Spin relaxation in antiferromagnetic Fe–Fe dimers slowed down by anisotropic DyIII ions

Summary By using Mössbauer spectroscopy in combination with susceptibility measurements it was possible to identify the supertransferred hyperfine field through the oxygen bridges between DyIII and FeIII in a {Fe4Dy2} coordination cluster. The presence of the dysprosium ions provides enough magnetic anisotropy to “block” the hyperfine field that is experienced by the iron nuclei. This has resulted in magnetic spectra with internal hyperfine fields of the iron nuclei of about 23 T. The set of data permitted us to conclude that the direction of the anisotropy in lanthanide nanosize molecular clusters is associated with the single ion and crystal field contributions and 57Fe Mössbauer spectroscopy may be informative with regard to the the anisotropy not only of the studied isotope, but also of elements interacting with this isotope.


Introduction
The huge Ising-type magnetic anisotropy of many lanthanide ions, which can be controlled by designing the ligand field, can slow down the relaxation of magnetisation and can be an effective source for the modulation of properties of transition metal molecular magnets [1]. The anisotropy of the lanthanide is severely affected by the symmetry of the crystal field and it can be controlled by a suitable design of the ligand field environment [2,3]. Today, the orientation of the principal axes of the magnetization of the lanthanide ions in low-symmetry environments can be determined theoretically and experimentally [4][5][6][7][8][9]. For molecular magnetism the Dy III ion has proved to be the most attractive [4][5][6][7][8][9][10][11][12] not only because of its large flexibility regarding the interaction between the single-ion electron density and the crystal field environment, and its predicted hard anisotropy using simple ligand field considerations, but also because of its huge field dependence of the relaxation time [13].
Designing the ligand field environment can help to control the magnetic anisotropy of some of the later lanthanides [2,3], but this is less useful for the Dy III ion. The unpredictable behaviour and the strong dependence of magnetic anisotropy and orientation of the easy axis of the magnetization of the Dy III ion on very small changes in the ligand environment was predicted by ab-initio calculations [5]. But only recently, we have shown that such radical changes can also be seen experimentally. By using Mössbauer spectroscopy we have shown how minor changes in the electronegativity of the atoms in the ligand sphere and in the donor-acceptor nature of the substituents, and their position on the aromatic ring, can control the shape anisotropy of the Dy III ions and, thus, their interaction with the iron centres [14,15]. Moreover, the reported compounds [14,15] -with an antiferromagnetic coupling in the central iron dimer -show a very intriguing effect: the collapse of the magnetic hyperfine splitting under the effect of the external magnetic field. This apparently paradoxical behaviour reveals how complex and casesensitive the properties of the Fe-Ln clusters can be. One of the reasons for this effect may well be that the externally applied magnetic field can affect the ground state of Dy III by lowering the energy of the system: This can result in a change of the direction of polarization, and thus the shape anisotropy of the Dy III ion and its interaction with the iron centres can be controlled. This means that the Ln anisotropy can be influenced not only by altering crystal field, but also by an external source. But, surprisingly, this is not always the case. It seems that the structural aspect can prevail over the others. Here, we report how, contrary to reported Fe 2 Dy 2 compounds [14,15], the application of an external magnetic field does not always affect the ground state of the Dy III ion and its relaxation time. Two compounds [Fe 4 Ln 2 (μ 3 -OH) 2 (L) 4 ((CH 3 ) 3 CCOO) 6 (N 3 ) 2 ]·(solv) (Ln = Dy III , L = N-(n-butyl)diethanolamine, solv = 3(MeCN), 1, see below in Figure 1) and Ln = Y III , L = N-methyldiethanolamine, solv = phenol, 2) are magnetically and spectroscopically studied and their properties are compared.

Results and Discussion
Compound 1 crystallizes in the triclinic space group P−1 with Z = 2; each Fe 4 Dy 2 aggregate ( Figure 1) occupies a general site with no crystallographically imposed symmetry. The central core of the aggregate possesses a {Fe III 4 Dy 2 (µ 3 -OH) 2 (µ 3 -OR) 2 } architecture, in which two of the Fe III (Fe(1) and Fe (3)) and the two Dy III ions, together with the two hydroxo ligands, are arranged in the well-known "butterfly" shape. The two Fe III ions form the "wingtips" and the Dy III ions define the "body" of the butterfly, with the two hydroxo ligands each bridging a FeDy 2 triangle. The typical butterfly topology has a planar Fe 2 Dy 2 unit, with the two (µ 3 -OH) bridges on opposite faces of the Fe 2 Dy 2 plane. In contrast, in 1 the Fe 2 Dy 2 butterfly is not planar; the two FeDy 2 triangles show a dihedral angle of 43.8°, and the two hydroxo ligands are on the same face of the Fe 2 Dy 2 unit. Each of the four Fe III ions in the aggregate is chelated by a fully-deprotonated (n-butyl)diethanolamine (nbdea) ligand. Of those chelating Fe(1) and Fe(3), one alkoxo arm bridges an Fe-Dy edge of the butterfly, while the other forms a (μ 3alkoxo) bridge between a Fe-Dy edge in the butterfly and a further Fe III centre (Fe (2) or Fe(4)). The nbdea ligands chelating Fe(2) and Fe(4) then each form two (µ2-alkoxo) bridges, to a Dy atom and to an Fe atom in the butterfly. Peripheral ligation is provided by four µ-pivalato ligands in their common syn,syn bridging mode. Two further unidentate pivalates each coordinate to a dysprosium, with the non-coordinated carboxylate oxygen atom accepting a hydrogen bond from a (μ 3 -OH) ligand. The coordination is completed by two azido anions coordinated to the outer iron atoms (Fe(2) and Fe(4)). All four Fe ions are six-coordinate with distorted octahedral geometries, while the Dy III ions are eight-coordinate with coordination polyhedra that may best be described as distorted bicapped trigonal prisms. The molecular structure of the Fe 4 Y 2 aggregate in 2 is very similar to that of the Fe 4 Dy 2 in 1, and differs only in the replacement of the n-butyl groups in 1 by methyl groups and the replacement of Dy III by Y III .
At temperatures higher than 20 K the Mössbauer spectra (MS) of 1 are paramagnetic ( Figure 2) and show two symmetric quadrupole doublets with average isomer shifts, δ, of 0.42 and 0.46 mm/s and quadrupole splittings, ΔE Q , of 0.51 and 1.08 mm/s, respectively, ( Table 1). This is typical for high spin, S = 5/2, Fe III ions of iron-oxo proteins and other relevant model compounds [16][17][18]. The presence of two doublets with different quadrupole splittings (ΔE Q ) indicates two Fe sites with different coordination spheres, in agreement with both the molecular structure and bond length distortion (BLD) calculations: Fe(1) and Fe(3) = 3.95 and 3.82, Fe(2) and Fe(4) = 3.30 and 3.19, respectively [19]. Consequently, we constrained the area ratio of doublets to 1:1. The low temperature (30 K) MS (not given here) for 1 is broad and shows a small onset of relaxation at an intermediate rate superimposed on the absorption peaks at the centre of the spectrum. At 3 K (Figure 2), a magnetic spectrum is obtained, indicating that the spin-relaxation time is slow with respect to the Mössbauer time scale. The spectrum has been fitted with two sextets with the parameters listed in Table 1. The best fits for the zero-field spectrum at 3 K were achieved through a free iteration method with two sextets with the effective hyperfine fields B eff = 23.5 and 23.2 T, respectively, at the nuclei.
When applying an external magnetic field one cannot see significant changes in the values of the hyperfine parameters. The spectra represent a superposition of two sextets with an area ratio 1:1. When the applied magnetic field is increased a behaviour that is typical for antiferromagnetically coupled molecular clusters can be seen [20,21]. The MS for 1 at 3 K, under the application of an external field (B appl = 1, 3 and 5 T), are shown in Figure 2. Since the high-spin Fe III ions are considered isotropic, it is expected that the local spins will align along (parallel or antiparallel) the direction of the applied field. Information about such an alignment can be derived from the relative intensity of the Δm = 0 and Δm = 1 lines of the sextet, which yield information about the angle θ between B eff and the γ-rays. It is important to note that upon application of the external field the intensity of the Δm = 0 lines does not change considerably (θ is almost constant) as it is to be expected for systems dominated by internal magnetic anisotropies. This indicates that even though the net moment of the cluster may be aligned along the direction of the applied magnetic field, the local magnetic moments tend to align approximately perpendicular to it. It appears that for 1 an applied field much larger than 5 T would be necessary to align the local magnetic moments completely along the direction of the field. An obvious change of the magnetization direction is suggested by the variation of the angle φ between the principal axis (V zz ) of the electrical field gradient (EFG) and B int . This angle can be calculated from the magnetic spectra according to the formula  Table 1 for the fitting parameters. a Relative to α-Fe at room temperature; b For magnetically-split spectra the quadrupole shifts, ε = ½ΔE Q (3cos 2 φ − 1). φ -Euler angle between the internal hyperfine field, B int , and the principal axis (V zz ) of the electrical field gradient. The quadrupole shifts are easy to observe from the magnetic spectra as a difference in the splitting of 1 and 2 and 5 and 6 iron(III) lines. δ -isomer shift, ΔE Q -quadrupole splitting, θ -angle between B eff and the direction of the γ-rays. The statistical errors are given in parentheses. The relative areas for the doublets and sextets have been constrained to a 1: , where ε are the quadrupole shift values determined from the magnetically ordered spectra and ΔE Q are the quadrupole splitting values determined from the paramagnetic spectra. A clear variation of the φ values for both sextets is observed from 36° at 3 K (without a magnetic field) to 39° at 3 K (magnetic field 5 T) for Fe 1,3 and from 70° at 3 K (without a magnetic field) to 62° at 3 K (magnetic field 5 T) for Fe 2,4 , respectively.
Another peculiarity observed from the magnetic spectra under an applied magnetic field is that one sextet is showing decreasing B eff values regardless of the increased B appl , while the second one shows an increased value for B eff . This is a microscopic confirmation of the magnetic structure with Fe 1,3 and Fe 2,4 moments being antiferromagnetically coupled. The decrease and increase of the B eff values at the nuclei with an increasing value of applied magnetic field is proof that the directions of the effective magnetic flux densities at the iron nuclei of iron have either the same or the opposite direction as the applied magnetic field. However, the difference in the change in the measured effective magnetic field for Fe 1,3 and Fe 2,4 sites is very different: 5.1 T and 1.2 T, respectively. The change of B eff with B appl for the Fe 1,3 sites is close to 1.0, which is simply the applied field. This means that B int (≈23.4 T) for these iron centers has a maximum (saturation) value. Contrary to Fe 1,3 , the change for Fe 2,4 is very small. We anticipate an almost identical B int for all sites and the above mentioned difference is due to a different reaction of the iron moments from the spin-coupled pairs to the applied field. It seems that the Fe 1,3 moments tend to align themselves parallel to the applied field, but those of Fe 2,4 have a spin-flop tendency into the plane perpendicular to the applied magnetic field. This could also be an explanation for the opposite evolution of the θ values (one is increasing and the other one is decreasing) with increasing B appl . Since the applied external magnetic field is perpendicular to the direction of γ-rays, the θ values should increase. The same conclusion can be made from the evolution of the Euler angles with B appl . While the angle φ for Fe 1,3 is almost invariable (it changes from 36° to 39°), a more visible and opposite change from 70° to 62° can be seen for Fe 2,4 , together with a tendency to smaller angles, i.e., angles that deviate less from the direction perpendicular to B appl , or parallel to the γ-rays, respectively. Such unusual features can be attributed to the presence of an antisymmetric exchange in the diferric units. But such conclusions should be treated with caution, because of the unknown role of the very anisotropic Dy III ions in this exchange.
To shed some light on the interaction inside of these clusters, the direct-current (dc) magnetic susceptibility of 1 has been measured in an applied magnetic field of 0.1 T between 300 and 1.8 K (Figure 3). At room temperature, the χ M T value of 43.44 cm 3 ·K·mol −1 is close to the expected value of 28.33 cm 3 ·K·mol −1 for two uncoupled Dy III ions (S = 5/2, L = 5, 6 H 15/2 , g = 4/3) plus the value obtained for the iron fragments from the Y III analogue. As shown in Figure 3, χ M T decreases with lowering temperatures in the range from 300 to 8 K and then increases sharply to reach a maximum of 33.00 cm 3 ·K·mol −1 at 1.8 K, which may be because of an intramolecular ferromagnetic interaction. If the Fe-Fe (Fe(1)-Fe (2)  Interestingly, the obtained J value for 2 is rather close to the value, approx. −8.3 cm −1 , obtained from the Gorun and Lippard [22] empirical relationship between J in diiron(III) complexes with oxide, hydroxide and alkoxide bridges and the parameter P that corresponds to the half of the length of the shortest Fe-O-Fe-bridge in the complex. This is also supported by the value J ≈ −8.7 cm −1 , which was determined by using another magnetostructural correlation originally developed for dimers that utilizes both the Fe-O distances and the Fe-O-Fe angles [23] and was later on improved and extended to polynuclear topologies [24,25]. In conclusion, all these experimental and theoretical data unambiguously prove that iron ions from the dinuclear units in compounds 1 and 2 are antiferromagnetically coupled.
Additionally, the Mössbauer spectrum in an applied external magnetic field of 5 T has been measured for 2 ( Figure 4). It confirms the diamagnetic ground state for the Fe 2 units. The simulation parameters were the field at the nucleus B eff = 5.0 T, ΔE Q = 0.80 mm/s, δ = 0.47 mm/s, and the asymmetry parameter η = 0.95. The experimental data fit very well with B eff = B appl , i.e., there is no noticeable contribution to the magnetic hyperfine interaction other than the applied field .
Mössbauer spectroscopy senses the internal hyperfine interactions near the nucleus of the studied isotope. There are four contributions that determine the internal hyperfine field B int of an iron atom: B fc (the Fermi contact interaction), B ls (the orbital momentum of the 3d electrons at the nucleus), B dd (the dipole field originating from the electronic shell) and B latt (the lattice contribution). In both studied compounds the last three contributions can be neglected. The main contribution only results from B fc . But in an applied external magnetic field this contribution can also be ignored for compound 2. The Mössbauer spectrum of compound 2 ( Figure 4) shows that even under an applied field of 5 T, there is no orientation of the zero spin of the cluster and each antiferromagnetically coupled dimer is still relaxing fast on the Mössbauer time scale. As a result, a typical MS for an iron ion with zero ground state is obtained. However, this does not mean that this contribution can be neglected for compound 1, too. This raises the question that if the Fe 2 units in compound 1 are antiferromagnetically coupled as in compound 2, why is the internal field felt by the iron nuclei so big to give a magnetic sextet? One contribution to the internal hyperfine field at the iron nuclei in compound 1 can result from the magnetic interaction with the anisotropic, magnetically aligned, Dy III ions, which provide enough magnetic anisotropy to "block" the hyperfine field experienced by the iron nuclei. Another contribution can be a supertransferred field from Dy III to Fe III ions. At this time we are not confident which of the two contributions prevails.
But even without invoking a large supertransferred hyperfine field and without ignoring the contribution of the Fermi contact to the field, it is quite possible to qualitatively understand the Mössbauer spectra of both 1 and 2. A determination of the zerofield splitting parameter for 1 would have been very useful, but it was not possible to determine. Depending on the sign of the zero field splitting parameter, D, in 1 at 3 K the iron(III) ions will be in a ground state that could be either |±5/2> or |±1/2>. If the relaxation between the positive and negative spin states becomes slow enough, the relaxation between the different M S states may still be rather fast. In this case the effective hyperfine field that is observed is the Boltzmann average of the fields associated with the |±5/2>, |±3/2>, and |±1/2> states, an average that may well be close to 23 T. This can explain why the internal field observed at 3 K, is 23 T and not 55 T, a value expected for S = 5/2, which will be in agreement with values obtained for oxides (≈11 T per S = 1/2) [26]. Such an unusual slowdown of the relaxation may well be the result of an interaction of local Fe moments with the total magnetisation vector on the Dy III dimer. For compound 2, it is most probable that D is larger than zero and the ground state is |±1/2>. The reversal of the spin in this state, and hence of the hyperfine field, is very fast compared to the Mössbauer time scale and no hyperfine field is observed. Why is the relaxation fast? The relaxation in the |±1/2> state is particularly fast because it involves only a change of M S of ±1 between the |+1/2> and the |−1/2> ground states.
A further peculiarity is the different evolution of the magnetic spectra with the external magnetic field. In contrast to previously reported studies about Fe 2 Dy 2 clusters [6], in which the magnetic hyperfine splitting collapses under the application of an external magnetic field, in the case of 1 this applied field results in the total effective magnetic field decreasing for one sextet and increasing for the other. This confirms that the Fe 1 and Fe 2 , and Fe 3 and Fe 4 pairs are antiferromagnetically coupled. No collapse of the magnetic structure is observed. An explanation may lie in the different communication between Dy and Fe ions. Contrary to previously reported Fe 2 Dy 2 com-pounds, in which single Dy III ions are in close proximity to either side of the Fe 2 fragments, in compound 1 the Dy ions are on the same side and ferromagnetically cooperating with each other. This gives rise to a total ground spin state which cannot be affected by external applied magnetic field.
It is worth mentioning that compound 1 is a single molecule magnet. It displays an out-of-phase response to the blocking temperature 2.5 K (at 1500 Hz), which is characteristic of a slow relaxation of the magnetization ( Figure 5). The characteristic measuring time for Mössbauer spectroscopy is about 10 −7 s, whereas that for ac magnetic susceptibility measurements is typically in the range between 10 0 and 10 −4 s (i.e., ac frequencies of 1-1500 Hz). Because of their different time windows, 57 Fe Mössbauer spectroscopy and ac magnetic susceptibility measurements provide an apparently different view of the relaxation dynamic: If a slow relaxation can be seen in the magnetic data at very low temperatures (1.8-3.0 K), then an intermediate relaxation can already be seen in the Mössbauer spectra at 30 K. Therefore, an accurate comparative analysis of the data obtained from these two methods cannot be done. Conclusion This communication once more shows how additional, casesensitive information about the unpredictable lanthanide anisotropy can be gathered by using 57 Fe Mössbauer spectroscopy. Due to the strong anisotropy of Dy ions, the magnetic susceptibility measurements provide only averaged information about the magnetic behaviour inside the molecules and one cannot distinguish all interactions inside the complex molecules. Mössbauer spectroscopy, on the contrary, provides us with microscopic information about the metal-metal communication and the relaxation dynamics on specific centres, in this case Fe nuclei in the presence of very anisotropic Ln centers.
Having identified the nature of the interaction in compounds 1 and 2, it will be of interest to explore the influence of incorporating other anisotropic lanthanides to shed light on the complex magnetism of lanthanide based SMMs.

Experimental
Unless otherwise stated, all reagents were obtained from commercial sources and were used as received without further purification. All reactions were carried out under ambient conditions. Elemental analyses for C, H, and N were performed by using an Elementar Vario EL analyzer. IR spectra were measured on a PerkinElmer Spectrum One spectrometer as KBr disks. Mössbauer spectroscopy: The Mössbauer spectra were acquired using a conventional spectrometer in the constantacceleration mode equipped with a 57 Co source (3.7 GBq) in a rhodium matrix. Isomer shifts are given relative to α-Fe at room temperature. The sample was inserted inside an Oxford Instruments Mössbauer-Spectromag 4000 Cryostat, which has a splitpair superconducting magnet system for applied fields up to 5 T, with the field of the sample oriented perpendicular to the γ-ray direction. The sample temperature can be varied between 3.0 and 300 K.

Preparation of [Fe 4 Dy 2 (OH) 2 (nbdea) 4 (O 2 CCMe 3 ) 6 (N 3 ) 2 ]-
X-Ray crystallography: Data were measured on Stoe IPDS II (1) or IPDS I (2) image plate diffractometers using graphitemonochromated Mo Kα radiation, and were corrected for polarisation and absorption. Structure solution (direct methods) and full-matrix least-squares refinement against F 2 (all data) was carried out by using the SHELXTL software package [27]. All ordered non-H atoms were refined anisotropically; disordered atoms were refined with partial occupancy and geometrical restraints, either anisotropically with rigid-bond restraints or isotropically.