Magnetism of isolated Mn 12 single-molecule magnets detected by magnetic circular dichroism Observation of spin tunneling with a magneto-optical technique

We report magnetic and magneto-optical measurements of two Mn 12 si gle-molecule magnet derivatives isolated in organic glasses. Field-dependent magnetic circular dichroism ~MCD! intensity curves~hysteresis cycles! are found to be essentially identical to superconducting quantum interference device magnetization results and provide experimental evidence for the potential of the optical technique for magnetic characterization. Optical observation of magnetic tunneling has been achieved by studying the decay of the MCD signal at weak applied magnetic field.

Individual molecules that act as magnets are appealing from both fundamental scientific and technological points of view, especially given their potential as quantum computing components. 1 Much attention has focused on the family of molecules based on a dodecamanganese core, denoted generally as ͓Mn 12 O 12 (O 2 CR) 16 (H 2 O) x ͔S x (Rϭsubstituent, x ϭ3 -4, Sϭsolvent).These systems behave as singlemolecule magnets ͑SMM's͒, 2 but the vast majority of the previous studies on them have centered on crystalline materials.It is an intriguing and important challenge to investigate these molecules when they are isolated from each other, but since this is not currently feasible, we have chosen, in the interim, to study ensembles of molecules isolated from each other in inert matrices.On the other hand, the development of methods for measurement of magnetic and spin properties of isolated molecules is important when the detection limits of traditional superconducting quantum interference device ͑SQUID͒ instruments are reached.Key questions include what techniques can be used to study these phenomena and whether tunneling can be observed in isolated molecules using these other techniques.In order to answer these questions we have used two techniques, magnetic susceptibility and magnetic circular dichroism ͑MCD͒, and we will show that the magnetic and optical responses are essentially identical.
To a first approximation, the effective spin Hamiltonian for a Mn 12 SMM is where Dϭ0.55 K is the zero-field splitting parameter for the ground-state manifold and Sϭ10.HЈ contains terms that do not commute with S z and are responsible for tunneling between different M S states.Isolated molecules of Mn 12 Ac (RϭCH 3 ) and Mn 12 Bz (RϭC 6 H 5 ) can be obtained by dissolving them in noncoordinating organic solvents. 3MCD requires optical isotropy and transparency, so the solvents were selected according to their facility for forming strain-free, transparent glasses at cryogenic temperatures. 4Two mixtures were employed: ͑1͒ CH 2 Cl 2 :toluene ͑1:1 by volume͒ and ͑2͒ CH 3 CN:dmf ͑where dmfϭN,NЈ-dimethylformamide, 1:2 in volume͒.The molecular magnetic moments are so small that the torque imparted by applied magnetic fields up to 5ϫ10 4 Oe is not enough to orient the molecules, which therefore remain randomly oriented in the frozen glass.
Magnetic measurements were performed using a commercial rf-SQUID magnetometer ͑MPMS2͒, with applied magnetic fields up to 5ϫ10 4 Oe.Samples of 0.06 ml of 6-g/l solution were placed in a cylindrical Teflon container, which was sealed with a screw-on lid.The field dependencies of the magnetization for Mn 12 Ac and Mn 12 Bz in a glass of CH 2 Cl 2 :toluene (Mn 12 Ac/CH 2 Cl 2 :tol and Mn 12 Bz/CH 2 Cl 2 :tol) at Tϭ1.8 K are shown in Figs.1͑a͒  and 1͑b͒, respectively ͑gray curves͒.The lack of orientation prevents in this case observation of the steplike behavior in the magnetization hysteresis cycles seen at certain resonant fields and characteristic of tunneling. 5 quantitative description of the dynamics of the magnetization for a single molecule depends on the angle between the applied magnetic field and the molecule's easy axis of magnetization and can be expressed in terms of the differential equation where ␣ϭdH/dt is the magnetic field sweeping rate, M eq (H,T,) is the equilibrium magnetization, and ⌫(H,T,) is the relaxation rate that can be written as ⌫ ϭ 0 exp(ϪU eff /k B T). Here, 0 is the attempt frequency and U eff is the effective potential-energy barrier, which includes the conditions of resonance that also depend on .At very low temperatures, when only the M S ϭϮ10 levels are significantly populated, the equilibrium magnetization is closely approximated by The first term inside the brackets of Eq. ͑3͒ confers the tanh dependence that is typical paramagnetic behavior of an isolated pair of Zeeman levels, which is a good approximation for the low-temperature limit.The second ͑linear͒ term arises from misalignment of the easy axis of magnetization of the particles with the field, which causes mixing of states that differ by Ϯ1 in their M S values.In order to simplify the analysis of the data, the linear contribution to the magnetization has been subtracted from the results shown in Fig. 1.
The remaining part is sensitive to relaxation mechanisms and, at temperatures below the blocking temperature, gives rise to hysteresis.The steps seen near zero field in Fig. 1 were observed at all temperatures between 1.8 and 3 K.They are consistent with the existence of two molecular species with different effective energy barriers and therefore different relaxation rates and blocking temperatures.While the species with the higher temperature barrier is blocked in this temperature range, the other remains superparamagnetic and thus under-goes a rapid change of magnetization near zero field.This hypothesis is confirmed by the presence of two frequency dependent peaks in both components of the ac-magnetic susceptibility of Mn 12 Ac/CH 2 Cl 2 :tol and Mn 12 Bz/CH 2 Cl 2 :tol. 6he high-temperature blocking peak is usually placed between 3.5 and 6 K, while the low-temperature peak appears around 2 K.The low-temperature peak has also been observed in certain Mn 12 derivatives, where it is ascribed to Jahn-Teller distortions of the core. 7The height of the zerofield step depends on the fraction of molecules that undergo the fast relaxation mechanism, which is calculated from the ac-susceptibility peaks to be about 15% for Mn 12 Ac/CH 2 Cl 2 :tol and 20% for Mn 12 Bz/CH 2 Cl 2 :tol.Another contribution to the zero-field step arises from the fact that all molecules undergo resonant tunneling between spin states at zero field, irrespective of their orientation ͑see be-low͒, but this is very small in comparison with the superparamagnetic contribution seen here, and thus it can be considered as irrelevant.
MCD is the differential absorption of left and right circularly polarized light by a sample in longitudinal magnetic field, 8 and can be written as ⌬AϭA L ϪA R .It provides a powerful tool for studying molecular systems with degenerate electronic states.For orbitally nondegenerate paramagnetic species, the intensity of the MCD associated with a given transition depends on the degree of spin-orbit coupling and varies with magnetic field and temperature in a manner that is determined by the ground-and excited-state parameters, including g factors and zero-field splittings ͑ZFS͒. 9An analysis of MCD of Mn 12 Ac has been published recently, 10 wherein a quantitative description of the polarization of each optical transition is given.We have investigated the MCD of Mn 12 SMM's using a spectrometer that is described elsewhere. 11We show here that this spectroscopic technique is not only related with magnetization but permits effectively the same measurements as SQUID magnetometry, as it can be inferred by comparision of quantitative description of MCD shown by McInnes et al. with Eqs.͑2͒,͑3͒.
MCD spectra at Tϭ4.2 K are shown in Fig. 2. Four bands are observed for both Mn 12 Ac/CH 2 Cl 2 :tol and Mn 12 Bz/CH 2 Cl 2 :tol, but the change of solvents leads to significant differences.In CH 3 CN:dmf the ϳ19 700-cm Ϫ1 band almost disappears and there is a relative enhancement of the band at ϳ21 100 cm Ϫ1 .McInnes et al. 10 have described the MCD spectra for Mn 12 SMMs in the low-temperature limit with a simple model comprising B and C terms. 8B terms are linearly proportional to the field and are associated with diamagnetism in either the ground or excited state of the electronic transition.C terms are associated with ground-state paramagnetism and, in the limit of a two-level Zeeman system assuming that equilibrium thermal populations are maintained, have the same tanh dependence on the applied magnetic field as the magnetization shown in Eq. ͑3͒.
The magnetic-field dependencies of the MCD signals at 21 200 cm Ϫ1 are shown in Figs.1͑a͒ and 1͑b͒ for Mn 12 Ac and Mn 12 Bz in both CH 2 Cl 2 :tol and CH 3 CN:dmf glasses.Measurements were made using the same experimental conditions as for the SQUID magnetization loops.The MCD signal was measured continuously while changing the field at a rate of ␣ϭ19.6 Oe/s.By subtracting the linear B-term contributions, the MCD results can be directly compared with the SQUID magnetization data.As seen in Fig. 1, the hysteresis loops measured by the two methods are essentially identical.Moreover, as shown in Fig. 1͑c͒, the MCD cycle measured for the 19 700-cm Ϫ1 band of Mn 12 Ac/CH 2 Cl 2 :tol ͑which has been assigned polarization properties significantly different from those of the 21 200-cm Ϫ1 band 8 ͒ is superimposable on the 21 200-cm Ϫ1 curve of the same sample after the linear contributions have been subtracted.
Comparing the MCD hysteresis cycles measured at the same wavelength for Mn 12 Ac/CH 2 Cl 2 :tol and Mn 12 Ac/CH 3 CN:dmf ͓Fig.1͑a͔͒, we see that, for the latter, there is a huge increase of the zero-field step.In addition, the remnant magnetization at zero field is reduced to about 30% of the saturation value, reproducing the previously reported results for the same system. 4As noted above, the magnitude of the zero-field step should be correlated with the relative intensity of the low-temperature blocking peak of the inphase component of the ac-magnetic susceptibility, both being determined by the proportion of molecules that undergo the fast relaxation mechanisms.Thus, it appears that there is a clear influence of the environment on the blocking barriers of these SMM's; the CH 3 CN:dmf glass induces a much greater proportion of fast-relaxing molecules than is the case for CH 2 Cl 2 :tol mixture.These results are confirmed by acmagnetic susceptibility measurements, where an increase of the high-or low-temperature blocking peak is observed for the glasses.For Mn 12 Bz the increase of fast-relaxing molecules due to the change of solvent is even greater ͓Fig.1͑b͔͒, and for Mn 12 Bz/CH 3 CN:dmf there is no hysteretic behavior, even down to 1.7 K.
MCD spectroscopy can also be used for zero-field-cooled ͑ZFC͒ experiments and the measurements of tunneling phenomena.ZFC dc susceptibility data obtained for Mn 12 Ac/CH 2 Cl 2 :tol and Mn 12 Bz/CH 2 Cl 2 :tol using the SQUID and by MCD spectroscopy at 21 200 cm Ϫ1 are shown in Figs.3͑a͒ and 3͑b͒.Results obtained for both techniques are in close accord.They show the blocking temperature peak at 3.5 K and the same Curie-Weiss ͓ϳ(T ϪT c ) Ϫ1 ͔ behavior at higher temperatures.The lowtemperature blocking peak is not clearly seen for these dc measurements because is out of the working temperature range.
The determination of information about tunneling in glasses is limited by the random orientation of the molecules.However, evidence of tunneling can be obtained by comparing the relaxation rates at zero field with those at small, nonzero fields.If relaxation resulted only from classical thermal effects, the highest energy barrier, and thus the slowest relaxation rate, should occur at zero field.When tunneling effects are significant, their contributions to relaxation will be greatest when conditions of resonance are attained between states of different M S .For a sample of randomly oriented SMM's, the only resonance that occurs simultaneously for all molecules is at zero field, which should therefore correspond to a local maximum of the relaxation rate.
Decay measurements of the MCD signal where performed at 21 200 cm Ϫ1 for Mn 12 Ac/CH 2 Cl 2 :tol at 2.2 K.A field of Ϫ2.5ϫ10 4 Oe was applied to saturate the sample, then rapidly changed to zero or other weak positive fields.After an initial rapid decrease of signal due to the superparamagnetic particles, the decay curves could be accurately fitted with the equation ⌬A(t)ϭ⌬A eq ϩ(⌬A sat Ϫ⌬A eq )exp(Ϫ⌫ eff t) where ⌫ eff represents an effective decay rate for the entire randomly oriented ensemble.The field dependence of ⌫ eff for Mn 12 Ac/CH 2 Cl 2 :tol is shown in Fig. 4. The maximum at zero field clearly confirms the presence of tunneling.To our knowledge, this is the first observation of spin tunneling with a magneto-optical method.
To summarize, we have shown that MCD is a powerful technique for magnetic characterization of SMM's.The MCD signal is directly proportional to magnetization, reproducing the magnetometry experiments and can be accurately described through Eqs.͑2͒, ͑3͒.Measurements performed on Mn 12 SMM's at visible wavelengths have permitted determination of properties from blocking temperatures to quantum tunneling.Further development of optical methods for magnetization measurements has a special appeal with regard to quantum computing applications.

FIG. 1 .
FIG. 1. Field dependence of SQUID magnetization ͑gray curves͒ and MCD at 21 200 cm Ϫ1 ͑black curves͒ for Mn 12 Ac ͑a͒ and Mn 12 Bz ͑b͒.In ͑a͒ and ͑b͒, the black solid curves indicate the magnitude of the MCD in 1:1 CH 2 Cl 2 :tol glasses, while the dashed lines correspond to the relevant SMM in a 1:2 CH 3 CN:dmf glass.For ͑c͒, the gray dotted curve indicates the magnetization of Mn 12 Ac/CH 2 Cl 2 :tol, while the black curves represent MCD measurements at 21 200 cm Ϫ1 ͑dotted line͒ and 19 700 cm Ϫ1 ͑dashed line͒.