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Cite this: Dalton Trans., 2011, 40, 6371
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Magnetic relaxation in basic iron(III) carboxylate [Fe3 O(O2 CPh)6 (H2 O)3 ]ClO4 ·py† Anastasia N. Georgopoulou, Yiannis Sanakis* and Athanassios K. Boudalis* Received 24th February 2011, Accepted 18th April 2011 DOI: 10.1039/c1dt10323g The magnetic properties of the antiferromagnetic basic iron(III) carboxylate [Fe3 O(O2 CPh)6 (H2 O)3 ]ClO4 ·py are studied by magnetic susceptometry and electron paramagnetic resonance spectrocopy. Ac susceptometry under moderate external magnetic fields reveals magnetic relaxation at liquid helium temperatures. The magnetic properties of polynuclear transition metal clusters (PTMCs) constitute a field of intense research in the last decades.1 Among the simplest PTMCs are the antiferromagnetic trinuclear clusters of general formula {M3 O}n+ where M = FeIII (S = 5/2), CrIII (S = 3/2), CuII (S = 1/2).2 Some of these (MIII = FeIII ) have shown relevance to bioinorganic systems,3,4 while recent studies have dealt with their relevance to quantum computing.5,6 Apart from the detailed characterization of the static magnetic properties, the determination of the dynamic magnetic behavior of such clusters is of special importance; the present work refers to the study of a member of this family of crystallographically imposed C 3 symmetry, the basic iron carboxylate [Fe3 O(O2 CPh)6 (H2 O)3 ]ClO4 ·py (1).7 The magnetic properties of these clusters are governed by the isotropic Heisenberg-Dirac-van Vleck Hamiltonian (eqn (1)) with i, j = 1, 2, 3.
∑ J Sˆ Sˆ
Hˆ HDvV = −2
ij
i
j
(1)
i, j
These studies further revealed that the two St = 1/2 states are separated. This separation requires that the J ij values are not equal. No magnetic susceptibility studies have been reported for 1. In the present work we have performed static magnetic susceptibility measurements that confirm (i) the antiferromagnetic interactions and (ii) the differentiation of the J ij value constants. X-band electron paramagnetic resonance spectroscopy indicates the contribution of antisymmetric exchange interactions. The magnetic relaxation properties of 1 were studied by alternating current susceptibility measurements. In the presence of moderate magnetic fields, out-of-phase signals are observed at liquid helium temperatures. Ac susceptibility studies, as a function of temperature and frequency, were performed to determine the mechanisms of magnetic relaxation. To the best of our knowledge, this is the first report where ac susceptibility measurements can be used to study the magnetic relaxation of a trinuclear cluster with an S = 1/2 ground state. Static magnetic properties Dc magnetic susceptibility studies (Fig. 1) revealed that the magnetic behavior of 1 is typical of basic iron(III) carboxylates. The c M T product at 300 K is 4.97 cm3 mol-1 K, much lower than the theoretically expected value for three non-interacting S = 5/2 spins (13.14 cm3 mol-1 K). Upon cooling it decreases to 0.26 cm3 mol-1 K at 2 K, below the theoretically expected value
The crystal structure of 1 reveals an equilateral configuration with the metal ions in a common octahedral environment and equal metal–metal distances.7 Magneto-structural correlations would suggest that the exchange coupling constants J ij in Hamiltonian (1) are all equal. For a coupled system comprising three halfinteger spin centers there are two states which are characterized by total spin St = 1/2. In the case of the equilateral configuration, these two states are degenerate and constitute the ground state of the system for J ij < 0. Incoherent inelastic neutron scattering (IINS) studies7 were consistent with antiferromagnetic coupling. NCSR “Demokritos”, Institute of Materials Science, Patriarchou Grigoriou & Neapoleos, 15310, Aghia Paraskevi Attikis, Greece. E-mail: tbou@ ims.demokritos.gr,
[email protected]; Fax: +30 210 6503365; Tel: +30 210 6503346 † Electronic Supplementary Information (ESI) available: Materials, experimental and theoretical methods; powder XRD and variable-temperature ac data (Fig. S1–S3); fitting parameters to ac data (Tables S1–S2). See DOI: 10.1039/b000000x/
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Fig. 1 c M T vs. T data of complex 1 (1 T) and best-fit curve (solution A) according to the model described in the text.
Dalton Trans., 2011, 40, 6371–6374 | 6371
for a S = 1/2 global spin (0.38 cm3 mol-1 K), suggesting possible antisymmetric exchange interactions [see below]. Interpretation of the magnetic behavior of 1 using an equilateral (1J) model was unsuccessful, thus the isosceles 2J model was used, according to the following spin Hamiltonian: ˆ = -2[J(Sˆ 1 Sˆ 2 + Sˆ 1 Sˆ 3 ) + J¢Sˆ 2 Sˆ 3 ] H
(2)
Fits were carried out over the 24–300 K range, to avoid the influence of the effects manifested at lower temperatures. The g0 parameter was fixed to 2. As is often the case for basic iron(III) carboxylates, two solutions were derived from the fits, one with |J| > |J¢| (J = -22.9 cm-1 , J¢ = -19.1 cm-1 , sol. A) and one with |J| < |J¢| (J = -20.2 cm-1 , J¢ = -25.0 cm-1 , sol. B). The dc magnetic susceptibility measurements cannot reveal the presence of the different magnetic configurations demonstrated in the IINS studies7 and the EPR results (see below). Therefore these values should be viewed as the average over a distribution of configurations. In any case, these average values are close to those determined by the IINS studies.8 EPR spectroscopy The S = 1/2 character of the ground state is further supported by X-band EPR spectroscopy. In Fig. 2 we show the spectrum from a fine powder sample of 1. The spectrum consists of a relatively sharp peak at g ª 2.0 (assigned to g ) and a multitude of derivative figures at higher magnetic fields in the 500–700 mT region (assigned to g^ ), consistent with S = 1/2 species with axial anisotropy. The spectrum can be reproduced by incorporating five S = 1/2 systems exhibiting axial anisotropy with g = 2.0027 and g^ = 1.260 (19%), 1.195 (16%), 1.135 (15%), 1.092 (30%), 1.040 (20%). These low g values are in qualitative agreement with the low c M T at liquid helium temperatures (see ESI†).
Whereas g is insensitive to AE, remaining equal to the intrinsic g0 of the individual ions, g^ depends strongly on this term and more specifically on the relationship between |d| and D, where D is the separation of the two S = 1/2 states.10 Distributions on these quantities lead to substantial broadening at g^ .3,11 The sharp peak at g ª 2.0 is attributed to g . This value is consistent with FeIII (S = 5/2), for which g0 (ª g0^ ) ª 2.0. The portion of the spectrum that corresponds to g^ exhibits resolved contributions from different axial signals. Following the methodology described previously3,11 we estimate that, for a D in the range of 18–28 cm-1 , the axial anisotropy may result for |d| in the range of 0.5–2.0 cm-1 , of the order of values found for similar complexes.3,10 The IINS studies for 1 indicated the presence of at least two different distinct populations of trimers characterized by different D.7,8 The present EPR results indicate the existence of more than two distinct populations, which are probably beyond the resolution of the IINS experiments (~10 cm-1 ). Dynamic magnetic properties The dynamic magnetic properties of 1 were studied by ac magnetic susceptibility measurements at liquid helium temperatures. At zero magnetic field no out-of-phase signals were observed. However, in the presence of external magnetic fields, out-of-phase signals (Fig. S2, ESI†) were observed up to ~5 K. Indicative data at 750 G are shown in Fig. 3.
Fig. 3 c M ¢ vs T and c M ¢¢ vs T data at various frequencies, under a magnetic field of 750 G.
Fig. 2 4.2 K X-band EPR (9.43 GHz) experimental spectrum (black line) from a powder sample of 1. The red line is a theoretical simulation assuming the contribution of five spectra shown separately (see text).
The axial anisotropy with g^ < 2.0 of the S = 1/2 ground state of the antiferromagnetic triangular clusters is due to the presence of antisymmetric exchange (AE), given by the Hamiltonian in eqn (3).9,10 ˆ AE = d·[Sˆ 1 ¥ Sˆ 2 + Sˆ 2 ¥ Sˆ 3 + Sˆ 3 ¥ Sˆ 1 ] H 6372 | Dalton Trans., 2011, 40, 6371–6374
(3)
The dependence of the susceptibility on the frequency of the oscillating field is described by the generalized Debye model12
c (w ) = c S +
cT − c S 1 + (iwt )1−a
(4)
where c T and c S are the isothermal (w→0) and adiabatic (w→•) susceptibilities, respectively, t is the characteristic relaxation time at the temperature of the experiment and a is a parameter ranging between 0 and 1, related to the dispersion of the relaxation times of the system (a = 0 for a monodisperse system and a = 1 for a system with an infinitely wide dispersion of relaxation times). This This journal is © The Royal Society of Chemistry 2011
model was used to simulate the c M ¢ and c M ¢¢ vs. frequency data for various temperature and magnetic field values. Representative plots are shown in Fig. 4. The determined parameters are listed in Table S1 and S2, ESI†. Represenative Cole–Cole plots are also shown in Fig. S3, ESI†. A non-zero a suggests a distribution of magnetic configurations and is in qualitative agreement with the presence of multiple species revealed by EPR spectroscopy.
Fig. 4 c M ¢ vs f and c M ¢¢ vs f data at various temperatures, under a field of 500 G. The solid lines are fits to equations S1 and S2, respectively.
The dependence of the relaxation time on temperature in the form of lnt vs 1/T is shown in Fig. 5 for three values of H DC . Thermally activated processes are inferred. The deviation from linearity indicates a complex dependence of the relaxation times with temperature. In order to model the data we have assumed that the relaxation time t is given by eqn (5). Δ
1 1 1 1 − = + = e kT + bT n t t orb t n t 0
(5)
t orb refers to an Orbach mechanism involving relaxation of the S = 1/2 ground state through an excited spin manifold lying at D above the ground state. We further assumed that this excited state corresponds to the second S = 1/2 state. Taking together the
Fig. 5 Fits of the relaxation times determined for various temperatures, to the composite model described in the text.
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Table 1 Fitting parameters for the data of Fig. 5 (eqn (5)) H (G)
t 0 (/10-10 s)
b (/103 s-1 K-n )
n
250 500 750
0.56 ± 0.16 2.0 ± 0.4 2.0 ± 0.7
3.5 ± 3.3 1.3 ± 0.3 2.7 ± 1.3
2.31 3.36 2.66
results from the static magnetic susceptibility measurements, EPR and IINS studies, an average D = 23 cm-1 was adopted. t n refers to a mechanism in which the relaxation time follows an empirical power law with temperature. The obtained parameters are listed in Table 1. Recently, it was shown that the magnetic relaxation properties of a ferromagnetically coupled tricopper cluster could be studied by ac susceptibility in the presence of moderate magnetic fields.13 Herein, we show that the same methodology can be applied for an antiferromagnetically coupled triferrric cluster with a ground state with the smallest possible spin value (S = 1/2). The temperature dependence of the relaxation times may be modelled on the assumption of two mechanisms. One is an Orbach mechanism involving relaxation through the excited S = 1/2 state and dominates at T > 4 K. The pre-exponential factor t 0 is in the expected range for paramagnetic relaxation.1 The second was approximated by an empirical power law and is more efficient below 4 K. Such a mechanism might be a combination of Raman, direct, or phonon bottleneck (PB) processes.14 Similar complex temperature dependence of the relaxation has been observed in the ferromagnetically coupled Cu3 complex.13 It has also been observed in mononuclear FeII (S = 2) complexes, exhibiting slow relaxation.15 The value of n for 1 may be suggestive for PB,16 however further work is required to fully elucidate its relaxation mechanism.
Acknowledgements We thank Dr Vasilis Psycharis for acquisition and interpretation of the powder XRD data.
References 1 D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets, Oxford University Press, New York, 2006. 2 R. D. Canon and R. P. White, Prog. Inorg. Chem., 1988, 36, 195. 3 A. K. Boudalis, Y. Sanakis, F. Dahan, M. Hendrich and J.-P. Tuchagues, Inorg. Chem., 2006, 45, 443. ¨ 4 M. Hogbom and P. Nordlund, FEBS Lett., 2004, 567, 179. 5 G. Mitrikas, Y. Sanakis, C. P. Raptopoulou, G. Kordas and G. Papavassiliou, Phys. Chem. Chem. Phys., 2008, 10, 743. 6 M. Trif, F. Troiani, D. Stepanenko and D. Loss, Phys. Rev. B, 2010, 82, 045429. 7 F. E. Sowrey, C. Tilford, S. Wocadlo, C. E. Anson, A. K. Powell, S. M. Bennington, W. Moontfrooij, U. A. Jayasooriya and R. D. Cannon, J. Chem. Soc., Dalton Trans., 2001, 862–866. 8 IINS data in ref. 7 were modelled assuming the presence of two distinct triangular configurations. For one, with isosceles geometry, J = -28.5 and J¢ = -25.6 cm-1 and the other with scalene one J 1 = -18.9, J 2 = -23.9 and J 3 = -21.4 cm-1 . See ESI for a discussion. 9 B. S. Tsukerblat, M. I. Belinskii and V. E. Fainzil’berg, Sov. Sci. Rev. B, 1987, 9, 337–481. 10 Y. V. Rakitin, Y. V. Yablokov and V. V. Zelentsov, J. Magn. Reson., 1981, 43, 288.
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11 Y. Sanakis, A. L. Macedo, I. Moura, J. G. Jose Moura, V. ¨ Papaefthymiou and E. Munck, J. Am. Chem. Soc., 2000, 122, 11855. 12 R. Sessoli and A. K. Powell, Coord. Chem. Rev., 2009, 253, 2328. 13 Y. Sanakis, M. Pissas, J. Krzystek, J. Telser and R. G. Raptis, Chem. Phys. Lett., 2010, 493, 185–190. 14 A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Dover Publications, Inc., New York, 1986.
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15 W. H. Harman, T. D. Harris, D. E. Freedman, H. Fong, A. Chang, J. D. Rinehart, A. Ozarowski, M. T. Sougrati, F. Grandjean, G. J. Long, J. R. Long and C. J. Chang, J. Am. Chem. Soc., 2010, 132, 18115. 16 M. Orendac, L. Sedlakova, E. Cizmar, A. Feher, S. A. Zvyagin, J. Wosnitza, W. H. Zhu, Z. M. Wang and S. Gao, Phys. Rev. B, 2010, 81, 214410.
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