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Low energy excitations in molecular antiferromagnetic rings, Fe10 and Fe12
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 1441–1443 www.elsevier.com/locate/jmmm
Low energy excitations in molecular antiferromagnetic rings, Fe10 and Fe12 S. Maegawaa,, T. Saganea, T. Itoua, A. Oyamadaa, S. Igarashib, Y. Yukawab a
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan Department of Environmental Science, Faculty of Science, Niigata University, Niigata 950-2181, Japan
b
Available online 7 November 2006
Abstract 1
H-NMR measurements have been performed to study the low energy excitations in molecular antiferromagnetic rings ½FeðOCH3 Þ2 ðO2 CCH2 ClÞ10 and ½FeðOCH3 Þ2 ðC5 H9 NO2 ÞðCIO4 Þ12 . The spin–lattice relaxation rates T 1 above 40 K show the spin 1 fluctuations in the continuous energy levels of the spin states reflecting the classical nature of the spin systems. On the other hand, the temperature dependence of the relaxation rates below 5 K is expressed by an activation-type function with a gap energy, reflecting their discrete energy levels, that is quantum nature of the spin systems. The field dependence of the gap energy in Fe10 is revealed by the T 1 1 measurements and is analyzed by the Hamiltonian with the exchange interaction and a single-ion-type anisotropy. The remarkable peak of the relaxation rates is observed around 15 K, which corresponds to the values of exchange interactions both in Fe10 and Fe12. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.60.k Keywords: Antiferromagnetic ring; NMR; Molecular magnet
Molecular magnetic rings attract much attention in the field of magnetism and technological applications. Intermediate characteristics between classical and quantum mechanical systems are expected to appear because of the finite number of spins in the magnetic rings. The molecule ½FeðOCH3 Þ2 ðO2 CCH2 ClÞ10 (abbreviated Fe10) and ½FeðOCH3 Þ2 ðC5 H9 NO2 ÞðCIO4 Þ12 (abbreviated Fe12) are composed of 10 and 12 Fe3þ ions with s ¼ 52, respectively. Each molecule can be regarded as an isolated nanoscale antiferromagnetic ring owing to the weak intermolecular interactions. These magnetic rings are expected to show characteristic quantum behaviors based on the discrete energy levels caused by the finite number of spins. We have studied the spin dynamics of Fe10 and Fe12 by means of magnetic susceptibility and 1H-NMR experiments. The susceptibility measurements confirmed that the total spin in the ground state of each ring is S ¼ 0 in both molecules. For Fe10, the fitting of the experimental results Corresponding author. Tel.: +81 75 753 6787; fax: +81 75 753 2946.
E-mail address: [email protected] (S. Maegawa). URL: http://nmr.jinkan.kyoto-u.ac.jp/maegawa/. 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.459
of the susceptibility with both the high temperature series expansions and the exact diagonalization of N ¼ 6 ring gives the same antiferromagnetic interactions; J ¼ 13:3 K [1]. This value is consistent with the value estimated by Taft et al. [2]. The estimation of the exchange interaction in Fe12 using the high temperature series expansions gives 21 K. The spin–lattice relaxation rates T 1 1 for both molecules increase with temperature monotonously above 40 K. The q-dependence of the susceptibility can be ignored at a higher temperature region. When the correlation function is assumed to decay as expðGtÞ and G is assumed to be independent of the temperature, the temperature dependence of T 1 is expressed as T 1 1 1 / wT. The agreement between the calculation using the above equation and the experimental results means that the nuclear relaxations in Fe10 and Fe12 are dominated by the paramagnetic fluctuations of the Fe spins within the quasi-continuous energy level. This demonstrates the classical nature of the spin systems at high temperatures. The rates T 1 1 deviate from the theoretical curve below 40 K, and show the peak around 15 K, as shown in Fig. 1.
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Fig. 1. Relaxation rates of Fe10 and Fe12.
The temperatures at the peaks are roughly comparable with the antiferromagnetic exchange interactions. The increase of relaxation rates with lowering temperature indicates that the susceptibility of q ¼ p mode becomes dominant instead of the static susceptibility due to the development of the antiferromagnetic correlations between Fe spins. On the other hand as lowering the temperature, the energy levels become discrete owing to the finite numbers of spins and the relaxation would be governed by the excitations between the energy levels. The peak of rates would be induced by the crossover of these mechanisms.The similar peaks of the relaxation rates have been reported in other antiferromagnetic rings, Cr8 and Fe6 [4]. As there exists no peak in the ferrimagnetic rings Mn6R6, the peak seems to be characteristics of the singlet ground state systems [5]. In Fig. 1 the relaxation rates are shown as a function of the inverse temperature for both molecules at various fields. The rates T 1 1 at low temperatures can be expressed by an exponential function of temperature. The lines in Fig. 1 are the fitting results with the activation-type function. The obtained activation energies are shown in Fig. 2 as a function of the field. The activation energies can be correctly obtained by the measurement in the temperature range well below the gap energies. As our experimental temperatures are above 1.4 K, the estimated values of energies that are smaller than the temperatures can have ambiguity and the correct values can be a little larger.
Fig. 2. Field dependence of gap energies for Fe10 (,) and Fe12ðDÞ. Estimations from the total spin Hamiltonian for the case of Fe10 are shown by lines. Broken lines indicate the energies for y ¼ 30 and 60 .
These values are shown in Fig. 2 by open circles for references. The low energy scheme of the system is analyzed by using the total spin Hamiltonian as H ¼ P þ DfS 2z 13SðS þ 1Þg þ gmB S H,
(1)
where P is the gap energy between the ground state and the S ¼ 1 state in the case of no anisotropy and no field, and D is the single-ion-type anisotropy [1]. Diagonalization of the 3 3 matrix of Eq. (1) for S ¼ 1 leads to the eigen energies that depend on the angle y of the field direction with respect to the spin coordinate. Using the following parameters, P ¼ 6:7 K, D ¼ 3:3 K and the g-value ¼ 1.95, the field dependences of the estimated gap energies for y ¼ 0; 30; 60 and 90 are shown by lines in Fig. 2. In the present case, as the sample is powder, the distribution weight of sin y dy in the powder average should be considered. The lowest excited state with y ¼ 90 would be mainly observed between 2.5 and 4.5 T, because the spins in the molecules that orient with the angle 90 contribute effectively to the relaxation. For the lower fields, it is necessary to consider that the excited states are composed of a mixture of the eigenstates j1; 1i; j1; 0i and j1; 1i. The mixing depends on the field. As the field is lowered, the first excited state becomes to be only composed of the j1; 0i state, thus the transition from the ground state j0; 0i to the j1; 0i state would not contribute to
ARTICLE IN PRESS S. Maegawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1441–1443
the relaxation. Therefore, the transition to the next higher energy level contributes to the relaxation below 2.5 T. The gap energies obtained from the NMR experiment clearly show the low-lying energy state of the system. Our D value is well consistent with the value of 3.23 K determined by the torque magnetometry [3]. Also the crossing field of 4.5 T estimated through NMR agrees well with that of 4.6 T obtained through the magnetization measurement [2]. The field dependence of the gap energy is also measured in Fe12, and is also consistent with the Zeeman splittings of the excited S ¼ 1 states. The experiment at lower temperatures are desired to obtain the precise values of the energy at high fields.
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References [1] S. Maegawa, Y. Sasaki, J. Phys. Soc. Japan 75 (2006) 034710. [2] K.L. Taft, C.D. Delfs, G.C. Papaefthymiou, S. Foner, D. Gatteschi, S.J. Lippard, J. Am. Chem. Soc. 116 (1994) 823. [3] A. Cornia, A.G.M. Lansen, M. Affronte, Phys. Rev. B 60 (1999) 12177. [4] S.H. Baek, M. Luban, A. Lascialfari, E. Micotti, Y. Furukawa, F. Borsa, J. van Slageren, A. Cornia, Phys. Rev. B 70 (2004) 134434. [5] T. Itou, S. Funahashi, A. Oyamada, S. Maegawa, K. Fujita, K. Amezawa, R. Yamaguchi, in: Proceedings of ICM06.
Journal of Magnetism and Magnetic Materials 310 (2007) 1441–1443 www.elsevier.com/locate/jmmm
Low energy excitations in molecular antiferromagnetic rings, Fe10 and Fe12 S. Maegawaa,, T. Saganea, T. Itoua, A. Oyamadaa, S. Igarashib, Y. Yukawab a
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan Department of Environmental Science, Faculty of Science, Niigata University, Niigata 950-2181, Japan
b
Available online 7 November 2006
Abstract 1
H-NMR measurements have been performed to study the low energy excitations in molecular antiferromagnetic rings ½FeðOCH3 Þ2 ðO2 CCH2 ClÞ10 and ½FeðOCH3 Þ2 ðC5 H9 NO2 ÞðCIO4 Þ12 . The spin–lattice relaxation rates T 1 above 40 K show the spin 1 fluctuations in the continuous energy levels of the spin states reflecting the classical nature of the spin systems. On the other hand, the temperature dependence of the relaxation rates below 5 K is expressed by an activation-type function with a gap energy, reflecting their discrete energy levels, that is quantum nature of the spin systems. The field dependence of the gap energy in Fe10 is revealed by the T 1 1 measurements and is analyzed by the Hamiltonian with the exchange interaction and a single-ion-type anisotropy. The remarkable peak of the relaxation rates is observed around 15 K, which corresponds to the values of exchange interactions both in Fe10 and Fe12. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.60.k Keywords: Antiferromagnetic ring; NMR; Molecular magnet
Molecular magnetic rings attract much attention in the field of magnetism and technological applications. Intermediate characteristics between classical and quantum mechanical systems are expected to appear because of the finite number of spins in the magnetic rings. The molecule ½FeðOCH3 Þ2 ðO2 CCH2 ClÞ10 (abbreviated Fe10) and ½FeðOCH3 Þ2 ðC5 H9 NO2 ÞðCIO4 Þ12 (abbreviated Fe12) are composed of 10 and 12 Fe3þ ions with s ¼ 52, respectively. Each molecule can be regarded as an isolated nanoscale antiferromagnetic ring owing to the weak intermolecular interactions. These magnetic rings are expected to show characteristic quantum behaviors based on the discrete energy levels caused by the finite number of spins. We have studied the spin dynamics of Fe10 and Fe12 by means of magnetic susceptibility and 1H-NMR experiments. The susceptibility measurements confirmed that the total spin in the ground state of each ring is S ¼ 0 in both molecules. For Fe10, the fitting of the experimental results Corresponding author. Tel.: +81 75 753 6787; fax: +81 75 753 2946.
E-mail address: [email protected] (S. Maegawa). URL: http://nmr.jinkan.kyoto-u.ac.jp/maegawa/. 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.459
of the susceptibility with both the high temperature series expansions and the exact diagonalization of N ¼ 6 ring gives the same antiferromagnetic interactions; J ¼ 13:3 K [1]. This value is consistent with the value estimated by Taft et al. [2]. The estimation of the exchange interaction in Fe12 using the high temperature series expansions gives 21 K. The spin–lattice relaxation rates T 1 1 for both molecules increase with temperature monotonously above 40 K. The q-dependence of the susceptibility can be ignored at a higher temperature region. When the correlation function is assumed to decay as expðGtÞ and G is assumed to be independent of the temperature, the temperature dependence of T 1 is expressed as T 1 1 1 / wT. The agreement between the calculation using the above equation and the experimental results means that the nuclear relaxations in Fe10 and Fe12 are dominated by the paramagnetic fluctuations of the Fe spins within the quasi-continuous energy level. This demonstrates the classical nature of the spin systems at high temperatures. The rates T 1 1 deviate from the theoretical curve below 40 K, and show the peak around 15 K, as shown in Fig. 1.
ARTICLE IN PRESS 1442
S. Maegawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1441–1443
Fig. 1. Relaxation rates of Fe10 and Fe12.
The temperatures at the peaks are roughly comparable with the antiferromagnetic exchange interactions. The increase of relaxation rates with lowering temperature indicates that the susceptibility of q ¼ p mode becomes dominant instead of the static susceptibility due to the development of the antiferromagnetic correlations between Fe spins. On the other hand as lowering the temperature, the energy levels become discrete owing to the finite numbers of spins and the relaxation would be governed by the excitations between the energy levels. The peak of rates would be induced by the crossover of these mechanisms.The similar peaks of the relaxation rates have been reported in other antiferromagnetic rings, Cr8 and Fe6 [4]. As there exists no peak in the ferrimagnetic rings Mn6R6, the peak seems to be characteristics of the singlet ground state systems [5]. In Fig. 1 the relaxation rates are shown as a function of the inverse temperature for both molecules at various fields. The rates T 1 1 at low temperatures can be expressed by an exponential function of temperature. The lines in Fig. 1 are the fitting results with the activation-type function. The obtained activation energies are shown in Fig. 2 as a function of the field. The activation energies can be correctly obtained by the measurement in the temperature range well below the gap energies. As our experimental temperatures are above 1.4 K, the estimated values of energies that are smaller than the temperatures can have ambiguity and the correct values can be a little larger.
Fig. 2. Field dependence of gap energies for Fe10 (,) and Fe12ðDÞ. Estimations from the total spin Hamiltonian for the case of Fe10 are shown by lines. Broken lines indicate the energies for y ¼ 30 and 60 .
These values are shown in Fig. 2 by open circles for references. The low energy scheme of the system is analyzed by using the total spin Hamiltonian as H ¼ P þ DfS 2z 13SðS þ 1Þg þ gmB S H,
(1)
where P is the gap energy between the ground state and the S ¼ 1 state in the case of no anisotropy and no field, and D is the single-ion-type anisotropy [1]. Diagonalization of the 3 3 matrix of Eq. (1) for S ¼ 1 leads to the eigen energies that depend on the angle y of the field direction with respect to the spin coordinate. Using the following parameters, P ¼ 6:7 K, D ¼ 3:3 K and the g-value ¼ 1.95, the field dependences of the estimated gap energies for y ¼ 0; 30; 60 and 90 are shown by lines in Fig. 2. In the present case, as the sample is powder, the distribution weight of sin y dy in the powder average should be considered. The lowest excited state with y ¼ 90 would be mainly observed between 2.5 and 4.5 T, because the spins in the molecules that orient with the angle 90 contribute effectively to the relaxation. For the lower fields, it is necessary to consider that the excited states are composed of a mixture of the eigenstates j1; 1i; j1; 0i and j1; 1i. The mixing depends on the field. As the field is lowered, the first excited state becomes to be only composed of the j1; 0i state, thus the transition from the ground state j0; 0i to the j1; 0i state would not contribute to
ARTICLE IN PRESS S. Maegawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1441–1443
the relaxation. Therefore, the transition to the next higher energy level contributes to the relaxation below 2.5 T. The gap energies obtained from the NMR experiment clearly show the low-lying energy state of the system. Our D value is well consistent with the value of 3.23 K determined by the torque magnetometry [3]. Also the crossing field of 4.5 T estimated through NMR agrees well with that of 4.6 T obtained through the magnetization measurement [2]. The field dependence of the gap energy is also measured in Fe12, and is also consistent with the Zeeman splittings of the excited S ¼ 1 states. The experiment at lower temperatures are desired to obtain the precise values of the energy at high fields.
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References [1] S. Maegawa, Y. Sasaki, J. Phys. Soc. Japan 75 (2006) 034710. [2] K.L. Taft, C.D. Delfs, G.C. Papaefthymiou, S. Foner, D. Gatteschi, S.J. Lippard, J. Am. Chem. Soc. 116 (1994) 823. [3] A. Cornia, A.G.M. Lansen, M. Affronte, Phys. Rev. B 60 (1999) 12177. [4] S.H. Baek, M. Luban, A. Lascialfari, E. Micotti, Y. Furukawa, F. Borsa, J. van Slageren, A. Cornia, Phys. Rev. B 70 (2004) 134434. [5] T. Itou, S. Funahashi, A. Oyamada, S. Maegawa, K. Fujita, K. Amezawa, R. Yamaguchi, in: Proceedings of ICM06.