- Email: [email protected]
13C and 1H spin-lattice relaxation in amorphous hydrogenated carbon
Solid Srate Communications,
Vol. 107. No. 7. pp. 349-352, 1998 0 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003X-1098/98 $19.00+.00
Pergamon
‘jC AND ‘H SPIN-LATTICE
RELAXATION
IN AMORPHOUS
HYDROGENATED
CARBON
D. ArEon,“.* J. Seliger,” R. Blinc,” I. Pocsikb and M. Koosb “J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia hResearch Institute for Solid State Physics of the Hungarian Academy of Sciences, Budapest XII, Konkoly Thege str 29-33, H-1525 Budapest, Hungary (Received 9 January
1999; accepted 27 April 1998 by P. Wachter)
The temperature dependences of the i3C and ‘H magnetization recovery and spin-lattice relaxation times have been measured in amorphous hydrogenated carbon (a-C : 13).The observed short and nearly temperature independent proton and 13C spin-lattice relaxation times demonstrate that the dominant spin-lattice relaxation mechanism is spin diffusion to paramagnetic impurities. The fact that the magnetization recovery curves clearly deviate from the single exponentiai form demonstrates that the p~amagnetic centers aggregate in clusters so that the unpaired electron distribution in a-C : H is strongly inhomogeneous. 0 I998 Elsevier Science Ltd. All rights reserved Keywords:
A. disordered
systems, E. nuclear resonances.
Recent studies [ 1, 21 of proton spin-lattice relaxation in hydrogenated amorphous carbon [3,4] (a-C : H) showed a rather unexpected behavior. The proton magnetization recovery could be described in terms of a bi-exponential approach to equilib~um yielding two time constants the values of which at room temperature and at a Larmor frequency 300 MHz are T,, = 120 ms and Tlb = 14 ms. This result has been interpreted in terms of the exl stence of two different types of proton clusters spatially separated from each other. The short T, compon~!nt has been attributed ]I, 21 to CH groups statistically distributed in the sp” and sp3 carbon network whereas the long TI component has been ascribed [ 1, 21 to short -CH* polymer-like chain units with an sp3 configuration. The two groups are proposed to be separated by “layers” of non-protonated sp2 carbons. The intermediate layer should be so large that spin diffusion between the two groups of protons is not effective. The total hydrogen content of the above sample was 35 at.%. The mechanism leading to the observed proton spinlattice relaxation behavior is however still noi. fully explained. The absolute values of the two T, components as well as their temperature dependences are hard to
* Corresponding
author. 349
understand within this model. The rather small value of the shorter T, component (5-15 ms) and its near temperature independence cannot be explained in terms of proton-proton dipolar interactions. This is particularly true as the proton density in the sp*-sp3 carbon cluster is relatively low and one would in fact expect a long T1 value rather than such a short one. The TI values of the component with the larger Ti slowly increases with decreasing temperature but no T1 minimum could be found. The activation energy is much smaller than the values usually found in organic materials [2]. In order to throw some additional light on the above problems we decided to determine the form of the 13C magnetization recovery and the temperature dependence of the 13C spin-lattice relaxation times. We wanted to see if the 13C spin-lattice relaxation times show a similarly anomalous behavior as the proton ones. We also hoped to determine the nature of the mechanism giving rise to the anomalously short proton and “C T, values in a-C : H. The a-C : H samples were prepared by deposition from an r.f. glow discharge plasma of benzene ]a]. The deposition conditions (self bias -400 V, pressure 80 mTorr) were such as to yield hard forms of a-C : H samples with a density of = 1.8 g cm-” and a hydrogen
‘jC AND ‘H SPIN-LA~ICE
350
content of * 35%. For sake of easy removal an Al plate was used as substrate. The 13Cspin-lattice relaxation measurements were performed between room temperature and 4.4 K at a Larmor frequency of 95.572 MHz in a 9 T superconducting magnet using the 180”-90” magnetization recovery technique. The proton spin-lattice relaxation measurements were performed at a Larmor frequency of 100.04 MHz. The 13C magnetization recovery curves [Fig. l(a)] could be fitted within the experimental accuracy by a two component relaxation function
RELAXATION IN CARBON T(K)
Sb
exp[- 7/T;“])
100
(1)
_ .~ i
20
10
40
60
I~O/~(
similar to the one reported for the proton [Fig, I(b)] magnetization recovery 11, 23. Here s, and sb correspond to the fraction of the magnetization inverted by the first pulse. The relative amplitudes of the two components are h4, = 0.30 and Mb = 0.70 whereas s, and sb are of the order of I .4. One component has a 13CT, of the order of Ti” L=:750 ms, whereas the T, of the other component is of the order of Tl” =; 60 ms. Both TI”’ and Tib’ are nearly temperature inde~ndent down to 4.4 IS (Fig. 2). This behavior is analogous to the bi-exponential relaxation behavior of the protons where the two time constants are however by a factor of about 4 shorter [Fig. I(b)]. Protons and ‘jC nuclei thus seem to be relaxed by a common relaxation mechanism. This mechanism must
1.0
40
200100
M(7) = MA 1 - s, exp[ - r/T?‘]) MO + bfb( 1 -
(b) ‘HNMR
0.5
Vol. 107, No. 7
80
1
K-’ )
Fig. 2. The temperature dependence of the two 13Cspin lattice relaxation time components Ty’ (A) and r’/’ (0). be extremely effective in order to produce such short T, values in the lo-60 ms range even at 4 K. The observed ‘“C spin-lattice relaxation is hard to understand within the relaxation mechanisms normally operating in polymers and organic solids. If the “C spinlattice relaxation would be determined by C-H dipolar interactions or ‘-‘Cchemical shift anisotropy fluctuations, we would within the model used to interpret the proton relaxation results [ 1,2] expect at least three different sets of ‘“C relaxation parameters - corresponding to the three different environments - and not just two. In addition C-H dipolar interactions and chemical shift anisotropy relaxation can not yield such a short i3C T1 which would be nearly temperature independent down to 4 K. The only possible mechanism which could yield such a behavior is coupling to paramagnetic centers. ESR measurements on one of our samples [5] have indeed shown the presence of 2.5 X 10’” free spins/gram, i.e. we have one unpaired electron per about 2400 carbon atoms. Spin diffusion can thus explain the short proton and 13C T, values and their near temperature independence but not the observed non-exponential magnetization recovery if the electron distribution in the sample is random. It is well known that in solids the direct electron nuclear coupling may induce nuclear spin flips unaccompanied by an electron fhp. This relaxation mechanism results for WIT% 1 in a nuclear spin lattice relaxation rate [6] (2) where
Fig. I. (a) ‘jC and (b) ‘H magnetization recovery curves in amorphous carbon sample analyzed by a two component relaxation function [equation (l)].
with r being the electron spin lattice relaxation time.
Vol. 107, No. 7
13C AND ‘H SPIN-LATTICE
RELAXATION
IN CARBON
351
This mechanism is very effective for nuclei close to the paramagnetic centers but rather ineffective for all other nuclei. The majority of nuclei are namely relatively far from the p~amagnetic center and are thus relaxed by spin-diffusion to paramagnetic impurities. Here [6] 1 - = 4irNbD Tl
(31
where N is the number of impurities per unit volume, D = W - a2 is the nuclear spin-diffusion constant with a being an inter-nuclear distance and W the probability of a spin-flop transition between nearest neighbors. b is the scattering amplitude of a single impurity and is of the order of the average inter-nuclear spacing [6]. Since the natural abundance of the ‘3C nuclei is rather low (1%) the spin diffusion induced relaxation rate is expected to be significantly smaller for the ‘“C than for the ‘H nuclei. In case of spin diffusion a large number of impllrities contribute to spin relaxation at a given lattice site and the magnetization spin recovery should be described by a single exponential [6]. This is contrary to the bi-exponential behavior reported in [ 1, 21 as well as to the behavior shown in Fig. 1. If however the electrons aggregate into clusters and are preferentially found in some regions of the sample and not in others we can obtain a multiexponential magnetization recovery behavior: We expect a bi-exponential relaxation behavior if we have two types of regions with different N. In case of a ~ontirluous distribution of clusters with different N, we may even expect a stretched exponential behavior. In order to check whether we have a two-cluster region or a multi cluster region case we tried to fit the observed ‘H and t3C magnetization recovery data not only to a bi-exponential but also to a strelched exponential magnetization recovery function ~(?)/~~
= 1 - s exp[ - (r/T1 >“I
Fig. 3. (a) 13C and (b) ‘H magnetization recovery curves in amorphous carbon sample analyzed by a stretched exponential relaxation function. a sizeable fraction of nuclei. To check on that we have studied samples with much lower electron concentrations (as measured by the ESR intensity) but essentially the same magnetization recovery behavior was obtained. We thus believe that the non-exponential magnetization recovery behavior is due to the existence of electron clustering. 1.00
--
.-~-
.-.
64
I
0.75
0.50 8
(4)
The obtained results are shown in Fig. 3. The stretched exponential fits are within the bounds of the experimental error not worse than the bi-expon~!ntiaI ones (Fig. 1). The s value is of the order of 1.8. The temperature dependences of the stretched exponent CIand the 13C spin-lattice relaxation parameter Ti are shown in Fig. 4. In the “C case CY= 0.6 whereas the I’,( 13C) parameter is 480 ms. In the proton case we have (Y= 0.68 whereas T,(H) is 83.5 ms at room temperature. The ‘H stretched exponentia1 fit [Fig. 3(b)] is ,?ven slightly better than the bi-exponential one ]Fig. l(b)]. It should be noted that a non-exponential magnetization recovery can be also obtained if the concentration of paramagnetic impurities is not small [7] so that direct electron nuclear coupling is rate determining for
(b)
I.O-
l**
.
I
l
l
.
*i
.
om b-
60
i,,,-_--
~_ -
/
i l
O* lOOOU( K’ ) Fig. 4. The temperature dependence of (a) the stretched exponent CY and (b) the t3C spin lattice relaxation parameter Tl .
352
“C AND ‘H SPIN-LATTICE
If this electron clustering indeed occurs one would expect to find a super-paramagnetic behavior at low temperatures. Such a behavior is well known to take place in magnetic molecular cluster systems [8] such as Mn12-acetate. At high temperatures the magnetization of the cluster exhibits a paramagnetic-like behavior. At low temperatures where the thermal energy becomes of the order of the anisotropic energy barrier for cluster reorientations the magnetization freezes out. Magnetic hysteresis in superparamagnets is a result of the time delay between the change of the external magnetic field and the response of the magnetization. At low enough temperatures one would thus expect to observe a magnetic hysteresis curve like in ferromagnets. Such a behavior was indeed observed in all our samples below 20 K [S]. In summary we have shown that within the limits of experimental error the 13C and the ‘H magnetization recovery can be described by a stretched exponential function just as well as by a bi-exponential one. The short and nearly temperature independent values of both the proton and ‘“C spin lattice relaxation times demonstrate that the dominant spin-lattice relaxation mechanism is spin diffusion to paramagnetic impurities. The fact that the magnetization recovery is not described by single exponential as expected in case of a random distribution of paramagnetic centers but shows a bi-exponential respectively stretched exponential form
RELAXATION
IN CARBON
Vol. 107, No. 7
further demonstrates that the paramagnetic centers aggregate in clusters so that the unpaired electron distribution is strongly inhomogeneous. Such an inhomogeneous electron distribution should result in a superparamagnetic behavior at low temperatures. This was indeed observed by SQUID magnetization measurements [ 51. REFERENCES 1.
2.
Jiiger, C., Sottwald, J., Spiess, H.W. and Newport, R.J., Phys. Rev., BSO, 1994, 846 and references therein. Pocsik, I., Koos, M., Moustafa, S.H., Lasanda, S., Banki, P. and Tompa, K., J. Non-Cryst. So/ids, 198-200,
3.
4.
1996,632.
Robertson, J., Adv. Phys., 35,1986,317; J., J. of Non-Crystalline Solids, 137, Robertson. J., J. of Non-Cryst. Solids, 1991, 825. Robertson, J., Progress in Solid State
Robertson, 1991, 138; 137-138, Chemistry,
21, 1991, 199.
5. 6. 7.
Blinc, R., Arcon, D., Cevc, P., Pocsik, I., Koos, M., Trontelj, Z. and ZaglieiE, to be published. Abragam, A., The Principles of Nuclear Magnetism. Clarendon, Oxford. 1961. Atsarkin, A.A. and Demidov, V.V., Sov. Phys. JETP, 52, 1980, 726.
8.
Gatteschi, D., Caneschi, A., Pardi, L. and Sessoli, R., Science, 265, 1994, 1054.
Vol. 107. No. 7. pp. 349-352, 1998 0 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003X-1098/98 $19.00+.00
Pergamon
‘jC AND ‘H SPIN-LATTICE
RELAXATION
IN AMORPHOUS
HYDROGENATED
CARBON
D. ArEon,“.* J. Seliger,” R. Blinc,” I. Pocsikb and M. Koosb “J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia hResearch Institute for Solid State Physics of the Hungarian Academy of Sciences, Budapest XII, Konkoly Thege str 29-33, H-1525 Budapest, Hungary (Received 9 January
1999; accepted 27 April 1998 by P. Wachter)
The temperature dependences of the i3C and ‘H magnetization recovery and spin-lattice relaxation times have been measured in amorphous hydrogenated carbon (a-C : 13).The observed short and nearly temperature independent proton and 13C spin-lattice relaxation times demonstrate that the dominant spin-lattice relaxation mechanism is spin diffusion to paramagnetic impurities. The fact that the magnetization recovery curves clearly deviate from the single exponentiai form demonstrates that the p~amagnetic centers aggregate in clusters so that the unpaired electron distribution in a-C : H is strongly inhomogeneous. 0 I998 Elsevier Science Ltd. All rights reserved Keywords:
A. disordered
systems, E. nuclear resonances.
Recent studies [ 1, 21 of proton spin-lattice relaxation in hydrogenated amorphous carbon [3,4] (a-C : H) showed a rather unexpected behavior. The proton magnetization recovery could be described in terms of a bi-exponential approach to equilib~um yielding two time constants the values of which at room temperature and at a Larmor frequency 300 MHz are T,, = 120 ms and Tlb = 14 ms. This result has been interpreted in terms of the exl stence of two different types of proton clusters spatially separated from each other. The short T, compon~!nt has been attributed ]I, 21 to CH groups statistically distributed in the sp” and sp3 carbon network whereas the long TI component has been ascribed [ 1, 21 to short -CH* polymer-like chain units with an sp3 configuration. The two groups are proposed to be separated by “layers” of non-protonated sp2 carbons. The intermediate layer should be so large that spin diffusion between the two groups of protons is not effective. The total hydrogen content of the above sample was 35 at.%. The mechanism leading to the observed proton spinlattice relaxation behavior is however still noi. fully explained. The absolute values of the two T, components as well as their temperature dependences are hard to
* Corresponding
author. 349
understand within this model. The rather small value of the shorter T, component (5-15 ms) and its near temperature independence cannot be explained in terms of proton-proton dipolar interactions. This is particularly true as the proton density in the sp*-sp3 carbon cluster is relatively low and one would in fact expect a long T1 value rather than such a short one. The TI values of the component with the larger Ti slowly increases with decreasing temperature but no T1 minimum could be found. The activation energy is much smaller than the values usually found in organic materials [2]. In order to throw some additional light on the above problems we decided to determine the form of the 13C magnetization recovery and the temperature dependence of the 13C spin-lattice relaxation times. We wanted to see if the 13C spin-lattice relaxation times show a similarly anomalous behavior as the proton ones. We also hoped to determine the nature of the mechanism giving rise to the anomalously short proton and “C T, values in a-C : H. The a-C : H samples were prepared by deposition from an r.f. glow discharge plasma of benzene ]a]. The deposition conditions (self bias -400 V, pressure 80 mTorr) were such as to yield hard forms of a-C : H samples with a density of = 1.8 g cm-” and a hydrogen
‘jC AND ‘H SPIN-LA~ICE
350
content of * 35%. For sake of easy removal an Al plate was used as substrate. The 13Cspin-lattice relaxation measurements were performed between room temperature and 4.4 K at a Larmor frequency of 95.572 MHz in a 9 T superconducting magnet using the 180”-90” magnetization recovery technique. The proton spin-lattice relaxation measurements were performed at a Larmor frequency of 100.04 MHz. The 13C magnetization recovery curves [Fig. l(a)] could be fitted within the experimental accuracy by a two component relaxation function
RELAXATION IN CARBON T(K)
Sb
exp[- 7/T;“])
100
(1)
_ .~ i
20
10
40
60
I~O/~(
similar to the one reported for the proton [Fig, I(b)] magnetization recovery 11, 23. Here s, and sb correspond to the fraction of the magnetization inverted by the first pulse. The relative amplitudes of the two components are h4, = 0.30 and Mb = 0.70 whereas s, and sb are of the order of I .4. One component has a 13CT, of the order of Ti” L=:750 ms, whereas the T, of the other component is of the order of Tl” =; 60 ms. Both TI”’ and Tib’ are nearly temperature inde~ndent down to 4.4 IS (Fig. 2). This behavior is analogous to the bi-exponential relaxation behavior of the protons where the two time constants are however by a factor of about 4 shorter [Fig. I(b)]. Protons and ‘jC nuclei thus seem to be relaxed by a common relaxation mechanism. This mechanism must
1.0
40
200100
M(7) = MA 1 - s, exp[ - r/T?‘]) MO + bfb( 1 -
(b) ‘HNMR
0.5
Vol. 107, No. 7
80
1
K-’ )
Fig. 2. The temperature dependence of the two 13Cspin lattice relaxation time components Ty’ (A) and r’/’ (0). be extremely effective in order to produce such short T, values in the lo-60 ms range even at 4 K. The observed ‘“C spin-lattice relaxation is hard to understand within the relaxation mechanisms normally operating in polymers and organic solids. If the “C spinlattice relaxation would be determined by C-H dipolar interactions or ‘-‘Cchemical shift anisotropy fluctuations, we would within the model used to interpret the proton relaxation results [ 1,2] expect at least three different sets of ‘“C relaxation parameters - corresponding to the three different environments - and not just two. In addition C-H dipolar interactions and chemical shift anisotropy relaxation can not yield such a short i3C T1 which would be nearly temperature independent down to 4 K. The only possible mechanism which could yield such a behavior is coupling to paramagnetic centers. ESR measurements on one of our samples [5] have indeed shown the presence of 2.5 X 10’” free spins/gram, i.e. we have one unpaired electron per about 2400 carbon atoms. Spin diffusion can thus explain the short proton and 13C T, values and their near temperature independence but not the observed non-exponential magnetization recovery if the electron distribution in the sample is random. It is well known that in solids the direct electron nuclear coupling may induce nuclear spin flips unaccompanied by an electron fhp. This relaxation mechanism results for WIT% 1 in a nuclear spin lattice relaxation rate [6] (2) where
Fig. I. (a) ‘jC and (b) ‘H magnetization recovery curves in amorphous carbon sample analyzed by a two component relaxation function [equation (l)].
with r being the electron spin lattice relaxation time.
Vol. 107, No. 7
13C AND ‘H SPIN-LATTICE
RELAXATION
IN CARBON
351
This mechanism is very effective for nuclei close to the paramagnetic centers but rather ineffective for all other nuclei. The majority of nuclei are namely relatively far from the p~amagnetic center and are thus relaxed by spin-diffusion to paramagnetic impurities. Here [6] 1 - = 4irNbD Tl
(31
where N is the number of impurities per unit volume, D = W - a2 is the nuclear spin-diffusion constant with a being an inter-nuclear distance and W the probability of a spin-flop transition between nearest neighbors. b is the scattering amplitude of a single impurity and is of the order of the average inter-nuclear spacing [6]. Since the natural abundance of the ‘3C nuclei is rather low (1%) the spin diffusion induced relaxation rate is expected to be significantly smaller for the ‘“C than for the ‘H nuclei. In case of spin diffusion a large number of impllrities contribute to spin relaxation at a given lattice site and the magnetization spin recovery should be described by a single exponential [6]. This is contrary to the bi-exponential behavior reported in [ 1, 21 as well as to the behavior shown in Fig. 1. If however the electrons aggregate into clusters and are preferentially found in some regions of the sample and not in others we can obtain a multiexponential magnetization recovery behavior: We expect a bi-exponential relaxation behavior if we have two types of regions with different N. In case of a ~ontirluous distribution of clusters with different N, we may even expect a stretched exponential behavior. In order to check whether we have a two-cluster region or a multi cluster region case we tried to fit the observed ‘H and t3C magnetization recovery data not only to a bi-exponential but also to a strelched exponential magnetization recovery function ~(?)/~~
= 1 - s exp[ - (r/T1 >“I
Fig. 3. (a) 13C and (b) ‘H magnetization recovery curves in amorphous carbon sample analyzed by a stretched exponential relaxation function. a sizeable fraction of nuclei. To check on that we have studied samples with much lower electron concentrations (as measured by the ESR intensity) but essentially the same magnetization recovery behavior was obtained. We thus believe that the non-exponential magnetization recovery behavior is due to the existence of electron clustering. 1.00
--
.-~-
.-.
64
I
0.75
0.50 8
(4)
The obtained results are shown in Fig. 3. The stretched exponential fits are within the bounds of the experimental error not worse than the bi-expon~!ntiaI ones (Fig. 1). The s value is of the order of 1.8. The temperature dependences of the stretched exponent CIand the 13C spin-lattice relaxation parameter Ti are shown in Fig. 4. In the “C case CY= 0.6 whereas the I’,( 13C) parameter is 480 ms. In the proton case we have (Y= 0.68 whereas T,(H) is 83.5 ms at room temperature. The ‘H stretched exponentia1 fit [Fig. 3(b)] is ,?ven slightly better than the bi-exponential one ]Fig. l(b)]. It should be noted that a non-exponential magnetization recovery can be also obtained if the concentration of paramagnetic impurities is not small [7] so that direct electron nuclear coupling is rate determining for
(b)
I.O-
l**
.
I
l
l
.
*i
.
om b-
60
i,,,-_--
~_ -
/
i l
O* lOOOU( K’ ) Fig. 4. The temperature dependence of (a) the stretched exponent CY and (b) the t3C spin lattice relaxation parameter Tl .
352
“C AND ‘H SPIN-LATTICE
If this electron clustering indeed occurs one would expect to find a super-paramagnetic behavior at low temperatures. Such a behavior is well known to take place in magnetic molecular cluster systems [8] such as Mn12-acetate. At high temperatures the magnetization of the cluster exhibits a paramagnetic-like behavior. At low temperatures where the thermal energy becomes of the order of the anisotropic energy barrier for cluster reorientations the magnetization freezes out. Magnetic hysteresis in superparamagnets is a result of the time delay between the change of the external magnetic field and the response of the magnetization. At low enough temperatures one would thus expect to observe a magnetic hysteresis curve like in ferromagnets. Such a behavior was indeed observed in all our samples below 20 K [S]. In summary we have shown that within the limits of experimental error the 13C and the ‘H magnetization recovery can be described by a stretched exponential function just as well as by a bi-exponential one. The short and nearly temperature independent values of both the proton and ‘“C spin lattice relaxation times demonstrate that the dominant spin-lattice relaxation mechanism is spin diffusion to paramagnetic impurities. The fact that the magnetization recovery is not described by single exponential as expected in case of a random distribution of paramagnetic centers but shows a bi-exponential respectively stretched exponential form
RELAXATION
IN CARBON
Vol. 107, No. 7
further demonstrates that the paramagnetic centers aggregate in clusters so that the unpaired electron distribution is strongly inhomogeneous. Such an inhomogeneous electron distribution should result in a superparamagnetic behavior at low temperatures. This was indeed observed by SQUID magnetization measurements [ 51. REFERENCES 1.
2.
Jiiger, C., Sottwald, J., Spiess, H.W. and Newport, R.J., Phys. Rev., BSO, 1994, 846 and references therein. Pocsik, I., Koos, M., Moustafa, S.H., Lasanda, S., Banki, P. and Tompa, K., J. Non-Cryst. So/ids, 198-200,
3.
4.
1996,632.
Robertson, J., Adv. Phys., 35,1986,317; J., J. of Non-Crystalline Solids, 137, Robertson. J., J. of Non-Cryst. Solids, 1991, 825. Robertson, J., Progress in Solid State
Robertson, 1991, 138; 137-138, Chemistry,
21, 1991, 199.
5. 6. 7.
Blinc, R., Arcon, D., Cevc, P., Pocsik, I., Koos, M., Trontelj, Z. and ZaglieiE, to be published. Abragam, A., The Principles of Nuclear Magnetism. Clarendon, Oxford. 1961. Atsarkin, A.A. and Demidov, V.V., Sov. Phys. JETP, 52, 1980, 726.
8.
Gatteschi, D., Caneschi, A., Pardi, L. and Sessoli, R., Science, 265, 1994, 1054.