxation above 150 K. This is believed to be associated with the excitation of phenyl ring librations which are known to couple strongly to the electronic excitations [6]. In order to
[I] K. Nagamine et al, Phys. Rev. Lett. 53 (1984) 1763; K. Ishida et al, Phys. Rev. Lett. 55 (1985) 2009. [2] F.L. Pratt et al, Synth. Met. 55 (1993) 677. [3] F.L. Pratt et al, Synth. Met. 69 (1995) 231. [4] F.L. Pratt et al, Hyperfine Interactions (1996, to be published). [S] R. Risch and K.W. Kehr, Phys. Rev. B46 (1992) 5246. [6] J.M. Ginder and A.J. Epstein, Phys. Rev. B41 (1990) 10674; A.J. Milton
and A.P.
Monkman,
J. Phys.
D:Appl.
Phys.
26 (1993)
[7] K. Mizoguchi and K. Kume, Sol. St. Comm. 89 (1994) 971.
1468.
Synthetic
Metals 84 (1997)
943-944
Muon studies of spin dynamics in polyaniline F.L. Pratt’~2, K. Ishida’, K. Nagamine’,
P.A. Pattenden’, Th. JestSid?, K.H. Chow’,
S.J.Blundel12, W. Hayes’and A.P. Monkman
‘Muon
Science Laboratory The Institute of Physical and Chemical Research (RIKEN), Rutherford Appleton Laboratoy, Chilton, Didcot OX1 1 OQX, U.K. 2 Department of Physics, University of Oxford, Clarendon Laboratoty, Parkr Road, Oxford OXI 3PU, U.K. ’ Department of Physics, University of Durham, South Road, Durham DHI 3LE, U.K.
Abstract
The muon is a valuable probe of spin excitations in polymers, as the muon implantation process itself generates a test excitation We report here studies on undoped whose dynamical properties can be studied via the evolution of the muon spin polarisation. polyaniline in its emeraldine base form (PANI:EB). Characteristic field dependences and cutoff frequencies for the muon spin relaxation are observed which are related to the spin diffusion. One-dimensional diffusion is seen at low temperatures and at short probe times. The on chain diffusion is observed to have a weak metallic temperature dependence whereas the interchain diffusion is strongly activated and phenyl ring rotations are seen to have an important effect on the diffusion processes. Keywords: Polyaniline
and derivatives
1. Introduction
Fundamental to the understanding of conducting polymer systems are the nature and properties of their charge and spin excitations which are strongly coupled to the underlying molecular structure of the polymer. The muon is a particularly sensitive probe of such soliton and polaron excitations as the muon implantation process itself can generate an excitation whose dynamical properties can be studied via the evolution of This was first demonstrated in the muon spin polarisation. polacetylene [I] and subsequent studies were reported for a range of conducting polymers [2-41. In previous studies the muon spin relaxation was fitted to an exponential ;ecay function which does not describe the relaxation so well over a wide time range. Risch and Kehr [5] recently derived a relaxation function that more properly describes the 1D diffusion of the spin defect; their longitudinal muon spin relaxation function in finite fields has the form: G(t)
= #(rf>
for
AT >> 1
(1)
where
where co, is the electronic Larmor frequency, w0 is the muonelectron hyperfine coupling and D,l is the one dimensional diffusion rate. When D,, is large compared to 0: / ds, relaxation parameter shows a I/B field dependence
the
which is independent of the spin flip rate and depends sensitively on the diffusion rate D,,. At low fields there will be a cutoff to the I/B field dependence at B, which may be due to a number of factors. There may be a crossover to a 3D diffusion regime when w, becomes smaller than the interchain ditision rate D, ; a crossover to a slow fluctuation regime will also occur if 0; / Jw becomes larger than D,, and also coupling to nuclear dipolar fields can become important in the region below IOG.
4(x) = exp(x) erfc(&) 2. Experimental
erfc signifies the complementary error function, ;i the electron spin flip rate, T the experimental timescale and r is a relaxation parameter. This reiaxation function goes as t?” at long times rather than decaying exponentially. r is given by 0379-6779/97/$17.00 0 1997 Else&r Science S.A. Ail rights reserved PII 80379-6779(96)04222-l
Results
We have carried out muon spin relaxation measurements in longitudinal and transverse applied fields for samples of PANI:EB at the RAL and PSI muon facilities using positive
FL. Pratt et al. /Synthetic
944
surface muons for times up to 32 ps, fields up to 6 kG and temperatures down to 6 K. We find that the measured relaxation can be well described using Eqn. 1 over a wide range of experimental conditions. The data are fitted with only two parameters; the field dependent initial amplitude and the field and temperature dependent relaxation parameter r. Some results for PANI:EB are shown in Fig. 1.
Metals
84 (1997)
943-944
derive the diffusion rate from the measured relaxation parameter via Eqn. 3, a value for the hyperfine coupling o. was required. We estimated this as w. = 27~ x 150 MHz from the longitudinal decoupling field of the initial muon asymmetry; the corresponding diffusion rate is shown in Fig. 3.
e 10”
2
-
e .-E v) 2 B 5x1013 t 10
30
100 Temperature
1000
100 Magnetic
Field
Fig. 3 The temperature dependence of the polaron diffusion rate D/i derived from the 1 kG data of Fig. 2 using the value ~0 = 2n x 150 MHz.
(G)
Fig. 1. Relaxation parameter r versus field for PANI:EB at 6K and 300K. The lines show the regions where I- obeys the l/B law. It can be seen in Fig. 1 that at 6 K the l/B regime of Eqn. 3 holds down to below 10 G whereas at 300 K the I/B regime only holds down to 300 G or so. This suggests that the interchain diffusion rate increases by around two orders of magnitude between 6 K and 300 K where it reaches a value of -1.6~10’~ rad/s. Since at 500 G and above the I/B field dependence is obeyed over a wide range of temperature, a field of 1 kG was chosen for a more detailed study of the temperature dependence of the relaxation. This is shown in Fig. 2. 5
G 1 c b s
” 4-
E 3. e I2
*a
, _
.
c 2.&? j,:
.
The difision rate shows a weak metallic temperature coefficient at low temperatures which becomes rather stronger above 150 K. Between 150 K and 200 K the diffusion rate is inversely proportional to temperature which is suggestive of phonon limited metallic transport. The temperature dependence of the diffusion parameters are summarised in Table 1. In contrast to Dll, the interchain diffusion D, increases sharply above 150 K, suggesting that ring rotation assists interchain transport but hinders intrachain motion. It is interesting to note that our values for D,, at 300 K and for the temperature dependence of D, are quite similar to an earlier ESR study of spin dynamics in metallic emeraldine salt PAN1 [S] but the temperature dependence of D,i is rather different in the undoped material studied here. Table 1 Estimated values for D/i and D, ( assuming D, = Bcl yeye) in units of rad/s at several temperatures, together with the estimated anisotropy Q/D,.
.
6K
K
150 K
300K
1.7x1014 <2x10* >lx106
1.1x10’4 4.4x109
7.4x1013 5.4x109
2.5~10~
1.4x104
50
. .
l
:
. l *
1.8x10’4 <2x108 >lx106
Dll DA W’,
10
300 (K)
30
100 Temperature
300
References
(K)
Fig. 2 Temperature dependence ot the relaxation parameter r for PANI:EB at 1 kG. From Fig. 2 it can be seen that there is a rapid increase in the relaxation above 150 K. This is believed to be associated with the excitation of phenyl ring librations which are known to couple strongly to the electronic excitations [6]. In order to
[I] K. Nagamine et al, Phys. Rev. Lett. 53 (1984) 1763; K. Ishida et al, Phys. Rev. Lett. 55 (1985) 2009. [2] F.L. Pratt et al, Synth. Met. 55 (1993) 677. [3] F.L. Pratt et al, Synth. Met. 69 (1995) 231. [4] F.L. Pratt et al, Hyperfine Interactions (1996, to be published). [S] R. Risch and K.W. Kehr, Phys. Rev. B46 (1992) 5246. [6] J.M. Ginder and A.J. Epstein, Phys. Rev. B41 (1990) 10674; A.J. Milton
and A.P.
Monkman,
J. Phys.
D:Appl.
Phys.
26 (1993)
[7] K. Mizoguchi and K. Kume, Sol. St. Comm. 89 (1994) 971.
1468.