- Email: [email protected]
Magnetization relaxation of Mn12-Ac in the presence of crystal imperfections
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e743–e744
Magnetization relaxation of Mn12-Ac in the presence of crystal imperfections S. Yoona,*, S.W. Yoona, M. Heua, S.-B. Choa, W.S. Jeonb, Y.J. Kimb, D.-Y. Jungb, Y.-J. Shinc, B.J. Suha,1 a
Department of Physics, The Catholic University of Korea, San 43-1 Yoggok-2-dong Wonmi-gu, Puchon 420-743, Republic of Korea b Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Republic of Korea c Department of Chemistry, The Catholic University of Korea, Puchon 420-743, Republic of Korea
Abstract Effects of crystal imperfection on the magnetic properties of Mn12-Ac have been studied. Crystal defects were introduced in the lattices of Mn12-Ac by a novel heat-treatment process. The magnetization relaxation associated with quantum tunneling of magnetization is strongly influenced by the existence of crystal defects. Experimental data are explained qualitatively in terms of the distribution of transverse anisotropy induced by the crystal imperfection. r 2003 Elsevier B.V. All rights reserved. PACS: 75.45.+j; 75.50.Xx Keywords: Mn12-Ac; Magnetization relaxation; Quantum tunneling of magnetization
An important issue as regards the study of molecular magnets is the mechanism responsible for the thermally assisted quantum tunneling of magnetization (QTM) in Mn12 clusters. Recent works emphasize the role of crystal defects on spin tunneling. It has been suggested that the local transverse anisotropy provided by dislocations [1,2] or solvent disorders [3,4] can cause QTM in Mn12-Ac. Also, experimental evidence on the increase of the tunneling rate with the density of crystal defects has been reported [5,6]. In this paper, we report the effects of crystal imperfections on the magnetization relaxation in Mn12-Ac. A fresh single crystal of Mn12-Ac of parallelepiped shape (B0.2 0.2 2.0 mm3) was first characterized by the SQUID magnetometer. The same sample was investigated again after warming the sample, as mounted on the probe of the magnetometer, from room temperature up to 50 C at the rate of 1 C/min and quenching below 0 C. The heat treatment supposes to *Corresponding author. Tel.: +82-32-340-3381; fax: +8232-340-3764. E-mail addresses: [email protected] (S. Yoon), [email protected] (B.J. Suh). 1 Also corresponding author. Tel.: +82-32-340-3385
introduce crystal defects only by affecting water of crystallization and acetic acid molecules, whereas Mn12O12 magnetic cluster itself is maintained. This process was chosen on the basis of an independent thermogravimetric analysis (TGA). As shown in Fig. 1, the TGA data display two main steps of the weight reduction in Mn12-Ac. The first step is due to the evaporation of water of crystallization and acetic acid molecules and the second one above 200 C is ascribed to the decomposition of Mn12O12 magnetic clusters. Moreover, the first step can be separated into two processes: a slow decrease up to 65 C and a rapid reduction around 75 C. On the basis of the relative bond strength and weight of molecules [7,8], the initial decrease until 65 C is ascribed to the evaporation of water molecules and the rapid reduction around 75 C to the evaporation of acetic acid molecules. Adopting the TGA results, we expect that the weight of the sample should be reduced by about 1% (corresponding to 30% loss of water molecules) during the heat treatment as marked in the inset of Fig. 1. Though the numbers derived above can be used only for reference, we can still say that the heat treatment introduces a considerable amount of crystal imperfections while the Mn12O12 magnetic cluster is preserved safely.
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.511
ARTICLE IN PRESS S. Yoon et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e743–e744
e744 100
mally activated relaxation, respectively. As seen in the figure, the characteristics of magnetization relaxation are changed by the heat treatment. Especially, the relaxation rate at H ¼ 0; where the relaxation is associated with quantum tunneling is increased in the sample with more crystal defects. The magnetization relaxation, when the transverse anisotropies are distributed, is given by [2] Z N MðtÞ ¼ 2 f ðEÞ exp½2GðEÞt dE;
4H2O:3.5% 2CH3COOH:5.8%
90
Weight(%)
Weight(%)
100
80 70
99 98.9% 98
97 20
40
T(˚C)
80
60
60 TGA of Mn12 Acetate Sweep Rate:1˚C/min
0
50 0
100
200 300 400 Temperature(˚C)
500
600
Fig. 1. Thermogravimetric analysis (TGA) of Mn12-Ac performed in argon atmosphere. From the fractional weights of [4H2O]/[Mn12-Ac]=3.5%, [2CH3COOH]/[Mn12-Ac]=5.8%, and [12MnO2]/[Mn12-Ac]=50.4%, the slow reduction of weight until B65 C is ascribed to the evaporation of water of crystallization, the rapid reduction around 75 C to the evaporation of acetic acid molecules, and the reduction above 200 C to the decomposition of Mn12O12 cluster into MnO and/or MnO2. 1.0
T=2.3K S0 S1
M(H) / Ms
0.5
0.0
-0.5
-1.0
0.8 0.7 0.6
0.4 H=0.66T S0 S1
0.3 -2
(a)
H=0 S0 S1
0.9
[M(t) - Ms] / [Min - Ms]
1.0
-1
0
Field (T)
1
0
2
(b)
1
2
3
4
Time(104 s)
Fig. 2. (a) Magnetization hysteresis loops of Mn12-Ac. The sweep rate of the field is 100 Oe/min. (b) Magnetization relaxation in Mn12Ac. Min ¼ 0:01058 and 0.00857 emu for S0 and S1, respectively, and Ms ¼ Min at H ¼ 0:66 T and Ms ¼ 0 at H ¼ 0:
Fig. 2(a) shows the magnetization hysteresis loops for the sample before (S0) and after (S1) the heat treatment. The saturation values of magnetization are Ms ¼ 0:01058 and 0.00857 emu for S0 and S1, respectively. In spite of B20% reduction of magnetization, the main features of both loops are surprisingly identical with quantum steps at the same fields (0, 0.44, 0.88 T). This suggests that the internal structure of the Mn12O12 cluster is preserved safely. On the other hand, the steps are considerably higher in S1 than in S0, indicating that the tunneling rate is enhanced by the introduction of crystal imperfections. Fig. 2(b) shows the magnetization relaxation at H ¼ 0 and 0.66 T, representing resonant tunneling and ther-
where f ðEÞ represents the distribution of the transverse anisotropy E and GðEÞ is the effective rate of relaxation. Using f ðEÞ ¼ ½2pðdEÞ2 1=2 exp½ðE=dEÞ2 and taking Eq. (3) in Ref. [6] for dðEÞ; solid curves in Fig. 2(b) were obtained. In the calculations, we used the following parameters: D ¼ 0:65 K (longitudinal anisotropy), g ¼ 1:97; G0 ¼ 1:3 106 s1 (attempt frequency), and dE ¼ 0:028 and 0.034 K for S0 and S1, respectively. Although the curves deviate from the experimental results, it should be noted that the same parameters are used for S0 and S1 and for both fields except dE that increases about 30% by the heat treatment. In addition, the theoretical calculations demonstrate that the effect of crystal imperfection is more pronounced in the relaxation associated with quantum tunneling, i.e. at H ¼ 0; in good agreement with experimental results. In summary, we have studied the effects of crystal imperfections on the magnetization relaxation in Mn12-Ac. From the TGA results and the field dependence of magnetization, it has been confirmed that the heat treatment does not affect the internal structure of Mn12O12 magnetic cluster but introduces a considerable amount of crystal defects. Thus, the remarkable change of the characteristics of magnetization relaxation after the heat treatment is ascribed only to the existence of crystal defects. In addition, it has been shown that a simple calculation including the distribution of transverse anisotropies reproduces the experimental results of magnetization relaxation. Our results support that the crystal imperfection plays an important role on the mechanism of QTM in Mn12-Ac. This work was supported by Korea Research Foundation (Grant no. KRF-2000-015-DP0116) and also by KOSEF via electron Spin Science Center at POSTECH.
References [1] [2] [3] [4] [5] [6] [7] [8]
E.M. Chudnovsky, et al., Phys. Rev. Lett. 87 (2001) 187203. D.A. Garanin, et al., Phys. Rev. B 65 (2002) 094423. A. Cornia, et al., Phys. Rev. Lett. 89 (2002) 257201. E. del Barco, et al., Europhys. Lett. 60 (2002) 768. J.M. Hernandez, et al., Phys. Rev. B 66 (2002) 161407. F. Torres, et al., cond-mat/0110538. T. Lis, Acta Crystallogr. B 36 (1980) 2042. A. Cornia, et al., Acta Crystallogr. C 58 (2002) m371.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e743–e744
Magnetization relaxation of Mn12-Ac in the presence of crystal imperfections S. Yoona,*, S.W. Yoona, M. Heua, S.-B. Choa, W.S. Jeonb, Y.J. Kimb, D.-Y. Jungb, Y.-J. Shinc, B.J. Suha,1 a
Department of Physics, The Catholic University of Korea, San 43-1 Yoggok-2-dong Wonmi-gu, Puchon 420-743, Republic of Korea b Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Republic of Korea c Department of Chemistry, The Catholic University of Korea, Puchon 420-743, Republic of Korea
Abstract Effects of crystal imperfection on the magnetic properties of Mn12-Ac have been studied. Crystal defects were introduced in the lattices of Mn12-Ac by a novel heat-treatment process. The magnetization relaxation associated with quantum tunneling of magnetization is strongly influenced by the existence of crystal defects. Experimental data are explained qualitatively in terms of the distribution of transverse anisotropy induced by the crystal imperfection. r 2003 Elsevier B.V. All rights reserved. PACS: 75.45.+j; 75.50.Xx Keywords: Mn12-Ac; Magnetization relaxation; Quantum tunneling of magnetization
An important issue as regards the study of molecular magnets is the mechanism responsible for the thermally assisted quantum tunneling of magnetization (QTM) in Mn12 clusters. Recent works emphasize the role of crystal defects on spin tunneling. It has been suggested that the local transverse anisotropy provided by dislocations [1,2] or solvent disorders [3,4] can cause QTM in Mn12-Ac. Also, experimental evidence on the increase of the tunneling rate with the density of crystal defects has been reported [5,6]. In this paper, we report the effects of crystal imperfections on the magnetization relaxation in Mn12-Ac. A fresh single crystal of Mn12-Ac of parallelepiped shape (B0.2 0.2 2.0 mm3) was first characterized by the SQUID magnetometer. The same sample was investigated again after warming the sample, as mounted on the probe of the magnetometer, from room temperature up to 50 C at the rate of 1 C/min and quenching below 0 C. The heat treatment supposes to *Corresponding author. Tel.: +82-32-340-3381; fax: +8232-340-3764. E-mail addresses: [email protected] (S. Yoon), [email protected] (B.J. Suh). 1 Also corresponding author. Tel.: +82-32-340-3385
introduce crystal defects only by affecting water of crystallization and acetic acid molecules, whereas Mn12O12 magnetic cluster itself is maintained. This process was chosen on the basis of an independent thermogravimetric analysis (TGA). As shown in Fig. 1, the TGA data display two main steps of the weight reduction in Mn12-Ac. The first step is due to the evaporation of water of crystallization and acetic acid molecules and the second one above 200 C is ascribed to the decomposition of Mn12O12 magnetic clusters. Moreover, the first step can be separated into two processes: a slow decrease up to 65 C and a rapid reduction around 75 C. On the basis of the relative bond strength and weight of molecules [7,8], the initial decrease until 65 C is ascribed to the evaporation of water molecules and the rapid reduction around 75 C to the evaporation of acetic acid molecules. Adopting the TGA results, we expect that the weight of the sample should be reduced by about 1% (corresponding to 30% loss of water molecules) during the heat treatment as marked in the inset of Fig. 1. Though the numbers derived above can be used only for reference, we can still say that the heat treatment introduces a considerable amount of crystal imperfections while the Mn12O12 magnetic cluster is preserved safely.
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.511
ARTICLE IN PRESS S. Yoon et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e743–e744
e744 100
mally activated relaxation, respectively. As seen in the figure, the characteristics of magnetization relaxation are changed by the heat treatment. Especially, the relaxation rate at H ¼ 0; where the relaxation is associated with quantum tunneling is increased in the sample with more crystal defects. The magnetization relaxation, when the transverse anisotropies are distributed, is given by [2] Z N MðtÞ ¼ 2 f ðEÞ exp½2GðEÞt dE;
4H2O:3.5% 2CH3COOH:5.8%
90
Weight(%)
Weight(%)
100
80 70
99 98.9% 98
97 20
40
T(˚C)
80
60
60 TGA of Mn12 Acetate Sweep Rate:1˚C/min
0
50 0
100
200 300 400 Temperature(˚C)
500
600
Fig. 1. Thermogravimetric analysis (TGA) of Mn12-Ac performed in argon atmosphere. From the fractional weights of [4H2O]/[Mn12-Ac]=3.5%, [2CH3COOH]/[Mn12-Ac]=5.8%, and [12MnO2]/[Mn12-Ac]=50.4%, the slow reduction of weight until B65 C is ascribed to the evaporation of water of crystallization, the rapid reduction around 75 C to the evaporation of acetic acid molecules, and the reduction above 200 C to the decomposition of Mn12O12 cluster into MnO and/or MnO2. 1.0
T=2.3K S0 S1
M(H) / Ms
0.5
0.0
-0.5
-1.0
0.8 0.7 0.6
0.4 H=0.66T S0 S1
0.3 -2
(a)
H=0 S0 S1
0.9
[M(t) - Ms] / [Min - Ms]
1.0
-1
0
Field (T)
1
0
2
(b)
1
2
3
4
Time(104 s)
Fig. 2. (a) Magnetization hysteresis loops of Mn12-Ac. The sweep rate of the field is 100 Oe/min. (b) Magnetization relaxation in Mn12Ac. Min ¼ 0:01058 and 0.00857 emu for S0 and S1, respectively, and Ms ¼ Min at H ¼ 0:66 T and Ms ¼ 0 at H ¼ 0:
Fig. 2(a) shows the magnetization hysteresis loops for the sample before (S0) and after (S1) the heat treatment. The saturation values of magnetization are Ms ¼ 0:01058 and 0.00857 emu for S0 and S1, respectively. In spite of B20% reduction of magnetization, the main features of both loops are surprisingly identical with quantum steps at the same fields (0, 0.44, 0.88 T). This suggests that the internal structure of the Mn12O12 cluster is preserved safely. On the other hand, the steps are considerably higher in S1 than in S0, indicating that the tunneling rate is enhanced by the introduction of crystal imperfections. Fig. 2(b) shows the magnetization relaxation at H ¼ 0 and 0.66 T, representing resonant tunneling and ther-
where f ðEÞ represents the distribution of the transverse anisotropy E and GðEÞ is the effective rate of relaxation. Using f ðEÞ ¼ ½2pðdEÞ2 1=2 exp½ðE=dEÞ2 and taking Eq. (3) in Ref. [6] for dðEÞ; solid curves in Fig. 2(b) were obtained. In the calculations, we used the following parameters: D ¼ 0:65 K (longitudinal anisotropy), g ¼ 1:97; G0 ¼ 1:3 106 s1 (attempt frequency), and dE ¼ 0:028 and 0.034 K for S0 and S1, respectively. Although the curves deviate from the experimental results, it should be noted that the same parameters are used for S0 and S1 and for both fields except dE that increases about 30% by the heat treatment. In addition, the theoretical calculations demonstrate that the effect of crystal imperfection is more pronounced in the relaxation associated with quantum tunneling, i.e. at H ¼ 0; in good agreement with experimental results. In summary, we have studied the effects of crystal imperfections on the magnetization relaxation in Mn12-Ac. From the TGA results and the field dependence of magnetization, it has been confirmed that the heat treatment does not affect the internal structure of Mn12O12 magnetic cluster but introduces a considerable amount of crystal defects. Thus, the remarkable change of the characteristics of magnetization relaxation after the heat treatment is ascribed only to the existence of crystal defects. In addition, it has been shown that a simple calculation including the distribution of transverse anisotropies reproduces the experimental results of magnetization relaxation. Our results support that the crystal imperfection plays an important role on the mechanism of QTM in Mn12-Ac. This work was supported by Korea Research Foundation (Grant no. KRF-2000-015-DP0116) and also by KOSEF via electron Spin Science Center at POSTECH.
References [1] [2] [3] [4] [5] [6] [7] [8]
E.M. Chudnovsky, et al., Phys. Rev. Lett. 87 (2001) 187203. D.A. Garanin, et al., Phys. Rev. B 65 (2002) 094423. A. Cornia, et al., Phys. Rev. Lett. 89 (2002) 257201. E. del Barco, et al., Europhys. Lett. 60 (2002) 768. J.M. Hernandez, et al., Phys. Rev. B 66 (2002) 161407. F. Torres, et al., cond-mat/0110538. T. Lis, Acta Crystallogr. B 36 (1980) 2042. A. Cornia, et al., Acta Crystallogr. C 58 (2002) m371.