High-frequency ESR and frequency domain magnetic resonance spectroscopic studies of single molecule magnets in frozen solution

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1 High-frequency ESR and frequency domain magnetic resonance spectroscopic studies of single molecule magnets in frozen solution F. El Hallak, 1 J. van Slageren, 1, * J. Gómez-Segura, 2 D. Ruiz-Molina, 2 and M. Dressel Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D Stuttgart, Germany 2 Institut de Ciència de Materials de Barcelona (CSIC), Campus Universitari, ES-08193, Bellaterra, Catalonia, Spain Received 7 December 2006; revised manuscript received 16 January 2007; published 7 March 2007 Frozen solutions of the single molecule magnet Mn 12 Piv Piv=pivalate or trimethylacetate are studied by magnetization and magnetic resonance investigations. ac magnetic susceptibility measurements show that the system is stable in solution. Interestingly, the barrier and prefactor for the thermally activated magnetization relaxation are the same as in the solid state. This means that this system is not influenced by its surroundings, in contrast to other Mn 12 derivatives. The zero-field-splitting spin Hamiltonian parameters of Mn 12 Piv in solution are determined by magnetic resonance spectroscopy methods to be very similar to those in the solid state. By these methods, it is also possible to distinguish between truly dissolved and precipitated species, which is not possible by magnetization measurements. DOI: /PhysRevB PACS number s : Xx, g, Fc, r INTRODUCTION Since their discovery in the early 1990s, 1 single molecule magnets SMMs have been the focus of many investigations, where one of the main interests has been the fact that these molecular exchange-coupled transition metal clusters show slow relaxation of the magnetization and magnetic hysteresis of purely molecular origin. 2,3 The origin of this effect, namely, the combination of a large spin ground state and a sizable Ising-like anisotropy, was clear almost from the beginning. This combination leads to an energy barrier toward inversion of the magnetic moment with a value of D S 2, where D is the second-order axial zero-field-splitting ZFS parameter in the simplest ZFS spin Hamiltonian Ĥ=DŜ 2 z. The thermally activated nature of the magnetization relaxation process leads to an Arrhenius-type temperature dependence of the relaxation time, i.e., = 0 exp E/k B T. 3 In the years since, many details of the magnetization relaxation process have also been elucidated, e.g., the coupling to phonons and the occurrence of underbarrier quantum tunneling of the magnetization, 4 6 the importance of the nuclear spins, 7,8 and the presence of local symmetry lowering 9,10 The molecular origin of the slow relaxation phenomenon and the absence of significant intermolecular interactions were proven by magnetometric studies in which the molecules were dissolved in solvents or dispersed in polymer matrices Surprisingly, the number of studies on SMMs in solution or in polymer matrices is rather limited, and they deal with only one type of SMM, namely, the Mn 12 clusters. Apart from the mentioned magnetometry investigations, only a number of magnetic circular dichroism studies have been published, but no other spectroscopic measurements. More detailed studies in which the SMMs are separated from each other would be interesting for a number of reasons. First of all, there are indications that intermolecular interactions play a significant role in the details of the magnetization relaxation process: the width of the zero-field step in the magnetic hysteresis curve of the best-known SMM Mn 12 Ac Ac=acetate is much smaller Oe than what would be expected on the basis of the calculation of the dipolar field created by neighboring molecules 520 Oe. 20 This was interpreted on the basis of collective effects playing a significant role. 20 Intermolecular dipolar interactions were shown to lead to the onset of ferromagnetic ordering. 21 Furthermore, the relaxation time measured in solution or polymer dispersion is generally much shorter than in crystalline samples. Thus, comparing measurements of the magnetization decay in zero field on single crystalline samples of Mn 12 Ac and on a frozen acetonitrile-dichloromethane-toluene 3:1:1 solution of the same, the latter relax an order of magnitude faster. 12 A smaller difference of a factor of 2 was observed comparing polycrystalline samples and frozen solutions of Mn 12 Ac, 13 where interestingly the difference disappears in applied magnetic fields. Finally, dispersing Mn 12 Pr Pr=propionate into polystyrene also leads to a lowering of the relaxation time as shown by the decrease in temperature of the maximum of the out-of-phase component of the 500 Hz ac magnetic susceptibility from T max =6.4 K in the polycrystalline sample to T max =4.2 K for a 3.6 wt % sample. 11 At first sight, these results are surprising as the relaxation process is assumed to be of solely molecular nature: purely molecular properties of SMMs should be the same irrespective of the surroundings of the molecules. Intermolecular dipolar interactions of the kind described above should not lead to a decrease of the relaxation time. However, changing the surroundings of the SMM molecules can cause two further types of change. First of all, the acoustic phonon frequencies may change, as they depend on the stiffness of the medium and its density. This will have a large influence on the relaxation time as this is proportional to the fifth power of the speed of sound in the material: = 0 exp E/k B T = 2 3 q4 c 5 / V 10 2 E/S 3. Here is the density of the material, c is the speed of sound, S is the spin, and V 10 is the spin-phonon coupling matrix element for the transition from the M S =±1 to M S =0 states. 3,22 Second, the modification of surroundings can change the spin Hamiltonian parameters: a distortion of the molecular geometry can change the axial zero-field splitting, leading to a change in the energy barrier height, but also lead to transverse anisotropy in second order, which is absent or virtually absent /2007/75 10 / The American Physical Society

2 EL HALLAK et al. in most Mn 12 derivatives in the crystalline state. This transverse anisotropy favors quantum tunneling of the magnetization, which leads to a lower effective energy barrier. One phenomenon that has also been observed to occur on dissolving Mn 12 molecules is that of isomerization. In this isomerization the Jahn-Teller elongation axis of one of the eight Mn 3+ ions, which are almost parallel in the normal complex, can tilt by ,23 25 This leads to a decrease in the axial ZFS, because the cluster ZFS tensor is a linear combination of the single ion ZFS tensors, 26 meaning that the direction of the single ion ZFS tensors is as important as their magnitudes. In addition the resulting symmetry lowering introduces a second-order transverse anisotropy. The combined result is a drastic decrease of the energy barrier, and hence this isomer is also known as the fast relaxing species. In addition, decreasing the crystallinity of the sample leads to an increase in the size of the distribution of the ZFS parameters and an increase in the second-order transverse anisotropy with a concurrent increase in magnetization relaxation rate. 27,28 The size of crystallites also influences the relaxation rate. The aim of our investigations was to study the influence of the molecular surroundings of Mn 12 SMMs on their magnetic properties. To this end we performed magnetometric and magnetic resonance studies on Mn 12 Piv in frozen solutions, where Piv stands for pivalate or trimethylacetate O 2 CCMe 3, which was chosen because of its high solubility in organic solvents. 29 Apart from magnetic hysteresis and ac susceptibility studies, we performed high-frequency electron spin resonance HFESR and frequency domain magnetic resonance spectroscopic 30 FDMRS measurements to characterize the magnetic anisotropy of Mn 12 Piv in frozen solutions in detail. The ultimate aim is to study the magneticdipolar interaction between the Mn 12 Piv molecules by means of the magnetic resonance line shape and linewidth. In the solid state, the distribution in a local effective dipolar field is expected to lead to inhomogeneous line broadening and therefore a Gaussian line shape. Diluting the molecules will diminish the dipolar interaction between the molecules as the third power of the average distance between them. This process should be accompanied by a gradual change of the line shape from Gaussian to Lorentzian as well as a narrowing of the line, as the linewidth becomes more and more determined by the natural lifetime, assuming that other distributions in the sample play a minor role. The FDMRS technique is more suited to these studies than HFESR, since the former does not rely on the application of an external magnetic field, which can distort the line shape. 31 EXPERIMENTAL SECTION The Mn 12 Piv was synthesized as previously described, 29 and characterized by elemental analysis and uv-visible and ir spectroscopic techniques. Magnetization and ac magnetic susceptibility oscillating field amplitude 1 G measurements were performed using a Quantum Design XL7 superconducting quantum interference device SQUID magnetometer. Frequency domain magnetic resonance spectroscopy and high-frequency ESR measurements were carried out on a FIG. 1. Color online Frequency-domain magnetic resonance spectra recorded on a pressed powder pellet mass mg of Mn 12 Piv at various temperatures as indicated symbols together with the fit drawn line using the parameters given in the text. No external field was applied H=0. previously described spectrometer, 30 in combination with an Oxford Instruments Spectromag 4000 split coil optical magnet. The samples for the frozen solution measurements were carefully filtered and inserted in a home-built cell with two 1-mm-thick quartz windows, and subsequently cooled down. The glass-forming solvent mixture used was toluenedichloromethane 10:1. The spectra were fitted using our simulation program written in MATHEMATICA. 32 RESULTS AND DISCUSSION The Mn 12 Piv complex was reported to have an energy barrier toward relaxation with a magnitude E=58 K, 29 very similar to that of the Mn 12 Ac parent compound E=62 K. 2 However, the ZFS spin Hamiltonian parameters are not known. Therefore we recorded FDMRS spectra on a pressed polycrystalline pellet of the complex at various temperatures in zero magnetic field Fig. 1. The shallow oscillation in the baseline is due to Fabry-Pérot-like interference of the radiation within the plane parallel pellet. 30 In addition to that three magnetic resonance lines can be observed at 9.96, 8.49, and 7.16 cm 1, respectively. The fit of the spectra Fig. 1 shows that the spin ground state is S=10 as in most Mn 12 derivatives. 3 The resonance lines can then be assigned to the M S = ±10 to M S = ±9 transition, the M S =±9toM S = ±8 transition, and the M S =±8 to M S = ±7 transition within that ground state, respectively. Using the spin Hamiltonian Ĥ =DŜ 2 z +B 0 4 Ô 0 4 +B 4 4 Ô 4 4, where the last two terms are the fourthorder axial and transverse ZFS, respectively, 33 the following parameter values Table I were found: D= cm 1 and B 0 4 = cm 1. The fits are not sensitive to the magnitude of B 4 4, and this parameter was therefore excluded. The obtained values are close to those reported for Mn 12 Ac average values D= 0.46 cm 1, B 0 4 = cm 1, 2 and very close to those of a derivative with one extra methylene group in its carboxylate ligand O 2 CCH 2 CMe 3 =t-buac Bu=butyl instead of O 2 CMe 3 =Piv which has a D value of cm 1, and B 0 4 = cm These results indicate that the Mn 12 O 12 core is very robust and that even the ZFS, which is extremely sensitive to small changes

3 HIGH-FREQUENCY ESR AND FREQUENCY DOMAIN TABLE I. Zero-field-splitting parameters obtained for Mn 12 Piv in various surroundings together with literature values for similar systems. D cm 1 B 4 0 cm 1 FWHM linewidth cm 1 Microcrystalline Mn 12 Piv Dissolved Mn 12 Piv Precipitated Mn 12 Piv Microcrystalline Mn 12 Ac a c Microcrystalline Mn 12 tbuac b a From Ref. 2. b From Ref. 34. c From Refs. 35 and 36. in the molecular geometry, is not affected by exchanging carboxylate ligands. Clearly, the line shape is well approximated using a Gaussian function, which indicates that the linewidth is determined by inhomogeneous distributions in the sample, which can be due to a distribution in magnetic dipolar fields or in the ZFS parameters themselves. The Gaussian linewidth is =0.14 cm 1, which corresponds to a full width at half maximum FWHM of 0.33 cm 1. This linewidth is slightly larger than that reported for Mn 12 Ac using the same measurement technique FWHM=0.23 cm 1. 20,35,36 ac susceptibility field amplitude 1 G measurements, performed on a 3.93 mm frozen solution of the sample in toluene-dichloromethane 10:1 v/v, show a strong frequency-dependent out-of-phase signal Fig. 2, which is a clear indication of superparamagnetic type slow relaxation of the magnetization. These results show that the Mn 12 Piv molecules stay intact in solution. The fit of the Arrhenius plot = 0 exp E/k B T of the relaxation time =1/ 2 ac yields an energy barrier of E= K and a preexponential factor of 0 = s. Performing the same measurement on a polycrystalline sample of Mn 12 Piv yields values of E= K and a prefactor of 0 = s, which are the same within experimental error. In contrast to what has been previously observed for other Mn 12 complexes, the Mn 12 Piv molecule seems to be completely insensitive to its surroundings in terms of both the energy barrier E as well as 0, which is a measure for the phonon-induced transitions between M S states on the same side of the energy barrier. The latter observation means that the acoustic phonon frequencies do not change significantly on going from the microcrystalline to the frozen solution sample. In addition to the peak in the range between 4 and 7 K, a second, much smaller peak is observed around 2 K, which is due to the Jahn-Teller isomer species see above. 14 The percentage of isomerized molecules, determined by the ratio of the T values at the maxima of both peaks, is virtually the same both in the solution 5.67% and in the microcrystalline 5.34% samples. This shows that in our studies the Jahn-Teller isomerization process does not occur in solution, in contrast to previous solution studies. 14,15 Magnetic hysteresis measurements were performed on the same 3.93 mm frozen solution Fig. 3. Measurements on a powder sample were performed for comparison. Below T 3 K, the sample shows clear magnetic hysteresis, which proves the integrity of the molecule even in solution. Even at FIG. 2. Color online In-phase top and out-of-phase bottom components of the ac susceptibility amplitude 1 G measured on a 3.93 mm solution of Mn 12 Piv in toluene-dichloromethane 10:1 at different frequencies as indicated. FIG. 3. Color online Magnetic hysteresis curve recorded on a a 3.93 mm solution of Mn 12 Piv in toluene-dichloromethane 10:1 at different temperatures as indicated

4 EL HALLAK et al. FIG. 4. Color online FDMRS spectra recorded on 21.3 and 9.2 mm frozen solutions of Mn 12 Piv in toluene-dichloromethane 10:1 at 5 K together with a fit of the higher-concentration spectrum with two Lorentz curves with linewidths of 0.39 lower frequency and 0.32 cm higher frequency. FIG. 5. Color online High-frequency ESR spectra =303 GHz recorded on 21.1 and 2.8 mm frozen solutions of Mn 12 Piv in toluene:dichloromethane 10:1 at 5 K which show the two resonances at H=0, and ±0.54 T due to the dissolved and precipitated species, respectively. The intensities have been normalized to the zero-field peak intensity. In these spectra the field is not modulated; hence the transmission is measured rather than the first derivative commonly obtained in ESR measurements. 7 T the magnetization does not saturate, because the fraction of molecules that are oriented largely perpendicular to the magnetic field experience the magnetic field in their hard planes, where saturation is achieved only at very high magnetic fields. With decreasing temperatures, the coercive field of the hysteresis curve increases, since the magnetization relaxation slows down. The other notable feature is the step in the hysteresis curve at zero field, the size of which increases with increasing temperature. This step is due to quantum tunneling of the magnetization as shown below. 2 The step size at the lowest employed temperature of 1.8 K amounts to about 20% of the total magnetization for both the frozen solution 19% of the total magnetization at zero field and the powder sample 21%. This indicates that the contribution of the fast relaxing species only ca. 5% of the total sample to this step size is minor even at the employed temperature, the relaxation of the fast relaxing species is fast compared to the measurement time scale, hence all of the fast relaxing species is expected to relax at the first level crossing, i.e., at zero field. The other steps that are observed in single crystals at regular longitudinal field intervals are absent due to the different orientations of the molecules leading to different effective longitudinal fields for each molecule at a certain applied field. This shows that even when the dipolar interaction between the molecules is diminished by a factor of ca. 130 for this concentration, the quantum tunneling process is still possible. In fact, since the step sizes are the same for the frozen solution sample and the powder sample the influence of the dipolar interaction on the tunneling process is negligible. To investigate the ZFS and the resonance line shape, FDMRS spectra were recorded on frozen solutions of Mn 12 Piv in toluene-dichloromethane 10:1 at two different concentrations of 21.3 and 9.2 mm Fig. 4. The spectra are normalized, i.e., divided by the spectrum recorded at high temperature T=50 K, in this case to get rid of the Fabry- Pérot-like interference as well as artifacts. 30,32 The former spectrum shows four magnetic resonance lines, two strong ones at 9.66 and cm 1 as well as two weaker ones at 8.55 and 8.34 cm 1. These two groups exhibit different temperature dependences in their intensities: while the higherfrequency lines become weaker with temperature, the intensity of the low-frequency lines increases on heating to 30 K. Within the higher-frequency set, the relative intensity of the two lines is concentration dependent: when the concentration is lowered, the lower-frequency line 9.66 cm 1 decreases in intensity with respect to the higher-frequency one cm 1. These observations can be explained as follows: in frozen solution two species exist, one that is truly dissolved which corresponds to the high-frequency line and one that is a microcrystalline precipitate the low-frequency line formed as the solution is cooled. This is supported by the fact that the low-frequency line disappears on lowering the concentration and also by quenching the solution in liquid nitrogen prior to insertion into the helium cryostat. It is further confirmed by HFESR measurements at various concentrations Fig. 5. The resonance frequency =303 GHz has been chosen such that the resonance due to the dissolved species lies at zero field. The resonance belonging to the precipitated species is located at H= ±0.54 T. At the higher concentration of 21.1 mm two peaks are clearly observed, while at the lower concentration of 2.8 mm the amount of precipitated species is virtually nil. In the FDMRS spectra Fig. 4, the two intense lines are then the M S = ±10 to M S = ±9 transitions of the two species, respectively, while the weaker lines correspond to the M S =±9 to M S = ±8 transitions. The observation of two resonance lines for each species allows the determination of the two parameters in the spin Hamiltonian Ĥ=D Ŝ z 2 +B 4 0 Ô 4 0 for each species which yields the following values Table I : D = cm 1, B 4 0 = cm 1 for the dissolved species, and D= cm 1, B 4 0 = cm 1 for the precipitate. The line shapes are neither clearly Lorentzian nor Gaussian. The lines of the higher-concentration spectrum corresponding to the M S = ±10 to M S = ±9 transitions of the two species were fitted by a sum of two Lorentzian lines, which gave a FWHM linewidth of 0.32 cm 1 for the dissolved species very close to that of the polycrystalline

5 HIGH-FREQUENCY ESR AND FREQUENCY DOMAIN sample, 0.33 cm 1, and a slightly larger one for the precipitated species 0.39 cm 1. The width of the line corresponding to the dissolved species is concentration independent, and hence probably determined by distributions in the ZFS parameters. CONCLUSION In conclusion, we have described measurements on frozen solutions of Mn 12 Piv. The results show that this member of the Mn 12 family is very robust and does not change properties on dissolving the molecules, in contrast to previous studies on other Mn 12 derivatives. Quantum tunneling of the magnetization was observed in solution, showing that collective processes do not necessarily play a role. However, the precipitation of the compound from solution at higher concentration on cooling prevented the study of a series of samples over a wide concentration range and other matrices such as polymers have to be employed. These results show the sensitivity of magnetic resonance spectroscopy as a local probe: it is capable of distinguishing between different species that vary only slightly in their spin Hamiltonian parameters, in this case the solvated and precipitated species. These cannot be distinguished by magnetization measurements. ACKNOWLEDGMENTS We acknowledge the financial support of the Deutsche Forschungsgemeinschaft DFG. D.R.-M. thanks the Ministerio de Educación y Ciencia Grant No. MAT C *Electronic address: slageren@pi1.physik.uni-stuttgart.de 1 R. Sessoli, D. Gatteschi, A. Caneschi, and M. A. Novak, Nature London 365, D. Gatteschi and R. Sessoli, Angew. Chem., Int. Ed. 42, D. Gatteschi, R. Sessoli, and J. Villain, Molecular Nanomagnets Oxford University Press, Oxford, D. A. Garanin and E. M. Chudnovsky, Phys. Rev. B 56, F. Luis, J. Bartolome, and J. F. Fernandez, Phys. Rev. B 57, M. N. Leuenberger and D. Loss, Phys. Rev. B 61, P. C. E. Stamp and I. S. Tupitsyn, Chem. Phys. 296, A. 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