J. Phys. Soc. Jpn. 77 (2008) 014301 (9 pages)  |Previous Article| |Next Article|  |Table of Contents|
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Theoretical Analysis of Magnetic Coupling in Sandwich Clusters V_n(C₆H₆)_n+1

Hongming Weng¹, Taisuke Ozaki¹, and Kiyoyuki Terakura^1,2,3

(Received August 29, 2007; Accepted October 23, 2007; Published December 25, 2007)

The mechanism of ferromagnetism stability in sandwich clusters V_n(C₆H₆)_n+1 has been studied by first-principles calculation and model analysis. It is found that each of the three types of bonds between V and benzene (Bz) plays different roles. V 3d_z² orbital, extending along the molecular axis, is weakly hybridized with Bz's HOMO-1 orbital to form the σ-bond. It is quite localized and singly occupied, which contributes 1 µ_B to the magnetic moment but little to the magnetic coupling between neighboring V magnetic moments. The in-plane d_x²-y², d_xy orbitals are hybridized with the LUMO of Bz and constitute the δ-bond. This hybridization is medium and crucial to the magnetic coupling though the δ states have no net contribution to the total magnetic moment. d_xz, d_yz, and HOMO of Bz form a quite strong π-bond to hold the molecular structure but they are inactive in magnetism because their energy levels are far away from the Fermi level. Based on the results of first-principles calculation, we point out that the ferromagnetism stability is closely related with the mechanism proposed by Kanamori and Terakura [J. Phys. Soc. Jpn. 70 (2001) 1433]. However, the presence of edge Bzs in the cluster introduces an important modification and suppresses significantly the ferromagnetism stability. A simple model is constructed to explain the essence of the physical picture. ©2008 The Physical Society of Japan

KEYWORDS: ferromagnetic cluster, benzene sandwiches, electronic and magnetic structure, ab initio calculation, tight-binding model
URL: http://jpsj.ipap.jp/link?JPSJ/77/014301/
DOI: 10.1143/JPSJ.77.014301

References | Citing Articles (4)

1. N. J. Long: Metallocenes (Blackwell Science, Oxford, U.K., 1998).
2. K. Miyajima, A. Nakajima, S. Yabushita, M. B. Knickelbein, and K. Kaya: J. Am. Chem. Soc. 126 (2004) 13202[CrossRef].
3. K. Miyajima, S. Yabushita, M. B. Knickelbein, and A. Nakajima: J. Am. Chem. Soc. 129 (2007) 8473[CrossRef].
4. T. Yasuike and S. Yabushita: J. Phys. Chem. A 103 (1999) 4533[CrossRef].
5. J. Wang, P. H. Acioli, and J. Jellinek: J. Am. Chem. Soc. 127 (2005) 2812[CrossRef].
6. A. K. Kandalam, B. K. Rao, P. Jena, and R. Pandey: J. Chem. Phys. 120 (2004) 10414[AIP Scitation].
7. Y. Mokrousov, N. Atodiresei, G. Bihlmayer, and S. Blügel: Int. J. Quantum Chem. 106 (2006) 3208.
8. M. B. Knickelbein: J. Chem. Phys. 121 (2004) 5281[AIP Scitation].
9. M. M. Rahman, H. Kasai, and E. S. Dy: Jpn. J. Appl. Phys. 44 (2005) 7954[IPAP].
10. V. V. Maslyuk, A. Bagrets, V. Meded, A. Arnold, F. Evers, M. Brandbyge, T. Bredow, and I. Mertig: Phys. Rev. Lett. 97 (2006) 097201[APS].
11. H. Xiang, J. Yang, J. G. Hou, and Q. Zhu: J. Am. Chem. Soc. 128 (2006) 2310[CrossRef].
12. J. Kanamori and K. Terakura: J. Phys. Soc. Jpn. 70 (2001) 1433[IPAP].
13. http://www.openmx-square.org/
14. T. Ozaki: Phys. Rev. B 67 (2003) 155108[APS]; T. Ozaki and H. Kino: Phys. Rev. B 69 (2004) 195113[APS]; T. Ozaki and H. Kino: J. Chem. Phys. 121 (2004) 10879[AIP Scitation]; T. Ozaki and H. Kino: Phys. Rev. B 72 (2005) 045121[APS].
15. J. P. Perdew, K. Burke, and M. Ernzerhof: Phys. Rev. Lett. 77 (1996) 3865[APS].
16. J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal: J. Phys.: Condens. Matter 14 (2002) 2745, [IoP STACKS]and references therein.
17. M. J. Han, T. Ozaki, and J. Yu: Phys. Rev. B 73 (2006) 045110[APS].
18. A supercell size of 13×13×15 in ų, larger than the automatically determined supercell size by openMX (with every side being expanded by about one Å), has been used for n=2. We find that the difference in total energy caused by this expansion of the supercell size is only a few tenth of meV.
19. If we adopt a standard constrained LDA calculation for estimating U, the obtained value is generally too large, more than 6.0 eV. An alternative approach was proposed by Solovyev et al. [Phys. Rev. B 53 (1996) 7158[APS]] for the U value in the t_2g system of LaMO₃ (M=Ti, V, Cr). In this approach, e_g states are allowed to screen the Coulomb interaction among t_2g electrons. The estimated U value is about 3.0 eV. As the analysis was made with the atomic sphere approximation, this value of U can be directly transferred to OpneMX. Of course, even for the same element, U depends on the system. However, for the present small cluster, screening of d electrons by other degrees of freedom will be less efficient. We therefore expect that U=3.0 eV should not be an overestimationl.
20. In order to see the possible variation in the energy difference between FM and AFM states in V₂Bz₃ depending on the computational details, we have performed some test calculations using OpenMX, VASP (Vienna ab-initio simulation package, http://cms.mpi.univie.ac.at/vasp/) and WIEN2k (http://www.wien2k.at/). VASP is a plane-wave pseudo-potential code while WIEN2k is a plane-wave all electron code. First, we calculated the total energy difference between FM and AFM states (ΔE =E_AFM-E_FM) for the same ideal structure of V₂Bz₃ where V–Bz distances are all equal. The results are as follows: ΔE= -0.003 eV (VASP), 0.006 eV (WIEN2k) and 0.007 eV (OpenMX). The result of WIEN2k is close to that of OpenMX both giving positive values, while VASP gives a negative value. As we are discussing a very small energy, it is not easy to identify the origin of the differences in ΔE. One possible reason for the difference, however, is that the core radius used in VASP is 2.3 a.u., being much larger than the value of 1.3 a.u. used in OpenMX. As the present system has a significant charge transfer from V to Bz, smaller core radius is required to guarantee the transferability of pseudopotential. As the all electron calculation by WIEN2k is heavy, the structural optimization was not performed by WIEN2k. With VASP, after structural optimization, ΔE becomes -0.012 eV. However, the energy difference becomes +0.007 eV in the GGA+U with U=5.0 eV. In VASP, U is included in the narrow projector space of PAW (Projector Augmented Wave) method, while U is active in the more extended localizes orbital in OpenMX. Judging from the energy levels, U=5.0 eV in VASP is nearly equivalent to U=3.0 eV in OpenMX. The supercell used in VASP and OpenMX calculations have been checked to ensure the convergency. In Wien2k, a supercell of 12×12×14 ų is used, which has been checked by VASP since both Wien2k and VASP fill the vacuum part with plane-waves. In Wien2k, R_mt*K_max=4 is used to control the cutoff energy with the smallest muffin-tin shere radius (R_mt) of H being 0.93 a.u., which corresponds to a cutoff energy around 250 eV. l_max=10 and G_max=20 a.u.^-1 are used for expansion of charge (also potential) within Muffin-tin sphere and interstitial part, respectively.
21. A. D. Becke: Phys. Rev. A 38 (1988) 3098[APS]; C. Lee, W. Yang, and R. G. Parr: Phys. Rev. B 37 (1988) 785[APS].