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Transverse anisotropy of the single-molecule magnet Mn12-PrCl
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
Transverse anisotropy of the single-molecule magnet Mn12-PrCl M. Heua,*, S.W. Yoona, W.S. Jeonb, D.-Y. Jungb, B.J. Suha, S. Yoona,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
Abstract We present magnetization measurements in the single-molecule magnet Mn12-PrCl. Both powdered and single crystalline samples have been characterized by measuring the magnetization as functions of temperature, magnetic field, and the angle between the easy axis of magnetization and the magnetic field. From the analyses of magnetization data, we found the second-order transverse anisotropy of E ¼ 0:15 K in Mn12-PrCl. r 2003 Elsevier B.V. All rights reserved. PACS: 75.45.+j; 75.50.Xx Keywords: Single-molecule magnet; Quantum tunneling of magnetization
Single-molecule magnets (SMMs) have attracted much attention because they provide opportunities for understanding magnetism at the molecular level and investigating macroscopic quantum phenomena [1,2]. One of the most extensively studied SMMs is [Mn12O12(O2CCH3)16(H2O)4] 2CH3CO2H 4H2O, known as Mn12-Ac [3,4]. Mn12-Ac molecule has spin 10 in the ground state and the symmetry of the molecule results in very strong uniaxial anisotropy. Thus the Hamiltonian of the molecule can be written as H# ¼ DSz2 gmB H . S; where H is the magnetic field. Since the energy barrier against magnetization reversal is rather large (DS2 B60 K), the magnetic relaxation becomes very slow at low temperatures and the magnetization curves show hysteric behavior. Also of interest is the existence of distinct steps in the hysteresis loops, which has been interpreted as a manifestation of quantum tunneling of magnetization (QTM). [Mn12O12(O2CCH2CH2Cl)16(H2O)4] CH2ClCH2CO2H, H, referred to as Mn12-PrCl, is a derivative compound of *Corresponding author. Tel.: +82-32-340-3383; fax: +8232-340-3764. E-mail addresses: [email protected] (M. Heu), [email protected] (S. Yoon). 1 Also to be corresponded at Tel.: +82-32-340-3381.
Mn12-Ac. It crystallizes in the triclinic structure, as compared to the tetragonal structure of Mn12-Ac, while maintaining the Mn12O12 core of Mn12-Ac [5]. Thus it is expected that Mn12-PrCl have the same ground-state spin and longitudinal anisotropy as those of Mn12-Ac, while the second-order transverse anisotropy should exist due to its lower symmetry. Then the Hamiltonian relevant to Mn12PrCl can be written as H# ¼ DSz2 þ EðSx2 Sy2 Þ gmB H . S: In the present work, we have performed magnetization measurements in Mn12-PrCl and compared the experimental results with the theoretical calculations to verify the existence of the second-order transverse anisotropy and to determine the anisotropy constants. Mn12-PrCl was prepared using the procedure reported previously [5], and the magnetization measurements were performed using the SQUID magnetometer. Firstly, a single crystal (B0.20 mg) was carefully placed on the probe rotator of the magnetometer so that the easy axis of magnetization of the crystal lies in the plane normal to the rotating axis of the probe rotator. Then, the magnetization of the crystal was measured at various angles of the easy axis with respect to the applied magnetic field. The direction of the field was perpendicular to the rotating axis of the probe rotator. Although great care was taken to achieve the best alignment, small deviations of a few degrees from the perfect alignment
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.649
ARTICLE IN PRESS e746
M. Heu et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
could not be avoided due to the technical difficulties in mounting a small piece of crystal on the probe rotator. The measurements were performed at four different temperatures (5, 10, 15, and 20 K) with the magnetic field of 1 T. Secondly, a few pieces of single crystals were gently ground into powder (4.2 mg) and fixed with eicosane in the gelatin capsule. The magnetization of the nonoriented powdered sample, thus prepared, was measured with the magnetic field of 1–5 T in the temperature range of 2–10 K. The measured magnetic moments were corrected for the diamagnetic backgrounds of the eicosane and the gelatin capsule. Fig. 1 shows the magnetization of the single crystal as a function of angle y between the easy axis of magnetization and the applied magnetic field. The anisotropic nature of Mn12-PrCl is readily seen in the figure with periods of 180 . The angle dependence of the magnetization can be calculated from the spin Hamiltonian H# ¼ DSz2 þ EðSx2 Sy2 Þ gmB H ½Sz cos y þ ðSx cos f þ Sy sin fÞsin y ; where f is the angle between the hard axis of magnetization and the direction of the magnetic field component perpendicular to the easy axis. The spin Hamiltonian was diagonalized numerically to obtain the eigenstates, and the macroscopic molar magnetization was calculated using the Boltzmann statistics. The calculated magnetization is shown in Fig. 1 as solid (dotted) curves for E ¼ 0:15 K (E ¼ 0). Solid curves (E ¼ 0:15 K) reproduce experimental data quite nicely while dotted curves (E ¼ 0) deviate from the experimental values around y ¼ 90 . Also, if f is different from zero, the calculated magnetization at y ¼ 90 , though not shown in the figure, becomes larger for a given E: These demonstrate that E ¼ 0:15 K is the lower limit and the second-order transverse anisotropy exists in Mn12-PrCl.
Fig. 1. Angle dependence of the magnetization of the single crystal of Mn12-PrCl. Solid (dotted) curves are the theoretical calculations with S ¼ 10; D ¼ 0:56 K, g ¼ 1:92; f ¼ 0 and E ¼ 0:15 K (E ¼ 0).
Fig. 2. Magnetization of the powdered sample of Mn12-PrCl. Solid (dotted) curves are the theretical calculations with S ¼ 10; D ¼ 0:56 K, g ¼ 1:87 and E ¼ 0:15 K (E ¼ 0).
The magnetization of the powdered sample is plotted in Fig. 2 as a function of H=T: The magnetization M=NmB (magnetic moment per molecule in unit of Bohr magneton) increases rapidly at small H=T; and then saturates at large H=Tð> 1 T=KÞ to the different value depending on the magnetic field; the saturation magnetization increases as the magnetic field increases. The magnetization of the powdered sample was calculated by taking average over all possible directions of the molecules with respect to the magnetic field [6]. Solid (dotted) curves in Fig. 2 are the calculated results for E ¼ 0:15 K (E ¼ 0). As in the case of the angle dependence of the magnetization, solid curves (E ¼ 0:15 K) reproduce the experimental data better than dotted curves (E ¼ 0), indicating the existence of the second-order transverse anisotropy in Mn12-PrCl. In summary, the angle dependence and the H=T dependence of the magnetization of Mn12-PrCl have been obtained. Theoretical calculations based on the single-molecule spin Hamiltonian reproduced the experimental data very well with the second-order anisotropy constants D ¼ 0:56 K and E ¼ 0:15 K. The obtained value of E=D ¼ 0:27 is much larger than B103 (if not zero) of Mn12-Ac [7] but comparable to B0.16 of Fe8 [8]. The existence of the second-order transverse anisotropy can, via the increase of tunnel splittings, explain the previous observation [9] that the magnetic relaxation rate of Mn12-PrCl was, as compared to Mn12-Ac, enhanced significantly at resonance fields while it was less influenced at off-resonance fields. This work was supported by Korea Research Foundation (KRF-2000-015-DP0116) and also by KOSEF via eSSC at POSTECH. S.Y. acknowledges support by the Research Fund of the Catholic University of Korea.
ARTICLE IN PRESS M. Heu et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
References [1] D. Gatteschi, Philos. Trans. R. Soc. London. A 357 (1999) 3079. [2] W. Wernsdorfer, et al., Nature 416 (2002) 406. [3] J.R. Friedman, et al., Phys. Rev. Lett. 76 (1996) 3830.
[4] [5] [6] [7] [8] [9]
e747
L. Thomas, et al., Nature 383 (1996) 145. C.-D. Park, et al., Bull. Korean Chem. Soc. 22 (2001) 453. A. Vermaas, et al., Chem. Phys. Lett. 27 (1974) 583. E. Del Barco, et al., Europhys. Lett. 60 (2002) 768. A.-L. Barra, et al., Europhys. Lett. 35 (1996) 133. S.W. Yoon, et al., Phys. Rev. B 67 (2003) 052402.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
Transverse anisotropy of the single-molecule magnet Mn12-PrCl M. Heua,*, S.W. Yoona, W.S. Jeonb, D.-Y. Jungb, B.J. Suha, S. Yoona,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
Abstract We present magnetization measurements in the single-molecule magnet Mn12-PrCl. Both powdered and single crystalline samples have been characterized by measuring the magnetization as functions of temperature, magnetic field, and the angle between the easy axis of magnetization and the magnetic field. From the analyses of magnetization data, we found the second-order transverse anisotropy of E ¼ 0:15 K in Mn12-PrCl. r 2003 Elsevier B.V. All rights reserved. PACS: 75.45.+j; 75.50.Xx Keywords: Single-molecule magnet; Quantum tunneling of magnetization
Single-molecule magnets (SMMs) have attracted much attention because they provide opportunities for understanding magnetism at the molecular level and investigating macroscopic quantum phenomena [1,2]. One of the most extensively studied SMMs is [Mn12O12(O2CCH3)16(H2O)4] 2CH3CO2H 4H2O, known as Mn12-Ac [3,4]. Mn12-Ac molecule has spin 10 in the ground state and the symmetry of the molecule results in very strong uniaxial anisotropy. Thus the Hamiltonian of the molecule can be written as H# ¼ DSz2 gmB H . S; where H is the magnetic field. Since the energy barrier against magnetization reversal is rather large (DS2 B60 K), the magnetic relaxation becomes very slow at low temperatures and the magnetization curves show hysteric behavior. Also of interest is the existence of distinct steps in the hysteresis loops, which has been interpreted as a manifestation of quantum tunneling of magnetization (QTM). [Mn12O12(O2CCH2CH2Cl)16(H2O)4] CH2ClCH2CO2H, H, referred to as Mn12-PrCl, is a derivative compound of *Corresponding author. Tel.: +82-32-340-3383; fax: +8232-340-3764. E-mail addresses: [email protected] (M. Heu), [email protected] (S. Yoon). 1 Also to be corresponded at Tel.: +82-32-340-3381.
Mn12-Ac. It crystallizes in the triclinic structure, as compared to the tetragonal structure of Mn12-Ac, while maintaining the Mn12O12 core of Mn12-Ac [5]. Thus it is expected that Mn12-PrCl have the same ground-state spin and longitudinal anisotropy as those of Mn12-Ac, while the second-order transverse anisotropy should exist due to its lower symmetry. Then the Hamiltonian relevant to Mn12PrCl can be written as H# ¼ DSz2 þ EðSx2 Sy2 Þ gmB H . S: In the present work, we have performed magnetization measurements in Mn12-PrCl and compared the experimental results with the theoretical calculations to verify the existence of the second-order transverse anisotropy and to determine the anisotropy constants. Mn12-PrCl was prepared using the procedure reported previously [5], and the magnetization measurements were performed using the SQUID magnetometer. Firstly, a single crystal (B0.20 mg) was carefully placed on the probe rotator of the magnetometer so that the easy axis of magnetization of the crystal lies in the plane normal to the rotating axis of the probe rotator. Then, the magnetization of the crystal was measured at various angles of the easy axis with respect to the applied magnetic field. The direction of the field was perpendicular to the rotating axis of the probe rotator. Although great care was taken to achieve the best alignment, small deviations of a few degrees from the perfect alignment
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.649
ARTICLE IN PRESS e746
M. Heu et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
could not be avoided due to the technical difficulties in mounting a small piece of crystal on the probe rotator. The measurements were performed at four different temperatures (5, 10, 15, and 20 K) with the magnetic field of 1 T. Secondly, a few pieces of single crystals were gently ground into powder (4.2 mg) and fixed with eicosane in the gelatin capsule. The magnetization of the nonoriented powdered sample, thus prepared, was measured with the magnetic field of 1–5 T in the temperature range of 2–10 K. The measured magnetic moments were corrected for the diamagnetic backgrounds of the eicosane and the gelatin capsule. Fig. 1 shows the magnetization of the single crystal as a function of angle y between the easy axis of magnetization and the applied magnetic field. The anisotropic nature of Mn12-PrCl is readily seen in the figure with periods of 180 . The angle dependence of the magnetization can be calculated from the spin Hamiltonian H# ¼ DSz2 þ EðSx2 Sy2 Þ gmB H ½Sz cos y þ ðSx cos f þ Sy sin fÞsin y ; where f is the angle between the hard axis of magnetization and the direction of the magnetic field component perpendicular to the easy axis. The spin Hamiltonian was diagonalized numerically to obtain the eigenstates, and the macroscopic molar magnetization was calculated using the Boltzmann statistics. The calculated magnetization is shown in Fig. 1 as solid (dotted) curves for E ¼ 0:15 K (E ¼ 0). Solid curves (E ¼ 0:15 K) reproduce experimental data quite nicely while dotted curves (E ¼ 0) deviate from the experimental values around y ¼ 90 . Also, if f is different from zero, the calculated magnetization at y ¼ 90 , though not shown in the figure, becomes larger for a given E: These demonstrate that E ¼ 0:15 K is the lower limit and the second-order transverse anisotropy exists in Mn12-PrCl.
Fig. 1. Angle dependence of the magnetization of the single crystal of Mn12-PrCl. Solid (dotted) curves are the theoretical calculations with S ¼ 10; D ¼ 0:56 K, g ¼ 1:92; f ¼ 0 and E ¼ 0:15 K (E ¼ 0).
Fig. 2. Magnetization of the powdered sample of Mn12-PrCl. Solid (dotted) curves are the theretical calculations with S ¼ 10; D ¼ 0:56 K, g ¼ 1:87 and E ¼ 0:15 K (E ¼ 0).
The magnetization of the powdered sample is plotted in Fig. 2 as a function of H=T: The magnetization M=NmB (magnetic moment per molecule in unit of Bohr magneton) increases rapidly at small H=T; and then saturates at large H=Tð> 1 T=KÞ to the different value depending on the magnetic field; the saturation magnetization increases as the magnetic field increases. The magnetization of the powdered sample was calculated by taking average over all possible directions of the molecules with respect to the magnetic field [6]. Solid (dotted) curves in Fig. 2 are the calculated results for E ¼ 0:15 K (E ¼ 0). As in the case of the angle dependence of the magnetization, solid curves (E ¼ 0:15 K) reproduce the experimental data better than dotted curves (E ¼ 0), indicating the existence of the second-order transverse anisotropy in Mn12-PrCl. In summary, the angle dependence and the H=T dependence of the magnetization of Mn12-PrCl have been obtained. Theoretical calculations based on the single-molecule spin Hamiltonian reproduced the experimental data very well with the second-order anisotropy constants D ¼ 0:56 K and E ¼ 0:15 K. The obtained value of E=D ¼ 0:27 is much larger than B103 (if not zero) of Mn12-Ac [7] but comparable to B0.16 of Fe8 [8]. The existence of the second-order transverse anisotropy can, via the increase of tunnel splittings, explain the previous observation [9] that the magnetic relaxation rate of Mn12-PrCl was, as compared to Mn12-Ac, enhanced significantly at resonance fields while it was less influenced at off-resonance fields. This work was supported by Korea Research Foundation (KRF-2000-015-DP0116) and also by KOSEF via eSSC at POSTECH. S.Y. acknowledges support by the Research Fund of the Catholic University of Korea.
ARTICLE IN PRESS M. Heu et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e745–e747
References [1] D. Gatteschi, Philos. Trans. R. Soc. London. A 357 (1999) 3079. [2] W. Wernsdorfer, et al., Nature 416 (2002) 406. [3] J.R. Friedman, et al., Phys. Rev. Lett. 76 (1996) 3830.
[4] [5] [6] [7] [8] [9]
e747
L. Thomas, et al., Nature 383 (1996) 145. C.-D. Park, et al., Bull. Korean Chem. Soc. 22 (2001) 453. A. Vermaas, et al., Chem. Phys. Lett. 27 (1974) 583. E. Del Barco, et al., Europhys. Lett. 60 (2002) 768. A.-L. Barra, et al., Europhys. Lett. 35 (1996) 133. S.W. Yoon, et al., Phys. Rev. B 67 (2003) 052402.