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Magnetic interactions and spin densities in molecular compounds: an example
Physica B 297 (2001) 213}220
Magnetic interactions and spin densities in molecular compounds: an example J. Schweizer *, S. Golhen, E. Lelie`vre-Berna, L. Ouahab, Y. Pontillon, E. Ressouche CEA-Grenoble, DRFMC/SPSMS, Laboratoire de Magne& tisme et Diwraction Neutronique, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France Laboratoire de Chimie du Solide et Inorganique Mole& culaire, UMR 6511, CNRS, Universite& de Rennes I, 35042 Rennes Cedex, France Institut Laue Langevin, rue des Martyrs, 156X, 38042 Grenoble Cedex 9, France
Abstract The discovery of ferromagnetism in the charge transfer salt [Fe(Cp*)]z>[TCNE]z\ has raised a lot of interest. The nature of this magnetic coupling was controversial. The group of Miller invoked a McConnell II mechanism, with con"guration interactions. Another view was given by Kahn and coworkers who proposed a coupling between spin carriers (McConnell I mechanism), implying a positive exchange due to an overlap between spin densities of opposed signs. In the "rst interpretation, there would be a positive spin density located on the carbon rings of the ferrocene, but in the second interpretation, this spin density should be negative. To clarify this mechanism, it was decided to investigate separately, by polarized neutron di!raction, the spin density of [TCNE]z\, associated with a nonmagnetic donor and the magnetization density of [Fe(Cp*)]z>, associated with a nonmagnetic acceptor. For [TCNE]z\, the measurement was straightfor ward: it was found that most of the spin density was located on the central carbon while a noticeable amount was delocalized on the terminal nitrogens. Several attempts to measure the magnetization density of [Fe(Cp*)]z> were unsuccessful due to a loss of symmetry on cooling. To overcome this di$culty, we have "nally measured the z magnetization density of [Fe(Cp*)] > in a crystal of space group P1 , where four of these ions are associated with the polyoxotungstate [SiW O ]\. We have found that the Fe atoms carry a moment of 2.0 and that the carbons of the rings carry !0.005$0.001 . The signs of these carbon spin populations are consistent with the McConnell I mechanism, but their magnitudes are too small to account for the experimental interactions. 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic interactions; Spin densities
1. Introduction The concern of chemists and physicists for molecular compounds increased abruptly in 1987 with
* Corresponding author. E-mail address: [email protected] (J. Schweizer).
the discovery by Miller et al. [1] of ferromagnetism in decamethylferrocenium tetracyanoethenide. This compound is the orthorhombic charge transfer salt [Fe(Cp*)]z>[TCNE]z\, built from linear chains of alternating metalloferrocenium donors D> and cyanocarbon acceptors A\ (Fig. 1). Each ion carries a spin , and the magnetic interactions in the crystal are strong enough to yield a Curie
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 8 5 9 - 0
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Fig. 1. The chain structure of the compound [Fe(Cp*)]z> [TCNE]z\.
temperature of 4.8 K [2,3]. Soon after that, other charge transfer materials were obtained along the same line with much higher Curie temperatures, as for instance the amorphous and unstable compound V[TCNE] CH Cl (¹ &400 K) [4]. It V W was then very important to understand the mechanism in these metallocenium}TCNE charge transfer salts and, to start with, in the compound [Fe(Cp*)]z>[TCNE]z\ itself. A "rst explanation, put forward by Miller et al. [5], proposed a McConnell II mechanism [6] to explain the positive coupling between the [Fe(Cp*)]z> and [TCNE]z\ ions along a chain: an admixture of the excited state [Fe(Cp*)]>> [TCNE]\\ in the [Fe(Cp*)]z>[TCNE]z\ ground
state. Due to the degeneracy of the [Fe(Cp*)]z> levels, this admixture could result in a ferromagnetic coupling. Along this line, Tchougree! et al. [7] attributed the ferromagnetism to a positive interaction between the d electrons of the cation with the electrons back-transferred from [TCNE]z\ to the empty orbitals of [Fe(Cp*)]z>, with a posit ive density on these orbitals. Another explanation, based on an earlier idea of McConnell [8] (the so-called McConnell I mechanism) was proposed by Kahn and coworkers [9}11]: in [Fe(Cp*)]z>, the spin density is localized mainly on the Fe(III) ion, but, induced by spin polarization, some density of opposite sign exists on the Cp rings which face the TCNE molecules. The ferromagnetic coupling, which exists between the [Fe(Cp*)]z> and the [TCNE]z\ units, would result from the negative Heitler}London spin exchange due to the overlap between the Cp rings and the TCNE atoms. The positive sign of the global interaction in this model would be the consequence of the negative sign of the spin density on the Cp rings. The sign of the spin density on the ligand orbitals has been looked at by NMR, but in a rather indirect way [12]. Actually, as the paramagnetic signal shift on the carbon atoms is very small, it is very di$cult to assess a sign for their spin density. It was then necessary to measure the signal shifts on carbon atoms separated by two bonds ( positions) from the system in the substituted systems [(iPrCp) Fe]> and [(tBuCp )Fe]> and to com pare to that of [(EtMe Cp) ]>. This comparison concluded that a negative sign exists on the ligand of the orbitals. The sign of the spin density on the Cp rings of [Fe(Cp*)]z>[TCNE]z\ being a key point in choos ing which of the two models is at the origin of the ferromagnetism in the chains, it was decided to measure it directly by polarized neutron di!raction (PND). Such experiments are performed with a single crystal at very low temperature, below or above ¹ , with a strong magnetic "eld applied to the sample. In the present case, several attempts were made to cool down a single crystal, but each time, the crystal broke down. Actually, an X-ray investigation [5] showed that, though an orthorhombic unit cell is well determined at room
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temperature, the crystal structure cannot be well de"ned: some atomic disorder exists at this temperature. Speci"c heat measurements [13] showed that the compound undergoes two transitions on cooling, at 282 and 249 K. These transitions correspond probably to a reduction of the atomic disorder. It results that a nice orthorhombic crystal at room temperature is neither orthorhombic nor single crystal at low temperature, which prevents the expected neutron investigation from being performed. As a result of this impossibility, a new strategy has been decided: to measure the spin density separately on each of the two moieties [TCNE]z\ and [Fe(Cp*)]z>, associated, respectively, in a charge transfer salt with a nonmagnetic donor D> and a nonmagnetic acceptor A\. These investigations should allow to "gure out which are the spin densities which interact in [Fe(Cp*)]z>[TCNE]z\ and what is the mechanism which is responsible for the ferromagnetic coupling. The present paper accounts for this study. The "rst step of this process, the determination of the spin of [TCNE]z\ on a single crystal of [Bu N]z>[TCNE]z\ went very well and has been published elsewhere in detail [14], but the second step, on the [Fe(Cp*)]z> radical, turned out to be much more tricky and, after several failures, has been just achieved [15]. We shall start with a report of this recent measurement, review the main results of the [TCNE]z\ study, "gure out the magnetic interactions in the light of these results and "nally compare with ab initio calculations. z 2. Magnetization density in [Fe(Cp* 2 )] >
The low-temperature neutron study of the [Fe(Cp*)]z> radical turned out to be very di$cult to perform. First a salt, [Fe(Cp*)]z>[SbF ]\, with nonmagnetic [SbF ]\ was selected. The crystals are orthorhombic at room temperature, but structural transitions occur on cooling and, at low temperature, the crystals break down and are no longer orthorhombic. Afterwards, we tried [Fe(Cp*)]z> [PF ]\ which is monoclinic at room temperature. But here also, below 80 K, the structure becomes triclinic and the samples at low temperatures were no longer single crystals.
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At this point of the investigation, we considered that the Fe(Cp*) molecule had an unfair tendency for atomic disorder at room temperature and another tendency to reduce this disorder at low temperatures, which results on cooling in crystal transitions with symmetry lowering and crystal breaking. In this case, the only possibility to keep a crystal single, down to the helium temperature, was to choose a crystal which is already triclinic at room temperature and which has no symmetry to lose. Therefore, we decided to measure the magnetization density of [Fe(Cp*)]z> in a crystal where four of these ions are associated with the polyoxotungstate [SiW O ]\, a crystal whose space group is already P1 at room temperature. The synthesis of the compound and the crystal and magnetic properties are reported in Ref. [16]. In this compound, only [Fe(Cp*)]z> is magnetic and the susceptibility follows a Curie}Weiss law with a very small negative value of the Curie temperature. In the triclinic structure, which is centric, the polyoxotungstate [SiW O ]\ anions have the -Keggin structure and are located at the origin of the cell. There are two independent [Fe(Cp*)]z> units in the asymmetric cell, the axes of which are almost parallel to one other and parallel to the a-axis of the cell (see Fig. 2). During the crystal growth, we noticed that besides the triclinic crystals (lattice constants at room temperature: a"14.247 As , b"15.003 As , c"15.418 As , "63.263, "83.413 and "69.773), two other crystal forms were present: monoclinic I and II. We were able to grow large single crystals of the triclinic form. We selected the largest one (15 mm) and glued it in order to have the common axis of the two [Fe(Cp*)]z> cations vertical. With this crystal, we performed two low-temperature neutron experiments: with unpolarized neutron to measure the nuclear structure factors F 's and with polarized neutrons to , measure the magnetic structure factors F 's. + The nuclear structure experiment was performed on the lifting counter di!ractometer D15 of the ILL at a temperature of 10 K. At this temperature the
Lattice constants at room temperature: monoclinic I: a"28.807 As , b"15.085 As , c"31.085 As , "117.013; monoclinic II: a"15.923 As , b"15.063 As , c"25.863 As , "96.393.
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of the ILL, also with a lifting detector, at a temperature of 4 K. The beam, of wavelength 0.843 As , was polarized vertically in the `upa and the `downa directions successively. A 4.6 T "eld, provided by a cryomagnet, was applied in the `upa direction, parallel to the common axis of the two [Fe(Cp*)]z> cations, and we measured the #ipping ratios (R"I>/I\) of 245 independent Bragg re#ections. Considering that the #ipping ratios are connected to the structure factors F 's and F 's by the follow, + ing relation:
Fig. 2. The crystal structure of the compound 4[Fe(Cp*)]z> [SiW O ]\.
lattice constants are the following: a"13.902 As , b"14.901 As , c"15.306 As , "62.643, "82.133 and "69.963. The integrated intensities of 2672 unique re#ections with a wavelength of 1.174 As were measured. The intensities have been corrected for absorption using the Cambridge Crystallography programme [17] with a linear absorption coe$cient of 1.90 cm\. It was not possible to get a good re"nement of the crystal structure, and particularly good values for the thermal parameters. Actually, the structure is centric, but the [SiW O ]\ anions which are located on the center of symmetry of the cell are not centric themselves. This leads to a statistical disorder of the anions. Therefore, to get the set of nuclear structure factors F 's necessary to process the polarized neu, tron experiment (see the following text), instead of determining these values from the re"ned crystal structure, we got them directly as the square roots of the measured intensities. The structure re"nement was only used to determine the normalization factor and the sign # or ! of the structure factor. The magnetic structure experiment was performed on the polarized neutron di!ractometer D3
F #2 sin F F #sin F , + +, R" , F !2 sin F F #sin F , , + + where is the angle between the scattering vector and the vertical axis, the determination of the F 's , as explained before and the measurement of the R's provided a measure of the F 's. + To be complete, the magnetization of the compound was measured in the same conditions as for the polarized neutron experiment: ¹"4 K and a magnetic "eld of 4.6 T applied along the common axis of the two [Fe(Cp*)]z> molecules. A magnetiz ation of 8.11 per cell was found, that is 2.03 per [Fe(Cp*)]z> molecule, which corresponds to the magnetic structure factor of re#ection (0,0,0). Altogether, we got 246 experimental F 's which + represent a fairly good set of data. The magnetic structure factors F (hkl) being the + Fourier coe$cients of the periodic spin (magnetization) density, this distribution can be obtained by an inversion process. There are di!erent ways to do it [18]. We have "rst applied the maximum entropy method which retrieves this density without any assumption on the atomic positions of the magnetic atoms [19,20]. A projection of the magnetization density along the b-axis of the cell is represented in Fig. 3. As expected, the magnetization is well localized on the two Fe atoms, but no density is found elsewhere. In particular, it is too weak to be detected by this method on the carbon atoms. A second approach is to use an atomic model [18]. What we have done is to determine the coe$cients of a Hartree}Fock type of magnetic moG lecular wave function constructed as a sum of atomic orbitals on the iron and the carbon atoms: " . G G G
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Table 1 Atomic spin populations (moments) in [Fe(Cp*)]z> Atom Fe1 (spin#orbit) Fe2 (spin#orbit) Ccp Cme m G Magnetization
m
G
1.932(18) 2.024(18) !0.005(1) 0.008(1) 8.03(8) 8.11(5)
They are the sum of a spin and an orbit contribution. The moments (or spin populations) on the carbons are weak, but signi"cant: negative on the Cp rings and positive and larger for the methyls. 3. Spin density in [TCNE]z\
Fig. 3. Projection of the magnetization density along the b-axis of 4[Fe(Cp*)]z>[SiW O ]\.
To allow for both positive and negative densities, the magnetization (spin) density is expanded as m(r)" m
, G G G G where the atomic moments m can be negative, with G absolute values which are the squares of the coe$cients . These coe$cients were re"ned to "t the G experimental F 's. For the Fe atoms, di!erent or+ bitals were tried. The orbitals of the carbon $ atoms were taken as p . Due to their weak values, X all the moments of the Cp rings, chemically equivalent but crystallographically inequivalent, were constrained to be equal. This constraint also stood for the methyl carbons. The results of the re"nement are reported in Table 1. The best re"nement was obtained for an orbital e (d , d ), which V\W VW means that the distribution around the irons is very anisotropic. The magnetic moments found on atoms Fe1 and Fe2 are, as expected, almost equal.
As this work has already been published in detail [14], we shall report here only the main results. The investigation was carried out on a [Bu N]> [TCNE]z\ single crystal, at a temperature of 1.8 K, with a "eld of 4.6 T applied successively along the [0, 1, 0] and the [1, 0, 1 ] directions of the crystal. The #ipping ratios of 211 Bragg re#ections were measured and allowed the reconstruction of the spin density maps, both by the maximum entropy method and by the multipole expansion. A projection of the density on the plane of the molecule is represented in Fig. 4. The spin populations, are reported in Table 2. As expected, the spin density exists only on the [TCNE]z\ anion. On this radical, most of the density is carried by the central carbons C1 and C2, but quite a noticeable amount is delocalized on the four terminal nitrogen atoms. On the intermediate carbons (C3}C6), a spin population de"nitely exists, but is negative. On all these atoms, the shape of the spin density corresponds to a 2p orbital. FurX thermore, on the central carbons C1 and C2, the spin density is not centered on these atoms, but is shifted backwards away from the midpoint of the central C}C bond (see Fig. 4). This point has been carefully analyzed [21] and is not an artifact of the data treatment. It represents the antibonding character of the SOMO.
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Fig. 4. Projection of the spin density on the plane of the TCNE molecule.
Table 2 Atomic spin populations in [TCNE]z\ Atom
Spin population
C1 C2
0.33 0.33
C3 C4 C5 C6
!0.05 !0.04 !0.03 !0.08
N3 N4 N5 N6
0.12 0.12 0.13 0.16
4. Discussion: the magnetic interactions in [Fe(Cp*2 )]z> [TCNE]z\ After having investigated separately the spin densities of the two moieties of [Fe(Cp*)]z> [TCNE]z\ , we can now check whether the di!erent models proposed to explain the intrachain magnetic interactions are relevant. Considering the geometry of the piling, as explained above, the orthorhombic unit cell is well de"ned
Fig. 5. Geometry of the [Fe(Cp*)]z>[TCNE]z\ alternance along the chain.
(a"10.606 As , b"16.184 As and c"14.597 As ) but the crystal structure of the compound is not well established, even at room temperature. The chains are parallel to the a-axis of the cell [5] and consist of alternating cations and disordered anions (see Fig. 5). Therefore, the relative orientation of the [TCNE]z\ anion embedded between the two Cp rings is not de"nite and di!erent geometries can occur, as in Fig. 6 where two of them (con"gurations A and B) are considered. Anyway, considering the spin densities which have been measured on each of the two moieties, it is clear that the direct exchange between [TCNE]z\ and the Cp planes of [Fe(Cp*)]z> means a direct exchange between the central carbons of [TCNE]z\ and the carbons of the Cp ring, the other atoms
J. Schweizer et al. / Physica B 297 (2001) 213}220
219
exchange is given by [23] j } "2k#4S, !! where k is the Coulombian exchange:
e k" 2!,# (1) ! (2)
2!,# (2) ! (1) , ! ! ! ! r where is the electron transfer:
Fig. 6. Two possible con"gurations for the [Fe(Cp*)]z> [TCNE]z\ piling.
being either too far away or carrying a too low spin density to contribute noticeably to the exchange. The spin density has been measured positive (spin population 0.33) on the central carbons of [TCNE]z\ and negative (spin population !0.005) on the Cp carbons. These signs are those proposed by the McConnell I mechanism where a negative exchange between spin densities of opposed signs results in a ferromagnetic coupling between the anions and the cations. We have, however, to check whether, with such spin densities, the value of the coupling in this model is compatible with the experimental value. The intrachain exchange J in the [FeCp*]z> z [TCNE] \ crystal was "rst assessed as 30 K [5], but this value has been reevaluated as it depends strongly on the model which is taken to analyze the data. For an Heisenberg model with no other interaction than the nearest-neighbor interactions, it has been estimated as 4.8 K. With longer distance interactions, including anion}anion and cation}cation interactions, a value of 3.0 K has been proposed [22]. The McConnell I mechanism relates the magnetic interactions between two ions [Fe(Cp*)]z> and [TCNE]z\ to the direct exchange which exists between all the pairs of atoms which interact significantly and which belong to the di!erent moieties. Here these pairs are formed by each of the two central carbons of [TCNE]z\ interacting with the overlapping Cp carbon of [Fe(Cp*)]z>. For each pair, in the case where each atom would carry the totality of the unpaired electron (s"), this
"
2!,# (1)H ! (1) ! ! and S the overlap integral: S"
2!,# (1) ! (1). ! ! As the contribution of the 2p orbital of each carbon to the molecular function is not one electron, but the coe$cient 2!,# or ! , the value of ! ! j } has to be multiplied by the product ( 2!,# ) ! ): !! ! ! j } "( 2!,# ) ! ) (2k#4S). !! ! ! We have calculated numerically this direct exchange for a pair of carbon atoms in a geometry represented in Fig. 7, where z is the distance (3.64 As ) between the TCNE and the Cp planes and where x depends on which carbon is considered and which is the con"guration of the piling. In this geometry, the negative overlap term 4S overcomes the positive Coulombian term 2k, resulting in negative values for j } . But as the two spin densities !! on C and on C are of opposite signs, this 2!,# ! exchange term is "nally positive. We have summed up, for each con"guration A and B, the contributions of the overlapping atoms to get a numerical value of J . We found very little di!erence between the two con"gurations: 0.59 K for con"guration A and 0.57 K for con"guration B. As the contributions of the di!erent pairs "nally average, this total value hardly depends on the con"guration. These results have to be compared to the 3.0}4.8 K estimated from the magnetic measurements. Therefore, the important point to be emphasized is the following: with the spin densities experimentally found on each of the two moieties of [Fe(Cp*)]z> [TCNE]z\, the direct Heitler}London spin exchange, which is put forward in the McConnell I mechanism and which anyway exists, gives the right sign but not the right order of magnitude for the intrachain magnetic exchange.
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References
Fig. 7. Geometry of the two carbon orbitals of atoms C and 2!,# C . !.
In conclusion, we can say that the strategy which was followed here, measuring independently the spin density of each of the two moieties of the [Fe(Cp*)]z> [TCNE]z\ compound was fruitful. We have shown that the signs of the spin populations are consistent with the McConnell I mechanism proposed by Kahn and his coworkers to explain the ferromagnetic interactions inside the [Fe(Cp*)]z> [TCNE]z\ chains. Furthermore, the values found for the spin populations in this investigation allowed to do a numerical calculation of the value of the intrachain exchange according to the McConnell I mechanism, a calculation which is not at all a theoretical ab initio calculation but a numerical application of the well}known expression for the Heitler}London spin exchange. We "nally concluded that this mechanism is partly responsible only for the magnetic interactions in this compound.
[1] J.S. Miller, A.J. Epstein, W.M. Rei!, Science 240 (1988) 40. [2] J.S. Miller, A.J. Epstein, W.M. Rei!, Chem. Rev. 88 (1988) 201. [3] J.S. Miller, A.J. Epstein, W.M. Rei!, Acc. Chem. Res. 21 (1988) 114. [4] J.M. Manriquez, G.T. Tee, R.S. McLean, A.J. Epstein, J. S. Miller; Science 252 (1991) 1415. [5] J.S. Miller, J.C. Calabrese, H. Rommelmann, S.R. Chittipeddi, J.H. Zhang, W.M. Rei!, A.J. Epstein, J. Am. Chem. Soc. 109 (1987) 769. [6] H.M. McConnell, Proc. R. A. Welch Foundation Chem. Res. 11 (1967) 144. [7] A.L. Tchougree!, I.A. Misurkin, Phys. Rev. B 46 (1992) 5357. [8] H.M. McConnell, Chem. Phys. 39 (1963) 1910. [9] C. Kollmar, M. Couty, O. Kahn, J. Am. Chem. Soc. 113 (1991) 7994. [10] C. Kollmar, O. Kahn, J. Chem. Phys. 96 (1992) 2988. [11] C. Kollmar, O. Kahn, Acc. Chem. Res. 26 (1993) 259. [12] J. BluK mel, N. Hebendanz, P. Hudeczek, F.H. KoK hler, W. Strauss, J. Am. Chem. Soc. 114 (1992) 4223. [13] M. Nakano, M. Sorai, Chem. Phys. Lett. 27 (1990) 169. [14] A. Zheludev, A. Grand, E. Ressouche, J. Schweizer, B.G. Morin, A.J. Epstein, D.A. Dixon, J.S. Miller, J. Am. Chem. Soc. 116 (1994) 7243. [15] A. Bencini, C. Carbonera, S. Golhen, E. Lelie`vre-Berna, L. Ouahab, J. PeH caut, Y. Pontillon, E. Ressouche J. Schweizer, C. R. Acad. Sci., to be published. [16] P. Le Margueres, L. Ouahab, S. Golhen, D. Grandjean, O. Pena, J.C. Jegaden, C.J. Gomez-Garcia, P. Delhaes, Inorg. Chem. 334 (1994) 5180. [17] P.J. Brown, J.C. Matthewman, The Cambridge Crystallography Subroutine Library, Rutherford Appleton Laboratory, RAL-93-009, February 1993. [18] J. Schweizer B. Gillon, in: Paul M. Lahti (Ed.), Magnetic Properties of Organic Materials, Marcel Dekker, New York, 1999, p. 449}473. [19] R.J. Papoular, B. Gillon, Europhys. Lett. 13 (1990) 429. [20] E. Ressouche, J. Schweizer, J. Neutron Res. 4 (1996) 15. [21] A. Zheludev, R.J. Papoular, E. Ressouche, J. Schweizer, in: G. Loupias, S. Rabii (Eds.), Extended abstracts of the Sagamore XI Conference on Charge, Spin and Momentum Densities, UniversiteH Pierre et Marie Curie, Paris, 1994, p. 20. [22] D.A. Dixon, A. Suna, J.S. Miller, A.J. Epstein, in: D. Gatteschi, et al., (Eds.), Magnetic Molecular Materials, Kluwer Academic, Dordrecht, 1991, p. 171. [23] O. Kahn, in: Molecular Magnetism, VCH, New York, 1993, p. 150.
Magnetic interactions and spin densities in molecular compounds: an example J. Schweizer *, S. Golhen, E. Lelie`vre-Berna, L. Ouahab, Y. Pontillon, E. Ressouche CEA-Grenoble, DRFMC/SPSMS, Laboratoire de Magne& tisme et Diwraction Neutronique, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France Laboratoire de Chimie du Solide et Inorganique Mole& culaire, UMR 6511, CNRS, Universite& de Rennes I, 35042 Rennes Cedex, France Institut Laue Langevin, rue des Martyrs, 156X, 38042 Grenoble Cedex 9, France
Abstract The discovery of ferromagnetism in the charge transfer salt [Fe(Cp*)]z>[TCNE]z\ has raised a lot of interest. The nature of this magnetic coupling was controversial. The group of Miller invoked a McConnell II mechanism, with con"guration interactions. Another view was given by Kahn and coworkers who proposed a coupling between spin carriers (McConnell I mechanism), implying a positive exchange due to an overlap between spin densities of opposed signs. In the "rst interpretation, there would be a positive spin density located on the carbon rings of the ferrocene, but in the second interpretation, this spin density should be negative. To clarify this mechanism, it was decided to investigate separately, by polarized neutron di!raction, the spin density of [TCNE]z\, associated with a nonmagnetic donor and the magnetization density of [Fe(Cp*)]z>, associated with a nonmagnetic acceptor. For [TCNE]z\, the measurement was straightfor ward: it was found that most of the spin density was located on the central carbon while a noticeable amount was delocalized on the terminal nitrogens. Several attempts to measure the magnetization density of [Fe(Cp*)]z> were unsuccessful due to a loss of symmetry on cooling. To overcome this di$culty, we have "nally measured the z magnetization density of [Fe(Cp*)] > in a crystal of space group P1 , where four of these ions are associated with the polyoxotungstate [SiW O ]\. We have found that the Fe atoms carry a moment of 2.0 and that the carbons of the rings carry !0.005$0.001 . The signs of these carbon spin populations are consistent with the McConnell I mechanism, but their magnitudes are too small to account for the experimental interactions. 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic interactions; Spin densities
1. Introduction The concern of chemists and physicists for molecular compounds increased abruptly in 1987 with
* Corresponding author. E-mail address: [email protected] (J. Schweizer).
the discovery by Miller et al. [1] of ferromagnetism in decamethylferrocenium tetracyanoethenide. This compound is the orthorhombic charge transfer salt [Fe(Cp*)]z>[TCNE]z\, built from linear chains of alternating metalloferrocenium donors D> and cyanocarbon acceptors A\ (Fig. 1). Each ion carries a spin , and the magnetic interactions in the crystal are strong enough to yield a Curie
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 8 5 9 - 0
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Fig. 1. The chain structure of the compound [Fe(Cp*)]z> [TCNE]z\.
temperature of 4.8 K [2,3]. Soon after that, other charge transfer materials were obtained along the same line with much higher Curie temperatures, as for instance the amorphous and unstable compound V[TCNE] CH Cl (¹ &400 K) [4]. It V W was then very important to understand the mechanism in these metallocenium}TCNE charge transfer salts and, to start with, in the compound [Fe(Cp*)]z>[TCNE]z\ itself. A "rst explanation, put forward by Miller et al. [5], proposed a McConnell II mechanism [6] to explain the positive coupling between the [Fe(Cp*)]z> and [TCNE]z\ ions along a chain: an admixture of the excited state [Fe(Cp*)]>> [TCNE]\\ in the [Fe(Cp*)]z>[TCNE]z\ ground
state. Due to the degeneracy of the [Fe(Cp*)]z> levels, this admixture could result in a ferromagnetic coupling. Along this line, Tchougree! et al. [7] attributed the ferromagnetism to a positive interaction between the d electrons of the cation with the electrons back-transferred from [TCNE]z\ to the empty orbitals of [Fe(Cp*)]z>, with a posit ive density on these orbitals. Another explanation, based on an earlier idea of McConnell [8] (the so-called McConnell I mechanism) was proposed by Kahn and coworkers [9}11]: in [Fe(Cp*)]z>, the spin density is localized mainly on the Fe(III) ion, but, induced by spin polarization, some density of opposite sign exists on the Cp rings which face the TCNE molecules. The ferromagnetic coupling, which exists between the [Fe(Cp*)]z> and the [TCNE]z\ units, would result from the negative Heitler}London spin exchange due to the overlap between the Cp rings and the TCNE atoms. The positive sign of the global interaction in this model would be the consequence of the negative sign of the spin density on the Cp rings. The sign of the spin density on the ligand orbitals has been looked at by NMR, but in a rather indirect way [12]. Actually, as the paramagnetic signal shift on the carbon atoms is very small, it is very di$cult to assess a sign for their spin density. It was then necessary to measure the signal shifts on carbon atoms separated by two bonds ( positions) from the system in the substituted systems [(iPrCp) Fe]> and [(tBuCp )Fe]> and to com pare to that of [(EtMe Cp) ]>. This comparison concluded that a negative sign exists on the ligand of the orbitals. The sign of the spin density on the Cp rings of [Fe(Cp*)]z>[TCNE]z\ being a key point in choos ing which of the two models is at the origin of the ferromagnetism in the chains, it was decided to measure it directly by polarized neutron di!raction (PND). Such experiments are performed with a single crystal at very low temperature, below or above ¹ , with a strong magnetic "eld applied to the sample. In the present case, several attempts were made to cool down a single crystal, but each time, the crystal broke down. Actually, an X-ray investigation [5] showed that, though an orthorhombic unit cell is well determined at room
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temperature, the crystal structure cannot be well de"ned: some atomic disorder exists at this temperature. Speci"c heat measurements [13] showed that the compound undergoes two transitions on cooling, at 282 and 249 K. These transitions correspond probably to a reduction of the atomic disorder. It results that a nice orthorhombic crystal at room temperature is neither orthorhombic nor single crystal at low temperature, which prevents the expected neutron investigation from being performed. As a result of this impossibility, a new strategy has been decided: to measure the spin density separately on each of the two moieties [TCNE]z\ and [Fe(Cp*)]z>, associated, respectively, in a charge transfer salt with a nonmagnetic donor D> and a nonmagnetic acceptor A\. These investigations should allow to "gure out which are the spin densities which interact in [Fe(Cp*)]z>[TCNE]z\ and what is the mechanism which is responsible for the ferromagnetic coupling. The present paper accounts for this study. The "rst step of this process, the determination of the spin of [TCNE]z\ on a single crystal of [Bu N]z>[TCNE]z\ went very well and has been published elsewhere in detail [14], but the second step, on the [Fe(Cp*)]z> radical, turned out to be much more tricky and, after several failures, has been just achieved [15]. We shall start with a report of this recent measurement, review the main results of the [TCNE]z\ study, "gure out the magnetic interactions in the light of these results and "nally compare with ab initio calculations. z 2. Magnetization density in [Fe(Cp* 2 )] >
The low-temperature neutron study of the [Fe(Cp*)]z> radical turned out to be very di$cult to perform. First a salt, [Fe(Cp*)]z>[SbF ]\, with nonmagnetic [SbF ]\ was selected. The crystals are orthorhombic at room temperature, but structural transitions occur on cooling and, at low temperature, the crystals break down and are no longer orthorhombic. Afterwards, we tried [Fe(Cp*)]z> [PF ]\ which is monoclinic at room temperature. But here also, below 80 K, the structure becomes triclinic and the samples at low temperatures were no longer single crystals.
215
At this point of the investigation, we considered that the Fe(Cp*) molecule had an unfair tendency for atomic disorder at room temperature and another tendency to reduce this disorder at low temperatures, which results on cooling in crystal transitions with symmetry lowering and crystal breaking. In this case, the only possibility to keep a crystal single, down to the helium temperature, was to choose a crystal which is already triclinic at room temperature and which has no symmetry to lose. Therefore, we decided to measure the magnetization density of [Fe(Cp*)]z> in a crystal where four of these ions are associated with the polyoxotungstate [SiW O ]\, a crystal whose space group is already P1 at room temperature. The synthesis of the compound and the crystal and magnetic properties are reported in Ref. [16]. In this compound, only [Fe(Cp*)]z> is magnetic and the susceptibility follows a Curie}Weiss law with a very small negative value of the Curie temperature. In the triclinic structure, which is centric, the polyoxotungstate [SiW O ]\ anions have the -Keggin structure and are located at the origin of the cell. There are two independent [Fe(Cp*)]z> units in the asymmetric cell, the axes of which are almost parallel to one other and parallel to the a-axis of the cell (see Fig. 2). During the crystal growth, we noticed that besides the triclinic crystals (lattice constants at room temperature: a"14.247 As , b"15.003 As , c"15.418 As , "63.263, "83.413 and "69.773), two other crystal forms were present: monoclinic I and II. We were able to grow large single crystals of the triclinic form. We selected the largest one (15 mm) and glued it in order to have the common axis of the two [Fe(Cp*)]z> cations vertical. With this crystal, we performed two low-temperature neutron experiments: with unpolarized neutron to measure the nuclear structure factors F 's and with polarized neutrons to , measure the magnetic structure factors F 's. + The nuclear structure experiment was performed on the lifting counter di!ractometer D15 of the ILL at a temperature of 10 K. At this temperature the
Lattice constants at room temperature: monoclinic I: a"28.807 As , b"15.085 As , c"31.085 As , "117.013; monoclinic II: a"15.923 As , b"15.063 As , c"25.863 As , "96.393.
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of the ILL, also with a lifting detector, at a temperature of 4 K. The beam, of wavelength 0.843 As , was polarized vertically in the `upa and the `downa directions successively. A 4.6 T "eld, provided by a cryomagnet, was applied in the `upa direction, parallel to the common axis of the two [Fe(Cp*)]z> cations, and we measured the #ipping ratios (R"I>/I\) of 245 independent Bragg re#ections. Considering that the #ipping ratios are connected to the structure factors F 's and F 's by the follow, + ing relation:
Fig. 2. The crystal structure of the compound 4[Fe(Cp*)]z> [SiW O ]\.
lattice constants are the following: a"13.902 As , b"14.901 As , c"15.306 As , "62.643, "82.133 and "69.963. The integrated intensities of 2672 unique re#ections with a wavelength of 1.174 As were measured. The intensities have been corrected for absorption using the Cambridge Crystallography programme [17] with a linear absorption coe$cient of 1.90 cm\. It was not possible to get a good re"nement of the crystal structure, and particularly good values for the thermal parameters. Actually, the structure is centric, but the [SiW O ]\ anions which are located on the center of symmetry of the cell are not centric themselves. This leads to a statistical disorder of the anions. Therefore, to get the set of nuclear structure factors F 's necessary to process the polarized neu, tron experiment (see the following text), instead of determining these values from the re"ned crystal structure, we got them directly as the square roots of the measured intensities. The structure re"nement was only used to determine the normalization factor and the sign # or ! of the structure factor. The magnetic structure experiment was performed on the polarized neutron di!ractometer D3
F #2 sin F F #sin F , + +, R" , F !2 sin F F #sin F , , + + where is the angle between the scattering vector and the vertical axis, the determination of the F 's , as explained before and the measurement of the R's provided a measure of the F 's. + To be complete, the magnetization of the compound was measured in the same conditions as for the polarized neutron experiment: ¹"4 K and a magnetic "eld of 4.6 T applied along the common axis of the two [Fe(Cp*)]z> molecules. A magnetiz ation of 8.11 per cell was found, that is 2.03 per [Fe(Cp*)]z> molecule, which corresponds to the magnetic structure factor of re#ection (0,0,0). Altogether, we got 246 experimental F 's which + represent a fairly good set of data. The magnetic structure factors F (hkl) being the + Fourier coe$cients of the periodic spin (magnetization) density, this distribution can be obtained by an inversion process. There are di!erent ways to do it [18]. We have "rst applied the maximum entropy method which retrieves this density without any assumption on the atomic positions of the magnetic atoms [19,20]. A projection of the magnetization density along the b-axis of the cell is represented in Fig. 3. As expected, the magnetization is well localized on the two Fe atoms, but no density is found elsewhere. In particular, it is too weak to be detected by this method on the carbon atoms. A second approach is to use an atomic model [18]. What we have done is to determine the coe$cients of a Hartree}Fock type of magnetic moG lecular wave function constructed as a sum of atomic orbitals on the iron and the carbon atoms: " . G G G
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217
Table 1 Atomic spin populations (moments) in [Fe(Cp*)]z> Atom Fe1 (spin#orbit) Fe2 (spin#orbit) Ccp Cme m G Magnetization
m
G
1.932(18) 2.024(18) !0.005(1) 0.008(1) 8.03(8) 8.11(5)
They are the sum of a spin and an orbit contribution. The moments (or spin populations) on the carbons are weak, but signi"cant: negative on the Cp rings and positive and larger for the methyls. 3. Spin density in [TCNE]z\
Fig. 3. Projection of the magnetization density along the b-axis of 4[Fe(Cp*)]z>[SiW O ]\.
To allow for both positive and negative densities, the magnetization (spin) density is expanded as m(r)" m
, G G G G where the atomic moments m can be negative, with G absolute values which are the squares of the coe$cients . These coe$cients were re"ned to "t the G experimental F 's. For the Fe atoms, di!erent or+ bitals were tried. The orbitals of the carbon $ atoms were taken as p . Due to their weak values, X all the moments of the Cp rings, chemically equivalent but crystallographically inequivalent, were constrained to be equal. This constraint also stood for the methyl carbons. The results of the re"nement are reported in Table 1. The best re"nement was obtained for an orbital e (d , d ), which V\W VW means that the distribution around the irons is very anisotropic. The magnetic moments found on atoms Fe1 and Fe2 are, as expected, almost equal.
As this work has already been published in detail [14], we shall report here only the main results. The investigation was carried out on a [Bu N]> [TCNE]z\ single crystal, at a temperature of 1.8 K, with a "eld of 4.6 T applied successively along the [0, 1, 0] and the [1, 0, 1 ] directions of the crystal. The #ipping ratios of 211 Bragg re#ections were measured and allowed the reconstruction of the spin density maps, both by the maximum entropy method and by the multipole expansion. A projection of the density on the plane of the molecule is represented in Fig. 4. The spin populations, are reported in Table 2. As expected, the spin density exists only on the [TCNE]z\ anion. On this radical, most of the density is carried by the central carbons C1 and C2, but quite a noticeable amount is delocalized on the four terminal nitrogen atoms. On the intermediate carbons (C3}C6), a spin population de"nitely exists, but is negative. On all these atoms, the shape of the spin density corresponds to a 2p orbital. FurX thermore, on the central carbons C1 and C2, the spin density is not centered on these atoms, but is shifted backwards away from the midpoint of the central C}C bond (see Fig. 4). This point has been carefully analyzed [21] and is not an artifact of the data treatment. It represents the antibonding character of the SOMO.
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Fig. 4. Projection of the spin density on the plane of the TCNE molecule.
Table 2 Atomic spin populations in [TCNE]z\ Atom
Spin population
C1 C2
0.33 0.33
C3 C4 C5 C6
!0.05 !0.04 !0.03 !0.08
N3 N4 N5 N6
0.12 0.12 0.13 0.16
4. Discussion: the magnetic interactions in [Fe(Cp*2 )]z> [TCNE]z\ After having investigated separately the spin densities of the two moieties of [Fe(Cp*)]z> [TCNE]z\ , we can now check whether the di!erent models proposed to explain the intrachain magnetic interactions are relevant. Considering the geometry of the piling, as explained above, the orthorhombic unit cell is well de"ned
Fig. 5. Geometry of the [Fe(Cp*)]z>[TCNE]z\ alternance along the chain.
(a"10.606 As , b"16.184 As and c"14.597 As ) but the crystal structure of the compound is not well established, even at room temperature. The chains are parallel to the a-axis of the cell [5] and consist of alternating cations and disordered anions (see Fig. 5). Therefore, the relative orientation of the [TCNE]z\ anion embedded between the two Cp rings is not de"nite and di!erent geometries can occur, as in Fig. 6 where two of them (con"gurations A and B) are considered. Anyway, considering the spin densities which have been measured on each of the two moieties, it is clear that the direct exchange between [TCNE]z\ and the Cp planes of [Fe(Cp*)]z> means a direct exchange between the central carbons of [TCNE]z\ and the carbons of the Cp ring, the other atoms
J. Schweizer et al. / Physica B 297 (2001) 213}220
219
exchange is given by [23] j } "2k#4S, !! where k is the Coulombian exchange:
e k" 2!,# (1) ! (2)
2!,# (2) ! (1) , ! ! ! ! r where is the electron transfer:
Fig. 6. Two possible con"gurations for the [Fe(Cp*)]z> [TCNE]z\ piling.
being either too far away or carrying a too low spin density to contribute noticeably to the exchange. The spin density has been measured positive (spin population 0.33) on the central carbons of [TCNE]z\ and negative (spin population !0.005) on the Cp carbons. These signs are those proposed by the McConnell I mechanism where a negative exchange between spin densities of opposed signs results in a ferromagnetic coupling between the anions and the cations. We have, however, to check whether, with such spin densities, the value of the coupling in this model is compatible with the experimental value. The intrachain exchange J in the [FeCp*]z> z [TCNE] \ crystal was "rst assessed as 30 K [5], but this value has been reevaluated as it depends strongly on the model which is taken to analyze the data. For an Heisenberg model with no other interaction than the nearest-neighbor interactions, it has been estimated as 4.8 K. With longer distance interactions, including anion}anion and cation}cation interactions, a value of 3.0 K has been proposed [22]. The McConnell I mechanism relates the magnetic interactions between two ions [Fe(Cp*)]z> and [TCNE]z\ to the direct exchange which exists between all the pairs of atoms which interact significantly and which belong to the di!erent moieties. Here these pairs are formed by each of the two central carbons of [TCNE]z\ interacting with the overlapping Cp carbon of [Fe(Cp*)]z>. For each pair, in the case where each atom would carry the totality of the unpaired electron (s"), this
"
2!,# (1)H ! (1) ! ! and S the overlap integral: S"
2!,# (1) ! (1). ! ! As the contribution of the 2p orbital of each carbon to the molecular function is not one electron, but the coe$cient 2!,# or ! , the value of ! ! j } has to be multiplied by the product ( 2!,# ) ! ): !! ! ! j } "( 2!,# ) ! ) (2k#4S). !! ! ! We have calculated numerically this direct exchange for a pair of carbon atoms in a geometry represented in Fig. 7, where z is the distance (3.64 As ) between the TCNE and the Cp planes and where x depends on which carbon is considered and which is the con"guration of the piling. In this geometry, the negative overlap term 4S overcomes the positive Coulombian term 2k, resulting in negative values for j } . But as the two spin densities !! on C and on C are of opposite signs, this 2!,# ! exchange term is "nally positive. We have summed up, for each con"guration A and B, the contributions of the overlapping atoms to get a numerical value of J . We found very little di!erence between the two con"gurations: 0.59 K for con"guration A and 0.57 K for con"guration B. As the contributions of the di!erent pairs "nally average, this total value hardly depends on the con"guration. These results have to be compared to the 3.0}4.8 K estimated from the magnetic measurements. Therefore, the important point to be emphasized is the following: with the spin densities experimentally found on each of the two moieties of [Fe(Cp*)]z> [TCNE]z\, the direct Heitler}London spin exchange, which is put forward in the McConnell I mechanism and which anyway exists, gives the right sign but not the right order of magnitude for the intrachain magnetic exchange.
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References
Fig. 7. Geometry of the two carbon orbitals of atoms C and 2!,# C . !.
In conclusion, we can say that the strategy which was followed here, measuring independently the spin density of each of the two moieties of the [Fe(Cp*)]z> [TCNE]z\ compound was fruitful. We have shown that the signs of the spin populations are consistent with the McConnell I mechanism proposed by Kahn and his coworkers to explain the ferromagnetic interactions inside the [Fe(Cp*)]z> [TCNE]z\ chains. Furthermore, the values found for the spin populations in this investigation allowed to do a numerical calculation of the value of the intrachain exchange according to the McConnell I mechanism, a calculation which is not at all a theoretical ab initio calculation but a numerical application of the well}known expression for the Heitler}London spin exchange. We "nally concluded that this mechanism is partly responsible only for the magnetic interactions in this compound.
[1] J.S. Miller, A.J. Epstein, W.M. Rei!, Science 240 (1988) 40. [2] J.S. Miller, A.J. Epstein, W.M. Rei!, Chem. Rev. 88 (1988) 201. [3] J.S. Miller, A.J. Epstein, W.M. Rei!, Acc. Chem. Res. 21 (1988) 114. [4] J.M. Manriquez, G.T. Tee, R.S. McLean, A.J. Epstein, J. S. Miller; Science 252 (1991) 1415. [5] J.S. Miller, J.C. Calabrese, H. Rommelmann, S.R. Chittipeddi, J.H. Zhang, W.M. Rei!, A.J. Epstein, J. Am. Chem. Soc. 109 (1987) 769. [6] H.M. McConnell, Proc. R. A. Welch Foundation Chem. Res. 11 (1967) 144. [7] A.L. Tchougree!, I.A. Misurkin, Phys. Rev. B 46 (1992) 5357. [8] H.M. McConnell, Chem. Phys. 39 (1963) 1910. [9] C. Kollmar, M. Couty, O. Kahn, J. Am. Chem. Soc. 113 (1991) 7994. [10] C. Kollmar, O. Kahn, J. Chem. Phys. 96 (1992) 2988. [11] C. Kollmar, O. Kahn, Acc. Chem. Res. 26 (1993) 259. [12] J. BluK mel, N. Hebendanz, P. Hudeczek, F.H. KoK hler, W. Strauss, J. Am. Chem. Soc. 114 (1992) 4223. [13] M. Nakano, M. Sorai, Chem. Phys. Lett. 27 (1990) 169. [14] A. Zheludev, A. Grand, E. Ressouche, J. Schweizer, B.G. Morin, A.J. Epstein, D.A. Dixon, J.S. Miller, J. Am. Chem. Soc. 116 (1994) 7243. [15] A. Bencini, C. Carbonera, S. Golhen, E. Lelie`vre-Berna, L. Ouahab, J. PeH caut, Y. Pontillon, E. Ressouche J. Schweizer, C. R. Acad. Sci., to be published. [16] P. Le Margueres, L. Ouahab, S. Golhen, D. Grandjean, O. Pena, J.C. Jegaden, C.J. Gomez-Garcia, P. Delhaes, Inorg. Chem. 334 (1994) 5180. [17] P.J. Brown, J.C. Matthewman, The Cambridge Crystallography Subroutine Library, Rutherford Appleton Laboratory, RAL-93-009, February 1993. [18] J. Schweizer B. Gillon, in: Paul M. Lahti (Ed.), Magnetic Properties of Organic Materials, Marcel Dekker, New York, 1999, p. 449}473. [19] R.J. Papoular, B. Gillon, Europhys. Lett. 13 (1990) 429. [20] E. Ressouche, J. Schweizer, J. Neutron Res. 4 (1996) 15. [21] A. Zheludev, R.J. Papoular, E. Ressouche, J. Schweizer, in: G. Loupias, S. Rabii (Eds.), Extended abstracts of the Sagamore XI Conference on Charge, Spin and Momentum Densities, UniversiteH Pierre et Marie Curie, Paris, 1994, p. 20. [22] D.A. Dixon, A. Suna, J.S. Miller, A.J. Epstein, in: D. Gatteschi, et al., (Eds.), Magnetic Molecular Materials, Kluwer Academic, Dordrecht, 1991, p. 171. [23] O. Kahn, in: Molecular Magnetism, VCH, New York, 1993, p. 150.