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The electronic structure and the ferromagnetic intermolecular interactions in the crystal of TEMPO radicals
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 301 (2006) 301–307 www.elsevier.com/locate/jmmm
The electronic structure and the ferromagnetic intermolecular interactions in the crystal of TEMPO radicals L. Zhua,, K.L. Yaoa,b, Z.L. Liua a
Department of Physics and State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China b International Center of Materials Physics, The Chinese Academy of Science, Shengyang 110015, China Received 18 April 2005; received in revised form 5 July 2005 Available online 10 August 2005
Abstract Based on the generalized gradient approximation, full potential linearized augmented plane wave (FP-LAPW) calculations have been performed to study the electronic band structure and the intermolecular ferromagnetic (FM) interactions for the two TEMPO radicals 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1) and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2). The total and the partial density of states and the atomic spin magnetic moments are calculated and discussed. The calculation revealed that the two TEMPO radicals have the intermolecular FM interactions, and the spontaneous magnetic moment is 1.0 mB per molecule of each crystal, which is in good agreement with the experimental value. It is found that the unpaired electrons in these compounds are localized in a molecular orbital constituted primarily of p* (NO) orbital, and the main contribution of the spin magnetic moment comes from the NO-free radical. The origin of FM is also studied in detail. r 2005 Elsevier B.V. All rights reserved. PACS: 75.50.y; 71.15.m; 71.20.b Keywords: DFT; The organic magnet; Electronic structure; Ferromagnetic properties
1. Introduction Ferromagnetic interactions in crystals of stable organic radicals have been much investigated in Corresponding author. Tel.: +0086 27 87556264; fax: +0086 27 87544525. E-mail addresses: [email protected] (L. Zhu), [email protected] (K.L. Yao).
connection with organic ferromagnets [1]. Since the discovery of the first genuine organic ferromagnetic radical crystal, p-nitrophenyl nitronyl nitroxide [2], organic-free radical magnetic compounds, which consist of only light elements such as H, C, N, O, have attracted much attention not only in the field of material science but also in the field of condensed matter physics [3–13]. Ferromagnetic interactions in crystals of stable organic
0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.07.006
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radicals have been intensively investigated for organic ferromagnets of nitroxides derivatives. The ferromagnetic interactions in these nitroxides seem to be related to a characteristic molecular arrangement in the crystal, namely, to close contacts between the oxygen of an NO site and methyl and/or methylene hydrogens at the bpositions of adjacent NO moieties [14]. In this arrangement, the spin-alternation mechanism probably gives rise to the intermolecular ferromagnetic coupling. Among the few-known compounds of this type is TEMPO radicals, some of which show intermolecular ferromagnetic interaction. Recently, intermolecular ferromagnetic interaction of crystalline and single-component organic radicals has been reported by use of nitroxide radicals as spin sources. Nogami et al. have reported organic ferro- and meta-magnets having a 2,2,6,6-tetramethylpiperidin-1-oxyl(TEMPO) radical group [14,15]. All of the TEMPO radical crystals have characteristic features that oxygen atoms of N–O radical sites of TEMPO moieties always locate near methyl- and/or methylenehydrogens at b-positions of N–O in the TEMPO moieties of adjacent molecules. A positive spin on the N–O radical induces negative spins on the b-hydrogen atoms due to an intramolecular spinpolarization, ON(m)–C(k)–C(m)–H(k), which in turn induces a positive spin on the N–O sites of the adjacent molecules. Among these TEMPO radical crystals are 4-Benzylideneamino-2,2,6, 6-tetramethylpiperidin-1-oxyl (1) [16,17] and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2) [18,19]. The molecular and crystal structures of 1 and 2 are shown in Fig. 1. The crystal structure of 1 viewed along the b-axis is shown in Fig. 2, which comes from the experiment [16]. As Fig. 2 shows, the phenyl ring and imino group are almost coplanar, and the averaged piperidine plane is twisted relative to the benzylideneamino moiety by an angle of 821. The phenyl rings stack to the b and c directions and, consequently, the TEMPO moieties gather to construct a two-dimensional N–O network parallel to the bc plane. The nearest-neighbor nitroxides are arranged along the c-axis with the O–O distance of 5.62 A˚. The angle between the nearest
Fig. 1. Molecular structure of 1 and 2. Thermal ellipsoids of C, N, and O atoms are drawn at the 50% probability level. The hydrogen atoms are given an arbitrary thermal parameter.
Fig. 2. Crystal structure of 1 viewed along the b-axis. Hydrogen atoms are omitted for clarity.
N–O bonds is 981, and that between the C–O–C planes surrounding the radical nitrogen is 541. The second nearest neighbors are arranged along the b-axis with the O–O distance of 6.15 A˚, with the angle between the N–O bonds 821 and that between the C–O–C planes 541. The intermolecular atomic distances: O–C(methyl), 3.74 A˚; O–H(methyl), 2.87. The nearest O–O distance in the neighboring sheets is 11.89 A˚. The sheet structure of the N–O sites in the crystal of 2 is similar to the case of 1(O–O distances: intrasheet,
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5.70 and 8.75 A˚; inter-sheet, 10.08 A˚). For simplicity, we do not show the sheet structure of 2. The angles between the N–O bonds are 142.31 and those between the C–O–C planes surrounding the radical nitrogen atom are 39.51 for crystal structure of 2. The organic radical crystal of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl was found to be a bulk ferromagnet, and has a ferromagnetic phase transition at 0.18 K. The organic radical crystal of 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl exhibited a Neel transition at about 0.12 K (TN) and a metamagnetic transition below TN (the coercive field was around 180 Oe at 40 mK). The two organic radical crystals all have intermolecular ferromagnetic interaction. To understand deeply the mechanism of the ferromagnetic interactions in this compound, a more detailed knowledge of the electronic band structure and the magnetic properties is still required. In this paper, we adopt the density-functional theory (DFT) with generalized gradient approximation (GGA) to calculate the electronic band structure and the ferromagnetic properties of 1 and 2 by the accurate full potential linearized augmented plane wave (FP-LAPW). The main goals of our work are to investigate the electronic structure and the magnetic coupling, and to analyze the observed ferromagnetic interaction via the density of states (DOS) and the atomic spin magnetic moments. This provides new insights to the origin of the strong ferromagnetic coupling in the compound, which should be useful for the design of novel ferromagnetic materials. 2. FP-LAPW parameters and the structure of 1 and 2 The first-principles electronic structure calculations employ the well-known FP-LAPW method, which has a good accuracy. In this method, no shape approximation on either the potential or the electronic charge density is made. We use the wien2k [20] package, which allows the inclusion of local orbits in basis, improving upon linearization and making a consistent treatment of semicore and valence in one energy window possible, hence ensuring proper orthogonality. In general,
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the local density approximation (LDA) and the GGA can be chosen in wien2k code. Considering the success of the GGA derived from their ability to correct some LDA deficiencies with a modest increase in computational workload, the GGA is mandatory for systems containing ‘‘weak’’ or hydrogen bonds such as molecular crystals; for these systems the intermolecular bond lengths are severely underestimated in LDA, but they can be appreciably improved in GGA. In addition, the GGA has been demonstrated to be capable of calculating organic magnets [21]. So in our calculations, the exchange and correlation effects are treated with the GGA according to Perdew et al. [22]. According to the experiment, 1 and 2 have monoclinic and orthorhombic lattice, respectively, and there are four molecules in one primitive unit cell. The lattice parameters we used in the present ( b ¼ 11:740ð2Þ A, ( calculation are a ¼ 12:684ð7Þ A, ( c ¼ 11:024ð3Þ A, a ¼ g ¼ 901, b ¼ 111:401, for 1, and ( b ¼ 5:697ð1Þ A, ( c ¼ 15:107ð2Þ A, ( a ¼ 20:084ð2Þ A, a ¼ b ¼ g ¼ 901, for 2, which are just the same as the experimental parameters. The atomic-sphere radii Rmt are chosen as 1.2, 1.2, 1.0, 0.6 a.u. for O, N, C, H respectively, for these two organic radical crystals. We chose the spin-polarized calculation in our calculation. We setup the expansion to l ¼ 10 and the charge density Fourier expansion cutoff Gmax ¼ 14 in the muffintins. One hundred k-points in the first Brillouin zone were adopted in the calculations. In order to achieve a satisfactory degree of convergence, the cutoff parameter is taken to be Rmt K max ¼ 2:5, where Kmax is the maximal value of the reciprocal lattice vector used in the plane wave expansion, which corresponds to about 121 485 plane waves for 1 and 140 700 plane waves for 2 at the equilibrium lattice constant and the plane-wave cutoff energy is 236 eV. We specify charge as the convergence criterion, and select charge convergence to 105.
3. Results and discussion To study the electronic structure and magnetic properties of these two TEMPO radicals, the total density of states (DOS) of the molecule, the total
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304
DOS (states/ev atom)
density of states of N(1), O(1) for 1 and 2 are calculated as shown in Fig. 3(a) and (b). Because the DOS distribution near the Fermi level determines the magnetic properties, we concentrate our attention on the DOS in the vicinity of the Fermi level, which is set to zero and ranges from 5 to 2 eV. From Fig. 3, we found that the total DOS distributions of the up- and down-spin states in the vicinity of the Fermi level are obviously split, one valence band is split into two subbands: one is the up-spin valence band, the other is the down-spin band. So the ordered spin arrangement of electrons is formed by the exchange correlation of the electrons, which provides the static magnetic moment of this compound. The up-spin total DOS
60 45 30 15 0
Total
0
O_total
0
N_total
6 3 0 2 0 -7
-6
-5
-4
DOS (states/ev atom)
(a)
-3 -2 -1 Energy (eV)
50 40 30 20 10 0 8 6 4 2 0 4
0
1
2
Total
0 O_total
0
N_total
2 0 -7 (b)
-6
-5
-4
-3 -2 -1 Energy (eV)
0
1
2
Fig. 3. Calculated total density of states (DOS) for molecule and O(1), N(1) atom of 1 and 2. The solid and dotted lines denote majority spin, respectively. The Fermi levels are located at 0 eV. (a) For 1, (b) for 2.
distribution of these two TEMPO radicals is about 0.85 eV lower than the corresponding down-spin total DOS distribution, so the valence orbital is a single occupied molecule orbital (SOMO). The down-spin bands corresponding to the up-spin top occupied bands are above the Fermi level, so electrons do not occupy the down-spin bands. This implies that the spin magnetic moment is 1.0 mB per molecule of each TEMPO radical crystal, which is in good agreement with the experimental result because there is an unpaired electron in the highest occupied molecular orbital (HOMO) of TEMPO radicals. In order to study the origin of the magnetic moment, we have studied the electronic structure of these compounds. According to the DOS distribution, we note that the upand down-spin subbands almost come from N(1), O(1) atoms, so the magnetic moment are mainly localized on the free radicals. In order to understand deeply the mechanism of the magnetic interactions in TEMPO radicals, we provide Fig. 4. Fig. 4(a) and (b) shows the partial density of states (PDOS) of 2-p orbital of O(1) and N(1) for 1 and 2. One can see that the partial DOS of O(1) 2-p and N(1) 2-p of each crystal have similar peaks and character, which means that there is hybridization between O(1) 2-p and N(1) 2-p orbitals. The unpaired electrons in these two TEMPO radicals are localized in the molecular orbital constituted primarily of the p*(NO) orbital, which is formed from 2-p (p) atomic orbital of N(1) and O(1). In this way, the net spin magnetic moment is formed from the free radicals. As for neighboring carbon atoms, there is an overlapping of orbitals inducing the net spin magnetic moment. Just because of the localized electrons of free radicals and the net spin magnetic moment of carbon atoms, the state ordered spin arrangement in three-dimensional network results in stable FM. On further consideration, we give the spin moments on atoms in Table 1 for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl, for which the spin moments are defined as the difference of the average number of occupied ions between spin up and spin down in the muffin-tin sphere. We also give the l-decomposed (s- and p-states) spin-up and spin-down electrons in each MT sphere of
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L. Zhu et al. / Journal of Magnetism and Magnetic Materials 301 (2006) 301–307
60 45 30 15 0 2
Table 1 Calculated magnetic moments in mB for partial atoms of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1)
Total
0
0
N_p
0.4 0.0 -7
-6
-5
-4
DOS (states/ev atom)
(a)
-3 -2 -1 Energy (eV)
50 40 30 20 10 0 2
0
Site
Spin
N(1) O(1) N(2) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) H(21) H(51) H(73) H(91) H(93)
0.188 0.188 0.001 0.000 0.0001 0.0015 0.0016 0.000 0.003 0.009 0.003 0.008 0.0001 0.0001 0.0008 0.0009 0.0001
O_p
1 0 0.8
305
1
2
Total
0
O_p
0
N_p
1 0 1.0
Table 2 Calculated l-decomposed (s- and p-states) spin-up and spindown electrons in each MT sphere for partial atoms of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1)
0.5 0.0 -7 (b)
-6
-5
-4
-3 -2 -1 Energy (eV)
0
1
2
Fig. 4. The calculated partial density of states (PDOS) for O(1), N(1) atom of 1 and 2. The solid and dotted lines denote majority and minority spin, respectively. The Fermi levels are located at 0 eV. (a) For 1, (b) for 2.
partial atoms for 1 in Table 2. From Table 1, we find that the magnetic moments almost come from N(1), O(1) atoms, which form the free radicals. Because of the spin polarization within the p orbital of the carbon atoms, the sign of the carbon spin population of the Diphenyl alternates as = þ = =þ, which means there exist antiferromagnetic exchange interactions in the system. To understand the mechanisms for the exchange coupling between the individual nitroxide molecules, we explain the ferromagnetic behavior in conjugated p radicals on the basis of an intermolecular coupling mechanism suggested by McConnell [23], which involves spin polarization effect leading to alternating positive and negative
Site
O(1) N(1) N(2) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) H(21) H(51) H(73) H(91) H(93)
Charge (spin-up)
Charge (spin-down)
s
p
s
p
0.5852 0.4329 0.4411 0.2158 0.2195 0.2077 0.2078 0.2210 0.2241 0.2262 0.2289 0.2154 0.0842 0.0901 0.0843 0.1004 0.0908
1.1229 0.7895 0.7051 0.3426 0.3505 0.3143 0.3147 0.3542 0.3603 0.3685 0.3742 0.3461 0.0015 0.0017 0.0015 0.0021 0.0018
0.5824 0.4232 0.4410 0.2158 0.2195 0.2074 0.2075 0.2209 0.2233 0.2245 0.2281 0.2141 0.0843 0.0902 0.0835 0.0995 0.0909
0.9388 0.6161 0.7045 0.3427 0.3505 0.3140 0.3143 0.3542 0.3583 0.3614 0.3722 0.3393 0.0015 0.0017 0.0015 0.0020 0.0018
spin densities on the carbon backbone of these molecules. In its original form the first McConnell mechanism refers to the intermolecular ferromagnetic coupling between organic radicals with
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alternating positive and negative spin densities in the conjugated p system of their carbon backbones. The two neighboring molecules have to be positioned in such a way that a site with positive spin density on one molecule is in registry with a site with negative spin density on the neighboring molecule in order to obtain ferromagnetic coupling. The sites with positive sign of spin density and negative sign of spin density are aligned in Table 1. A positive spin density on the NO-site induces a negative spin density on the methyl- and/ or methylene-hydrogens connected to b-carbons, due to an intramolecular spin-polarization, which in turn induces positive spin densities on the NO sites of the adjacent molecules caused by the orbital overlap between hydrogens and the p*(N–O) orbital of the adjacent molecule, = ONð"Þ2Ca ð#Þ2Cb ð"Þ2Hb ð#Þ ð"ÞON\ , thereby leading to parallel spin-alignments of NO sites in crystals. This mechanism of ferromagnetic interaction is illustrated schematically in Fig. 5. We believe that TEMPO derivatives tend to form these characteristic molecular arrangements in crystals and this is the reason for the high probability of finding ferromagnetic radicals in TEMPO derivatives. A similar structure in aromatic moieties may give similar arrangements to TEMPO moieties in crystals, thus leading to intermolecular ferromagnetic interactions in a series of these materials. In
the present calculations, the spin magnetic moments is 0.18805/N(1) and 0.188493/O(1) for 1, and 0.18276/N(1) and 0.17950/O(1) for 2, which shows that the spin states of the free radical N(1) and O(1) atoms of these two organic radical crystals are almost symmetric. From Table 2 we can find that the spin magnetic moments of N(1) and O(1) for crystals 1 mainly come from the p orbitals. In the present paper, we also performed the total energy calculations corresponding to the ferromagnetic and paramagnetic phases with the same parameter (number of k-points, Kmax, etc.) for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl (1). The self-consistent field (SCF) interactions converge to a ferromagnetic state; the total energy in the ferromagnetic state E ¼ 6406:603 Ry for 1. An artificial paramagnetic state was used to obtain the total energy for the paramagnetic state E ¼ 6406:534 Ry for 1. Thus the total energy difference between the ferromagnetic state and the paramagnetic state is about 0.938 eV. There are 260 valence electrons in the supercell, so the energy difference between the ferromagnetic state and the paramagnetic state per electron is estimated to be 3.61 meV. Thus the ferromagnetic state is more stable than the paramagnetic state. It is reasonably consistent with ac magnetic susceptibility measurements which show that the ferromagnetic coupling of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl only exists at a low temperature [16,17].
4. Conclusions
Fig. 5. A possible spin-polarization mechanism illustrating intermolecular ferromagnetic interactions found for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl. Only TEMPO portions are drawn for the sake of simplicity.
In this work, we have studied the origin of the magnetism and the magnetic interactions in two TEMPO radicals by employing ab initio method of the full potential linearized augmented plane wave within density functional theory. The electronic structure, the total and partial density of states and the atomic spin magnetic moments of these two TEMPO radicals are obtained. It is shown that these two TEMPO radicals have a ferromagnetic property at low temperatures. The analysis of the DOS and the atomic spin magnetic moments reveals that the spin magnetic moment is
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1.0 mB per molecule of each radical crystals, and the magnetic moment mainly comes from the p*(NO) orbital. Because of the hybridization between the 2-p orbital of O(1) and N(1) atoms and the overlap of orbital of neighboring carbon and hydrogen atoms, the unpaired localized electrons of free radicals and the net spin magnetic moment of carbon atoms are formed. This contributes to the magnetism and ferromagnetic interaction between the neighboring radicals, which are in good agreement with the experimental result.
Acknowledgements This work was supported by the National Natural Science Foundation of China under the Grant nos. 10174023 and 20490210. The authors thank T. Ishida for giving us the crystal data. References [1] H. Iwamura, Adv. Phys. Org. Chem. 26 (1990) 179. [2] M. Tamura, Y. Nakazawa, D. Shiomi, K. Nozawa, Y. Hosokoshi, M. Ishikawa, M. Takahashi, M. Kinoshita, Chem. Phys. Lett. 186 (1991) 401. [3] K.L. Yao, L. Zhu, Z.L. Liu, Solid State Commun. 132 (10) (2004) 657. [4] Z. Fang, Z.L. Liu, K.L. Yao, Z.G. Li, Phys. Rev. B 51 (1995) 1304. [5] Y.F. Duan, K.L. Yao, Phys. Rev. B 63 (2001) 134434.
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[6] W.Z. Wang, Z.L. Liu, K.L. Yao, Phys. Rev. B 55 (1997) 12989. [7] W.Z. Wang, J. Chem. Phys. 108 (7) (1998) 2867. [8] W.Z. Wang, K.L. Yao, H.Q. Lin, Chem. Phys. Lett. 274 (1997) 221. [9] K.L. Yao, S.J. Luo, Z.L. Liu, Physica B 325 (2003) 380. [10] S.J. Luo, K.L. Yao, J. Magn. Magn. Mater. 257 (2003) 11. [11] S.J. Luo, K.L. Yao, Phys. Rev. B 67 (2003) 214429. [12] W.D. Zou, Z.L. Liu, K.L. Yao, J. Magn. Magn. Mater. 263 (2003) 360. [13] W.D. Zou, Z.L. Liu, K.L. Yao, Physica B 337 (2003) 298. [14] T. Nogami, T. Ishida, M. Yasui, F. Iwasaki, N. Takeda, M. Masayasu, T. Kawakami, K. Yamaguchi, Bull. Chem. Soc. Japan 69 (1996) 1841. [15] K. Togashi, R. Imachi, K. Tomioka, H. Tsuboi, T. Ishida, T. Nogami, N. Takeda, M. Ishikawa, Bull. Chem. Soc. Japan 69 (1996) 2821. [16] T. Nogami, K. Tomioka, T. Ishida, H. Yoshikawa, M. Yasui, F. Iwasaki, H. Iwamura, N. Takeda, M. Ishikawa, Chem. Lett. (1994) 29. [17] K. Tomioka, S. Mitsubori, T. Ishida, T. Nogami, H. Iwamura, Chem. Lett. (1993) 1239. [18] T. Ishida, K. Tomioka, T. Nogami, H. Yoshikawa, M. Yasui, F. Iwasaki, N. Takeda, M. Ishikawa, Chem. Phys. Lett. 247 (1995) 7. [19] K. Tomioka, T. Ishida, T. Nogami, H.H. Iwamura, Chem. Lett. (1993) 625. [20] P. Blaha, K. Schwarz, Georg. K.H. Madsen, D. Kvasnicka, J. Luitz, Wien2k, An Augmented Plane Wave+ Local Orbitals Program for Calculation Crystal Properties, Karlheinz Schwarz, Techn. Universit Wien, Austria, 2001, ISBN 3-9501031-1-2. [21] L. Ducase, A. Fritsh, Chem. Phys. Lett. 286 (1998) 183. [22] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [23] H.M. McConnell, J. Chem. Phys. 39 (1963) 1910.
Journal of Magnetism and Magnetic Materials 301 (2006) 301–307 www.elsevier.com/locate/jmmm
The electronic structure and the ferromagnetic intermolecular interactions in the crystal of TEMPO radicals L. Zhua,, K.L. Yaoa,b, Z.L. Liua a
Department of Physics and State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China b International Center of Materials Physics, The Chinese Academy of Science, Shengyang 110015, China Received 18 April 2005; received in revised form 5 July 2005 Available online 10 August 2005
Abstract Based on the generalized gradient approximation, full potential linearized augmented plane wave (FP-LAPW) calculations have been performed to study the electronic band structure and the intermolecular ferromagnetic (FM) interactions for the two TEMPO radicals 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1) and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2). The total and the partial density of states and the atomic spin magnetic moments are calculated and discussed. The calculation revealed that the two TEMPO radicals have the intermolecular FM interactions, and the spontaneous magnetic moment is 1.0 mB per molecule of each crystal, which is in good agreement with the experimental value. It is found that the unpaired electrons in these compounds are localized in a molecular orbital constituted primarily of p* (NO) orbital, and the main contribution of the spin magnetic moment comes from the NO-free radical. The origin of FM is also studied in detail. r 2005 Elsevier B.V. All rights reserved. PACS: 75.50.y; 71.15.m; 71.20.b Keywords: DFT; The organic magnet; Electronic structure; Ferromagnetic properties
1. Introduction Ferromagnetic interactions in crystals of stable organic radicals have been much investigated in Corresponding author. Tel.: +0086 27 87556264; fax: +0086 27 87544525. E-mail addresses: [email protected] (L. Zhu), [email protected] (K.L. Yao).
connection with organic ferromagnets [1]. Since the discovery of the first genuine organic ferromagnetic radical crystal, p-nitrophenyl nitronyl nitroxide [2], organic-free radical magnetic compounds, which consist of only light elements such as H, C, N, O, have attracted much attention not only in the field of material science but also in the field of condensed matter physics [3–13]. Ferromagnetic interactions in crystals of stable organic
0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.07.006
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radicals have been intensively investigated for organic ferromagnets of nitroxides derivatives. The ferromagnetic interactions in these nitroxides seem to be related to a characteristic molecular arrangement in the crystal, namely, to close contacts between the oxygen of an NO site and methyl and/or methylene hydrogens at the bpositions of adjacent NO moieties [14]. In this arrangement, the spin-alternation mechanism probably gives rise to the intermolecular ferromagnetic coupling. Among the few-known compounds of this type is TEMPO radicals, some of which show intermolecular ferromagnetic interaction. Recently, intermolecular ferromagnetic interaction of crystalline and single-component organic radicals has been reported by use of nitroxide radicals as spin sources. Nogami et al. have reported organic ferro- and meta-magnets having a 2,2,6,6-tetramethylpiperidin-1-oxyl(TEMPO) radical group [14,15]. All of the TEMPO radical crystals have characteristic features that oxygen atoms of N–O radical sites of TEMPO moieties always locate near methyl- and/or methylenehydrogens at b-positions of N–O in the TEMPO moieties of adjacent molecules. A positive spin on the N–O radical induces negative spins on the b-hydrogen atoms due to an intramolecular spinpolarization, ON(m)–C(k)–C(m)–H(k), which in turn induces a positive spin on the N–O sites of the adjacent molecules. Among these TEMPO radical crystals are 4-Benzylideneamino-2,2,6, 6-tetramethylpiperidin-1-oxyl (1) [16,17] and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2) [18,19]. The molecular and crystal structures of 1 and 2 are shown in Fig. 1. The crystal structure of 1 viewed along the b-axis is shown in Fig. 2, which comes from the experiment [16]. As Fig. 2 shows, the phenyl ring and imino group are almost coplanar, and the averaged piperidine plane is twisted relative to the benzylideneamino moiety by an angle of 821. The phenyl rings stack to the b and c directions and, consequently, the TEMPO moieties gather to construct a two-dimensional N–O network parallel to the bc plane. The nearest-neighbor nitroxides are arranged along the c-axis with the O–O distance of 5.62 A˚. The angle between the nearest
Fig. 1. Molecular structure of 1 and 2. Thermal ellipsoids of C, N, and O atoms are drawn at the 50% probability level. The hydrogen atoms are given an arbitrary thermal parameter.
Fig. 2. Crystal structure of 1 viewed along the b-axis. Hydrogen atoms are omitted for clarity.
N–O bonds is 981, and that between the C–O–C planes surrounding the radical nitrogen is 541. The second nearest neighbors are arranged along the b-axis with the O–O distance of 6.15 A˚, with the angle between the N–O bonds 821 and that between the C–O–C planes 541. The intermolecular atomic distances: O–C(methyl), 3.74 A˚; O–H(methyl), 2.87. The nearest O–O distance in the neighboring sheets is 11.89 A˚. The sheet structure of the N–O sites in the crystal of 2 is similar to the case of 1(O–O distances: intrasheet,
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5.70 and 8.75 A˚; inter-sheet, 10.08 A˚). For simplicity, we do not show the sheet structure of 2. The angles between the N–O bonds are 142.31 and those between the C–O–C planes surrounding the radical nitrogen atom are 39.51 for crystal structure of 2. The organic radical crystal of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl was found to be a bulk ferromagnet, and has a ferromagnetic phase transition at 0.18 K. The organic radical crystal of 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl exhibited a Neel transition at about 0.12 K (TN) and a metamagnetic transition below TN (the coercive field was around 180 Oe at 40 mK). The two organic radical crystals all have intermolecular ferromagnetic interaction. To understand deeply the mechanism of the ferromagnetic interactions in this compound, a more detailed knowledge of the electronic band structure and the magnetic properties is still required. In this paper, we adopt the density-functional theory (DFT) with generalized gradient approximation (GGA) to calculate the electronic band structure and the ferromagnetic properties of 1 and 2 by the accurate full potential linearized augmented plane wave (FP-LAPW). The main goals of our work are to investigate the electronic structure and the magnetic coupling, and to analyze the observed ferromagnetic interaction via the density of states (DOS) and the atomic spin magnetic moments. This provides new insights to the origin of the strong ferromagnetic coupling in the compound, which should be useful for the design of novel ferromagnetic materials. 2. FP-LAPW parameters and the structure of 1 and 2 The first-principles electronic structure calculations employ the well-known FP-LAPW method, which has a good accuracy. In this method, no shape approximation on either the potential or the electronic charge density is made. We use the wien2k [20] package, which allows the inclusion of local orbits in basis, improving upon linearization and making a consistent treatment of semicore and valence in one energy window possible, hence ensuring proper orthogonality. In general,
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the local density approximation (LDA) and the GGA can be chosen in wien2k code. Considering the success of the GGA derived from their ability to correct some LDA deficiencies with a modest increase in computational workload, the GGA is mandatory for systems containing ‘‘weak’’ or hydrogen bonds such as molecular crystals; for these systems the intermolecular bond lengths are severely underestimated in LDA, but they can be appreciably improved in GGA. In addition, the GGA has been demonstrated to be capable of calculating organic magnets [21]. So in our calculations, the exchange and correlation effects are treated with the GGA according to Perdew et al. [22]. According to the experiment, 1 and 2 have monoclinic and orthorhombic lattice, respectively, and there are four molecules in one primitive unit cell. The lattice parameters we used in the present ( b ¼ 11:740ð2Þ A, ( calculation are a ¼ 12:684ð7Þ A, ( c ¼ 11:024ð3Þ A, a ¼ g ¼ 901, b ¼ 111:401, for 1, and ( b ¼ 5:697ð1Þ A, ( c ¼ 15:107ð2Þ A, ( a ¼ 20:084ð2Þ A, a ¼ b ¼ g ¼ 901, for 2, which are just the same as the experimental parameters. The atomic-sphere radii Rmt are chosen as 1.2, 1.2, 1.0, 0.6 a.u. for O, N, C, H respectively, for these two organic radical crystals. We chose the spin-polarized calculation in our calculation. We setup the expansion to l ¼ 10 and the charge density Fourier expansion cutoff Gmax ¼ 14 in the muffintins. One hundred k-points in the first Brillouin zone were adopted in the calculations. In order to achieve a satisfactory degree of convergence, the cutoff parameter is taken to be Rmt K max ¼ 2:5, where Kmax is the maximal value of the reciprocal lattice vector used in the plane wave expansion, which corresponds to about 121 485 plane waves for 1 and 140 700 plane waves for 2 at the equilibrium lattice constant and the plane-wave cutoff energy is 236 eV. We specify charge as the convergence criterion, and select charge convergence to 105.
3. Results and discussion To study the electronic structure and magnetic properties of these two TEMPO radicals, the total density of states (DOS) of the molecule, the total
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DOS (states/ev atom)
density of states of N(1), O(1) for 1 and 2 are calculated as shown in Fig. 3(a) and (b). Because the DOS distribution near the Fermi level determines the magnetic properties, we concentrate our attention on the DOS in the vicinity of the Fermi level, which is set to zero and ranges from 5 to 2 eV. From Fig. 3, we found that the total DOS distributions of the up- and down-spin states in the vicinity of the Fermi level are obviously split, one valence band is split into two subbands: one is the up-spin valence band, the other is the down-spin band. So the ordered spin arrangement of electrons is formed by the exchange correlation of the electrons, which provides the static magnetic moment of this compound. The up-spin total DOS
60 45 30 15 0
Total
0
O_total
0
N_total
6 3 0 2 0 -7
-6
-5
-4
DOS (states/ev atom)
(a)
-3 -2 -1 Energy (eV)
50 40 30 20 10 0 8 6 4 2 0 4
0
1
2
Total
0 O_total
0
N_total
2 0 -7 (b)
-6
-5
-4
-3 -2 -1 Energy (eV)
0
1
2
Fig. 3. Calculated total density of states (DOS) for molecule and O(1), N(1) atom of 1 and 2. The solid and dotted lines denote majority spin, respectively. The Fermi levels are located at 0 eV. (a) For 1, (b) for 2.
distribution of these two TEMPO radicals is about 0.85 eV lower than the corresponding down-spin total DOS distribution, so the valence orbital is a single occupied molecule orbital (SOMO). The down-spin bands corresponding to the up-spin top occupied bands are above the Fermi level, so electrons do not occupy the down-spin bands. This implies that the spin magnetic moment is 1.0 mB per molecule of each TEMPO radical crystal, which is in good agreement with the experimental result because there is an unpaired electron in the highest occupied molecular orbital (HOMO) of TEMPO radicals. In order to study the origin of the magnetic moment, we have studied the electronic structure of these compounds. According to the DOS distribution, we note that the upand down-spin subbands almost come from N(1), O(1) atoms, so the magnetic moment are mainly localized on the free radicals. In order to understand deeply the mechanism of the magnetic interactions in TEMPO radicals, we provide Fig. 4. Fig. 4(a) and (b) shows the partial density of states (PDOS) of 2-p orbital of O(1) and N(1) for 1 and 2. One can see that the partial DOS of O(1) 2-p and N(1) 2-p of each crystal have similar peaks and character, which means that there is hybridization between O(1) 2-p and N(1) 2-p orbitals. The unpaired electrons in these two TEMPO radicals are localized in the molecular orbital constituted primarily of the p*(NO) orbital, which is formed from 2-p (p) atomic orbital of N(1) and O(1). In this way, the net spin magnetic moment is formed from the free radicals. As for neighboring carbon atoms, there is an overlapping of orbitals inducing the net spin magnetic moment. Just because of the localized electrons of free radicals and the net spin magnetic moment of carbon atoms, the state ordered spin arrangement in three-dimensional network results in stable FM. On further consideration, we give the spin moments on atoms in Table 1 for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl, for which the spin moments are defined as the difference of the average number of occupied ions between spin up and spin down in the muffin-tin sphere. We also give the l-decomposed (s- and p-states) spin-up and spin-down electrons in each MT sphere of
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L. Zhu et al. / Journal of Magnetism and Magnetic Materials 301 (2006) 301–307
60 45 30 15 0 2
Table 1 Calculated magnetic moments in mB for partial atoms of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1)
Total
0
0
N_p
0.4 0.0 -7
-6
-5
-4
DOS (states/ev atom)
(a)
-3 -2 -1 Energy (eV)
50 40 30 20 10 0 2
0
Site
Spin
N(1) O(1) N(2) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) H(21) H(51) H(73) H(91) H(93)
0.188 0.188 0.001 0.000 0.0001 0.0015 0.0016 0.000 0.003 0.009 0.003 0.008 0.0001 0.0001 0.0008 0.0009 0.0001
O_p
1 0 0.8
305
1
2
Total
0
O_p
0
N_p
1 0 1.0
Table 2 Calculated l-decomposed (s- and p-states) spin-up and spindown electrons in each MT sphere for partial atoms of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1)
0.5 0.0 -7 (b)
-6
-5
-4
-3 -2 -1 Energy (eV)
0
1
2
Fig. 4. The calculated partial density of states (PDOS) for O(1), N(1) atom of 1 and 2. The solid and dotted lines denote majority and minority spin, respectively. The Fermi levels are located at 0 eV. (a) For 1, (b) for 2.
partial atoms for 1 in Table 2. From Table 1, we find that the magnetic moments almost come from N(1), O(1) atoms, which form the free radicals. Because of the spin polarization within the p orbital of the carbon atoms, the sign of the carbon spin population of the Diphenyl alternates as = þ = =þ, which means there exist antiferromagnetic exchange interactions in the system. To understand the mechanisms for the exchange coupling between the individual nitroxide molecules, we explain the ferromagnetic behavior in conjugated p radicals on the basis of an intermolecular coupling mechanism suggested by McConnell [23], which involves spin polarization effect leading to alternating positive and negative
Site
O(1) N(1) N(2) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) H(21) H(51) H(73) H(91) H(93)
Charge (spin-up)
Charge (spin-down)
s
p
s
p
0.5852 0.4329 0.4411 0.2158 0.2195 0.2077 0.2078 0.2210 0.2241 0.2262 0.2289 0.2154 0.0842 0.0901 0.0843 0.1004 0.0908
1.1229 0.7895 0.7051 0.3426 0.3505 0.3143 0.3147 0.3542 0.3603 0.3685 0.3742 0.3461 0.0015 0.0017 0.0015 0.0021 0.0018
0.5824 0.4232 0.4410 0.2158 0.2195 0.2074 0.2075 0.2209 0.2233 0.2245 0.2281 0.2141 0.0843 0.0902 0.0835 0.0995 0.0909
0.9388 0.6161 0.7045 0.3427 0.3505 0.3140 0.3143 0.3542 0.3583 0.3614 0.3722 0.3393 0.0015 0.0017 0.0015 0.0020 0.0018
spin densities on the carbon backbone of these molecules. In its original form the first McConnell mechanism refers to the intermolecular ferromagnetic coupling between organic radicals with
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alternating positive and negative spin densities in the conjugated p system of their carbon backbones. The two neighboring molecules have to be positioned in such a way that a site with positive spin density on one molecule is in registry with a site with negative spin density on the neighboring molecule in order to obtain ferromagnetic coupling. The sites with positive sign of spin density and negative sign of spin density are aligned in Table 1. A positive spin density on the NO-site induces a negative spin density on the methyl- and/ or methylene-hydrogens connected to b-carbons, due to an intramolecular spin-polarization, which in turn induces positive spin densities on the NO sites of the adjacent molecules caused by the orbital overlap between hydrogens and the p*(N–O) orbital of the adjacent molecule, = ONð"Þ2Ca ð#Þ2Cb ð"Þ2Hb ð#Þ ð"ÞON\ , thereby leading to parallel spin-alignments of NO sites in crystals. This mechanism of ferromagnetic interaction is illustrated schematically in Fig. 5. We believe that TEMPO derivatives tend to form these characteristic molecular arrangements in crystals and this is the reason for the high probability of finding ferromagnetic radicals in TEMPO derivatives. A similar structure in aromatic moieties may give similar arrangements to TEMPO moieties in crystals, thus leading to intermolecular ferromagnetic interactions in a series of these materials. In
the present calculations, the spin magnetic moments is 0.18805/N(1) and 0.188493/O(1) for 1, and 0.18276/N(1) and 0.17950/O(1) for 2, which shows that the spin states of the free radical N(1) and O(1) atoms of these two organic radical crystals are almost symmetric. From Table 2 we can find that the spin magnetic moments of N(1) and O(1) for crystals 1 mainly come from the p orbitals. In the present paper, we also performed the total energy calculations corresponding to the ferromagnetic and paramagnetic phases with the same parameter (number of k-points, Kmax, etc.) for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl (1). The self-consistent field (SCF) interactions converge to a ferromagnetic state; the total energy in the ferromagnetic state E ¼ 6406:603 Ry for 1. An artificial paramagnetic state was used to obtain the total energy for the paramagnetic state E ¼ 6406:534 Ry for 1. Thus the total energy difference between the ferromagnetic state and the paramagnetic state is about 0.938 eV. There are 260 valence electrons in the supercell, so the energy difference between the ferromagnetic state and the paramagnetic state per electron is estimated to be 3.61 meV. Thus the ferromagnetic state is more stable than the paramagnetic state. It is reasonably consistent with ac magnetic susceptibility measurements which show that the ferromagnetic coupling of 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin1-oxyl only exists at a low temperature [16,17].
4. Conclusions
Fig. 5. A possible spin-polarization mechanism illustrating intermolecular ferromagnetic interactions found for 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl. Only TEMPO portions are drawn for the sake of simplicity.
In this work, we have studied the origin of the magnetism and the magnetic interactions in two TEMPO radicals by employing ab initio method of the full potential linearized augmented plane wave within density functional theory. The electronic structure, the total and partial density of states and the atomic spin magnetic moments of these two TEMPO radicals are obtained. It is shown that these two TEMPO radicals have a ferromagnetic property at low temperatures. The analysis of the DOS and the atomic spin magnetic moments reveals that the spin magnetic moment is
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1.0 mB per molecule of each radical crystals, and the magnetic moment mainly comes from the p*(NO) orbital. Because of the hybridization between the 2-p orbital of O(1) and N(1) atoms and the overlap of orbital of neighboring carbon and hydrogen atoms, the unpaired localized electrons of free radicals and the net spin magnetic moment of carbon atoms are formed. This contributes to the magnetism and ferromagnetic interaction between the neighboring radicals, which are in good agreement with the experimental result.
Acknowledgements This work was supported by the National Natural Science Foundation of China under the Grant nos. 10174023 and 20490210. The authors thank T. Ishida for giving us the crystal data. References [1] H. Iwamura, Adv. Phys. Org. Chem. 26 (1990) 179. [2] M. Tamura, Y. Nakazawa, D. Shiomi, K. Nozawa, Y. Hosokoshi, M. Ishikawa, M. Takahashi, M. Kinoshita, Chem. Phys. Lett. 186 (1991) 401. [3] K.L. Yao, L. Zhu, Z.L. Liu, Solid State Commun. 132 (10) (2004) 657. [4] Z. Fang, Z.L. Liu, K.L. Yao, Z.G. Li, Phys. Rev. B 51 (1995) 1304. [5] Y.F. Duan, K.L. Yao, Phys. Rev. B 63 (2001) 134434.
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