Decoherence in crystals of quantum molecular magnets.

Quantum decoherence is a central concept in physics. Applications such as quantum information processing depend on understanding it; there are even fundamental theories proposed that go beyond quantum mechanics, in which the breakdown of quantum theory would appear as an 'intrinsic' decoherence, mimicking the more familiar environmental decoherence processes. Such applications cannot be optimized, and such theories cannot be tested, until we have a firm handle on ordinary environmental decoherence processes. Here we show that the theory for insulating electronic spin systems can make accurate and testable predictions for environmental decoherence in molecular-based quantum magnets. Experiments on molecular magnets have successfully demonstrated quantum-coherent phenomena but the decoherence processes that ultimately limit such behaviour were not well constrained. For molecular magnets, theory predicts three principal contributions to environmental decoherence: from phonons, from nuclear spins and from intermolecular dipolar interactions. We use high magnetic fields on single crystals of Fe(8) molecular magnets (in which the Fe ions are surrounded by organic ligands) to suppress dipolar and nuclear-spin decoherence. In these high-field experiments, we find that the decoherence time varies strongly as a function of temperature and magnetic field. The theoretical predictions are fully verified experimentally, and there are no other visible decoherence sources. In these high fields, we obtain a maximum decoherence quality-factor of 1.49 × 10(6); our investigation suggests that the environmental decoherence time can be extended up to about 500 microseconds, with a decoherence quality factor of ∼6 × 10(7), by optimizing the temperature, magnetic field and nuclear isotopic concentrations.

Collective coupling of a macroscopic number of single-molecule magnets with a microwave cavity mode.

We report the observation of strong coupling of a macroscopic ensemble of ∼1016 Fe8 molecular nanomagnets to the resonant mode of a microwave cavity. We use millimeter-wave spectroscopy to measure the splitting of the system's resonant frequency induced by the coupling between the spins and the cavity mode. The magnitude of this splitting is found to scale with √N, where N is the number of collectively coupled spins. We control N by changing the system's temperature and, thereby, the populations of the relevant spin energy levels. Strong coupling is observed for two distinct transitions between spin energy states. Our results indicate that at low temperatures nearly all of the spins in the sample couple with the cavity's resonant mode even though there is substantial inhomogeneous broadening of the Fe8 spin resonances.

Asymmetric Berry-phase interference patterns in a single-molecule magnet.

A Mn(4) single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (H(T)) dependence of the magnetization tunneling probability when a longitudinal field (H(L)) is present, contrary to symmetric patterns observed for H(L)=0. Reversal of H(L) results in a reflection of the transverse-field asymmetry about H(T)=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.

Density Functional Calculations of Electronic Structure, Charge Distribution, and Spin Coupling in Manganese-Oxo Dimer Complexes.

We have calculated the electronic structures of five different manganese-oxo dimer complexes using density functional methods combined with the broken symmetry and spin projection concepts. The number of carboxylate, oxo, and peroxo bridging ligands was varied, and the terminal ligands were triazacyclononane (TACN). The formal Mn oxidation states varied from Mn(III)(2) and Mn(III)Mn(IV) to Mn(IV)(2). These complexes have been synthesized and their X-ray structures and magnetic properties measured previously. We have calculated the Heisenberg spin coupling parameters J and resonance delocalization parameters B for all of these systems. Despite the very small energy differences involved, there is a good correspondence between calculated and experimental Heisenberg J parameters. We have analyzed potential changes in the calculated effective Heisenberg coupling J(eff) for the mixed-valence Mn(III)Mn(IV) complexes when partial or complete delocalization due to the B parameter is taken into account. These changes depend also on the energy of the relevant intervalence band. Surprisingly, in the two mixed-valence systems studied, the high spin S = (5)/(2) state lies below S = (7)/(2). This is consistent with spin coupling between Mn with site spins S(1) = 1, S(2) = (3)/(2), corresponding to intermediate spin Mn(I) and Mn(II) respectively, instead of the coupling expected from the formal oxidation states, S(1) = 2, S(2) = (3)/(2) from high spin Mn(III) and Mn(IV). The spin and charge distributions in the broken symmetry ground states are also consistent with intermediate spin S(1) = 1, S(2) = (3)/(2). The calculated charge distributions show strong metal-ligand covalency. In fact, as the formal oxidation states of the Mn sites increase, the net Mn charges generally show a slow decrease, consistent with a very strong ligand --> metal charge transfer, particularly from &mgr;-oxo or &mgr;-peroxo ligands. TACN is a better donor ligand than carboxylate, even when calculated on a per donor atom basis. The ligand atom charge transfer order is peroxo >/= oxo >> TACN > acetate. The TACN > acetate ordering is expected from the spectrochemical series, but the strong charge transfer and strong metal-ligand covalency of peroxo and oxo ligands with the Mn sites cannot be simply related to their positions in the spectrochemical series. In the Mn(IV)(2)(&mgr;-O)(2)(&mgr;-O(2))(TACN)(2), each peroxo oxygen has a small charge (-0.3), much less than found for each &mgr;-O atom (-0.7). The high-spin S = 3 state lies quite low in energy, 8 kcal/mol from our calculations and about 4 kcal/mol based on the experimental Heisenberg spin coupling parameters. Potential molecular oxygen dissociation pathways involving a spin S = 1 state are discussed. Effective ligand field diagrams are constructed from the calculated energy levels which display the competition between spin polarization splitting and the ligand field t(2g)-e(g) splitting and allow comparisons of electronic structure among different complexes. The electronic structure and spin coupling of these complexes was also compared to the corresponding "core-only" complexes where both TACN ligands were removed, yielding a far weaker ligand field. There is a strong ferromagnetic shift in the "core-only" complexes compared with the complete TACN complexes, also showing the effects of a weaker ligand field.

Magnetic quantum tunneling: key insights from multi-dimensional high-field EPR.

Multi-dimensional high-field/frequency electron paramagnetic resonance (HFEPR) spectroscopy is performed on single-crystals of the high-symmetry spin S = 4 tetranuclear single-molecule magnet (SMM) [Ni(hmp)(dmb)Cl](4), where hmp(-) is the anion of 2-hydroxymethylpyridine and dmb is 3,3-dimethyl-1-butanol. Measurements performed as a function of the applied magnetic field strength and its orientation within the hard-plane reveal the four-fold behavior associated with the fourth order transverse zero-field splitting (ZFS) interaction, (1/2)B(S + S), within the framework of a rigid spin approximation (with S = 4). This ZFS interaction mixes the m(s) = +/-4 ground states in second order of perturbation, generating a sizeable (12 MHz) tunnel splitting, which explains the fast magnetic quantum tunneling in this SMM. Meanwhile, multi-frequency measurements performed with the field parallel to the easy-axis reveal HFEPR transitions associated with excited spin multiplets (S < 4). Analysis of the temperature dependence of the intensities of these transitions enables determination of the isotropic Heisenberg exchange constant, J = -6.0 cm(-1), which couples the four spin s = 1 Ni(II) ions within the cluster, as well as a characterization of the ZFS within excited states. The combined experimental studies support recent work indicating that the fourth order anisotropy associated with the S = 4 state originates from second order ZFS interactions associated with the individual Ni(II) centers, but only as a result of higher-order processes that occur via S-mixing between the ground state and higher-lying (S < 4) spin multiplets. We argue that this S-mixing plays an important role in the low-temperature quantum dynamics associated with many other well known SMMs.

Manifestation of spin selection rules on the quantum tunneling of magnetization in a single-molecule magnet.

We present low temperature magnetometry measurements on a new Mn3 single-molecule magnet in which the quantum tunneling of magnetization (QTM) displays clear evidence for quantum mechanical selection rules. A QTM resonance appearing only at high temperatures demonstrates tunneling between excited states with spin projections differing by a multiple of three. This is dictated by the C3 molecular symmetry, which forbids pure tunneling from the lowest metastable state. Transverse field resonances are understood by correctly orienting the Jahn-Teller axes of the individual manganese ions and including transverse dipolar fields. These factors are likely to be important for QTM in all single-molecule magnets.

High frequency EPR on dilute solutions of the single molecule magnet Ni(4).

Dilute frozen solutions of the single molecule magnet Ni(4) (S=4) have been studied using 130 GHz electron paramagnetic resonance (EPR). Despite the random orientation of the molecules, well defined EPR absorption peaks are observed due to the strong variation of the splittings between the different spin states on magnetic field. Temperature dependent studies above 4 K and comparison with simulations enable identification of the spin transitions and determination of the Hamiltonian parameters. The latter are found to be close to those of Ni(4) single crystals. No echo was detected from Ni(4) in pulsed experiments, which sets an upper bound of about 50 ns on the spin coherence time.

Single-molecule magnets: structure and properties of [Mn18O14(O2CMe)18(hep)4(hepH)2(H2O)2](ClO4)2 with spin S = 13.

The reaction of 2-(hydroxyethyl)pyridine (hepH) with a 2:1 molar mixture of [Mn3O(O2CMe)6(py)3]ClO4 and [Mn3O(O2CMe)6(py)3] in MeCN afforded the new mixed-valent (16Mn(III), 2Mn(II)), octadecanuclear complex [Mn18O14(O2CMe)18(hep)4(hepH)2(H2O)2](ClO4)2 (1) in 20% yield. Complex 1 crystallizes in the triclinic space group P. Direct current magnetic susceptibility studies in a 1.0 T field in the 5.0-300 K range, and variable-temperature variable-field dc magnetization studies in the 2.0-4.0 K and 2.0-5.0 T ranges were obtained on polycrystalline samples. Fitting of magnetization data established that complex 1 possesses a ground-state spin of S = 13 and D = -0.18 K. This was confirmed by the value of the in-phase ac magnetic susceptibility signal. Below 3 K, the complex exhibits a frequency-dependent drop in the in-phase signal, and a concomitant increase in the out-of-phase signal, consistent with slow magnetization relaxation on the ac time scale. This suggests the complex is a single-molecule magnet (SMM), and this was confirmed by hysteresis loops below 1 K in magnetization versus dc field sweeps on a single crystal. Alternating current and direct current magnetization data were combined to yield an Arrhenius plot from which was obtained the effective barrier (U(eff)) for magnetization reversal of 21.3 K. Below 0.2 K, the relaxation becomes temperature-independent, consistent with relaxation only by quantum tunneling of the magnetization (QTM) through the anisotropy barrier via the lowest-energy MS = +/-13 levels of the S = 13 spin manifold. Complex 1 is thus the SMM with the largest ground-state spin to display QTM.

Manganese-histidine cluster as the functional center of the water oxidation complex in photosynthesis.

The recent model of Kambara and Govindjee for water oxidation [Kambara T. and Govindjee (1985) Proc. Natl. Acad. Sci. U.S.A., 82:6119-6123] has been extended in this paper by examining all the data in order to identify the most likely candidate for the 'redox-active ligand' (RAL), suggested to operate between the water oxidizing complex (WOC) and Z, the electron donor to the reaction center P680. We have concluded that a very suitable candidate for RAL is the imidazole moiety of a histidine residue. The electrochemical data available on imidazole derivatives play heavily in this identification of RAL. Thus, we suggest that histidine might play the role of an electron mediator between the WOC and Z. A model of S-states in terms of their plausible chemical identity is presented here.

High-frequency EPR study of the ferrous ion in the reduced rubredoxin model.

High-frequency (94-371 GHz) EPR data are reported for powdered samples of [PPh4]2[Fe(SPh)4], an accurate model for the reduced site of rubredoxins. This is the first HFEPR investigation of an S = 2 ferrous complex, illustrating the utility of this technique for the investigation of integer-spin systems. A full-matrix diagonalization approach is used to simulate spectra over the 94-371 GHz frequency range, providing the spin-Hamiltonian parameters g, D, and E. It is observed that g is anisotropic, characterized by gx = gy = 2.08 and gz = 2.00, and that D = +5.84 cm(-1) and E = +1.42 cm(-1), where the uncertainty in each parameter is estimated as +/- 2%. The spin-Hamiltonian for [PPh4]2[Fe(SPh)4] is related to fundamental properties, such as the crystal-field splitting and the spin-orbit coupling of Fe2+. It is shown that the conventional spin-Hamiltonian accurately represents the electronic structure of the Fe2+ ion in this molecule. Through a comparison with Fe(SPh)4(PPh4)2, the zero-field splitting of the Fe2+ site in reduced rubredoxin is estimated to be D = +5.3 cm(-1) and E = +1.5 cm(-1). This is one of the few HFEPR investigations of a rhombic, high-spin system; as such, it is a step toward the eventual investigation of similar Fe2+ sites in proteins.

Quantum superposition of high spin states in the single molecule magnet Ni4.

Quantum tunneling of the magnetization in a single molecule magnet has been studied in experiments that combine microwave spectroscopy with high sensitivity magnetic measurements. By monitoring spin-state populations in the presence of microwave radiation, the energy splittings between low lying superpositions of high-spin states of single molecule magnet Ni4 (S=4) have been measured. Absorption linewidths give an upper bound on the rate of decoherence. Pulsed microwave experiments provide a measure of energy relaxation time, which is found to increase with frequency.

Single-molecule magnets: preparation and properties of mixed-carboxylate complexes.

Methods are reported for the preparation of mixed-carboxylate versions of the [Mn(12)O(12)(O(2)CR)(16)(H(2)O)(4)] family of single-molecule magnets (SMMs). [Mn(12)O(12)(O(2)CCHCl(2))(8)(O(2)CCH(2)Bu(t))(8)(H(2)O)(3)] (5) and [Mn(12)O(12)(O(2)CHCl(2))(8)(O(2)CEt)(8)(H(2)O)(3)] (6) have been obtained from the 1:1 reaction of the corresponding homocarboxylate species. Complex 5.CH(2)Cl(2).H(2)O crystallizes in the triclinic space group P1 with, at -165 degrees C, a = 15.762(1), b = 16.246(1), c = 23.822(1) A, alpha = 103.92(1), beta = 104.50(1), gamma = 94.23(1) degrees, Z = 2, and V = 5674(2) A(3). Complex 6.CH(2)Cl(2) crystallizes in the triclinic space group P1 with, at -158 degrees C, a = 13.4635(3), b = 13.5162(3), c = 23.2609(5) A, alpha = 84.9796(6), beta = 89.0063(8), gamma = 86.2375(6) degrees, Z = 2, and V = 4207.3(3) A(3). Complexes 5 and 6 both contain a [Mn(12)O(12)] core with the CHCl(2)CO(2-) ligands ordered in the axial positions and the RCO(2-) ligands (R = CH(2)Bu(t) (5) or Et (6)) in equatorial positions. There is, thus, a preference for the CHCl(2)CO(2-) to occupy the sites lying on the Mn(III) Jahn-Teller axes, and this is rationalized on the basis of the relative basicities of the carboxylate groups. Direct current magnetic susceptibility studies in a 10.0 kG field in the 2.00-300 K range indicate a large ground-state spin, and fitting of magnetization data collected in the 10.0-70.0 kG field and 1.80-4.00 K temperature range gave S = 10, g = 1.89, and D = -0.65 K for 5, and S = 10, g = 1.83, and D = -0.60 K for 6. These values are typical of [Mn(12)O(12)(O(2)CR)(16)(H(2)O)(4)] complexes. Alternating current susceptibility studies show the out-of-phase susceptibility (chi(M)' ') signals characteristic of the slow relaxation in the millisecond time scale of single-molecule magnets. Arrhenius plots obtained from chi(M)' ' versus T data gave effective barriers to relaxation (U(eff)) of 71 and 72 K for 5 and 6, respectively. (1)H NMR spectra in CD(2)Cl(2) show that 5 and 6 are the main species present on dissolution, but there is evidence for some ligand distribution between axial and equatorial sites, by intra- and/or intermolecular exchange processes.

Symmetry of magnetic quantum tunneling in single molecule magnet Mn12-acetate.

The symmetry of magnetic quantum tunneling has been studied in the prototype single molecule magnet Mn12-acetate using a micro-Hall effect magnetometer and superconducting high field vector magnet system. An average crystal fourfold symmetry is shown to be due to local molecular environments of twofold symmetry that are rotated by 90 degrees with respect to one another, confirming that disorder which lowers the molecule symmetry is as important to magnetic quantum tunneling. We have studied a subset of these lower (twofold) site symmetry molecules and present evidence for a Berry phase effect consistent with a local twofold symmetry.

Spin-spin cross relaxation in single-molecule magnets.

The one-body tunnel picture of single-molecule magnets (SMMs) is not always sufficient to explain the measured tunnel transitions. An improvement to the picture is proposed by including also two-body tunnel transitions such as spin-spin cross relaxation (SSCR) which are mediated by dipolar and weak superexchange interactions between molecules. A Mn4 SMM is used as a model system. At certain external fields, SSCRs lead to additional quantum resonances which show up in hysteresis loop measurements as well-defined steps. A simple model is used to explain quantitatively all observed transitions.

Single-molecule magnets: site-specific ligand abstraction from [Mn12O12(O2CR)16(H2O)4] and the preparation and properties of [Mn12O12(NO3)4(O2CCH2Bu(t))12(H2O)4].

Site-selective carboxylate abstraction has been achieved from [Mn(12)O(12)(O(2)CR)(16)(H(2)O)(4)] complexes by treatment with HNO(3) in MeCN. The reaction of the R = Ph or CH(2)Bu(t)() complexes with 4 equiv of HNO(3) gives [Mn(12)O(12)(NO(3))(4)(O(2)CR)(12)(H(2)O)(4)] (R = CH(2)Bu(t) (6) or Ph (7)) in analytical purity. Complex 6.MeNO(2) crystallizes in monoclinic space group C2/c with the following cell parameters at -168 degrees C: a = 21.280(5), b = 34.430(8), c = 33.023(8) A, beta = 104.61(1) degrees, V = 23413 A, and Z = 8. The four NO(3)(-) groups are not disordered and are bound in bridging modes at axial positions formerly occupied by bridging carboxylate groups. (1)H NMR spectroscopy in CD(2)Cl(2) and CDCl(3) shows retention of the solid-state structure on dissolution in these solvents. DC magnetic susceptibility (chi(M)) and magnetization (M) studies have been carried out in the 2.00-300 K and 1.0-7.0 T ranges. Fits of M/Nmu(B) versus H/T plots gave S = 10, g = 1.92, and D = -0.40 cm(-1), where D is the axial zero-field splitting parameter. AC magnetic susceptibility studies on 6 have been performed in the 1.70-10.0 K range in a 3.5 Oe field oscillating at frequencies up to 1500 Hz. Out-of-phase magnetic susceptibility (chi(M)' ') signals were observed in the 4.00-8.00 K range which were frequency-dependent. Thus, 6 displays the slow magnetization relaxation diagnostic of a single-molecule magnet (SMM). The data were fit to the Arrhenius law, and this gave the effective barrier to relaxation (U(eff)) of 50.0 cm(-1) (72.0 K) and a pre-exponential (1/tau(0)) of 1.9 x 10(8) s(-1). Complex 6 also shows hysteresis in magnetization versus DC field scans, and the hysteresis loops show steps at regular intervals of magnetic field, the diagnostic evidence of field-tuned quantum tunneling of magnetization. High-frequency EPR (HFEPR) spectroscopy on oriented crystals of complex 6 shows resonances assigned to transitions between zero-field split M(s) states of the S = 10 ground state. Fitting of the data gave S = 10, g = 1.99, D = -0.46 cm(-1), and B(4)(0) = -2.0 x 10(-5), where B(4)(0) is the quartic zero-field coefficient. The combined results demonstrate that replacement of four carboxylate groups with NO(3)(-) groups leads to insignificant perturbation of the magnetic properties of the Mn(12) complex. Complex 6 should now be a useful starting point for further reactivity studies, taking advantage of the good leaving group properties of the NO(3)(-) ligands.

Tetranuclear manganese carboxylate complexes with a trigonal pyramidal metal topology via controlled potential electrolysis.

Controlled potential electrolysis (CPE) procedures are described that provide access to complexes with a [Mn4(mu 3-O)3(mu 3-O2CR)]6+ core (3MnIII,MnIV) and a trigonal pyramidal metal topology, starting from species containing the [Mn4(mu 3-O)2]8+ core (4MnIII). [Mn4O2(O2CMe)6(py)2(dbm)2] (6): triclinic, P1, a = 10.868(3) A, b = 13.864(3) A, c = 10.625(3) A, alpha = 108.62(1) degrees, beta = 118.98(1) degrees, gamma = 89.34(2) degrees, V = 1307 A3, Z = 1, T = -131 degrees C, R (Rw) = 3.24 (3.70)%. [Mn4O2(O2CPh)6(py)(dbm)2] (8): monoclinic, P2(1)/c, a = 14.743(6) A, b = 15.536(8) A, c = 30.006(13) A, beta = 102.79(1) degrees, V = 6702 A3, Z = 4, T = -155 degrees C, R (Rw) = 4.32 (4.44)%. Both 6 and 8 contain a [Mn4O2]8+ core; 8 only has one py group, the fourth MnIII site being five-coordinate. (NBun4)[Mn4O2(O2CPh)7(dbm)2] (10) is available from two related procedures. CPE of 10 at 0.65 V vs ferocene in MeCN leads to precipitation of [Mn4O3(O2CPh)4(dbm)3] (11); similarly, CPE of 6 at 0.84 V in MeCN/CH2Cl2 (3:1 v/v) gives [Mn4O3(O2CMe)4(dbm)3] (12). Complex 11: monoclinic, P2(1)/n, a = 15.161(3) A, b = 21.577(4) A, c = 22.683(5) A, beta = 108.04(3) degrees, V = 7056 A3, Z = 4, T = -100 degrees C, R (wR2) = 8.63 (21.80)%. Complex 12: monoclinic, P2(1)/n, a = 13.549(2) A, b = 22.338(4) A, c = 16.618(2) A, beta = 103.74(1) degrees, V = 4885 A3, Z = 4, T = -171 degrees C, R (Rw) = 4.63 (4.45)%. Both 11 and 12 contain a [Mn4(mu 3-O)3(mu-O2CR)] core with a Mn4 trigonal pyramid (MnIV at the apex) and the RCO2- bridging the MnIII3 base. However, in 11, the carboxylate is eta 2,mu 3 with one O atom terminal to one MnIII and the other O atom bridging the other two MnIII ions, whereas in 12 the carboxylate is eta 1,mu 3, a single O atom bridging three MnIII ions. Variable-temperature, solid-state magnetic susceptibility studies on 11 and 12 show that, for both complexes, there are antiferromagnetic exchange interactions between MnIII/MnIV pairs, and ferromagnetic interactions between MnIII/MnIII pairs. In both cases, the resultant ground states of the complex is S = 9/2, confirmed by magnetization vs field studies in the 2.00-30.0 K and 0.50-50 kG temperature and field ranges, respectively.

Mixed-valence tetranuclear manganese single-molecule magnets.

The preparations, X-ray structures, and detailed physical characterizations are presented for two new mixed-valence tetranuclear manganese complexes that function as single-molecule magnets (SMM's): [Mn4(hmp)6Br2(H2O)2]Br2-4H2O (2) and [Mn4(6-me-hmp)6Cl4]-4H2O (3), where hmp(-) is the anion of 2-hydroxymethylpyridine and 6-me-hmp(-) is the anion of 6-methyl-2-hydroxymethylpyridine. Complex 2-4H2O crystallizes in the space group P2(1)/c, with cell dimensions at -160 degrees C of a = 10.907(0) A, b = 15.788(0) A, c = 13.941(0) A, beta = 101.21(0) degrees, and Z = 2. The cation lies on an inversion center and consists of a planar Mn4 rhombus that is mixed-valence, Mn2(III)Mn2(II). The hmp(-) ligands function as bidentate ligands and as the only bridging ligands in 2-4H2O. Complex 3-4H2O crystallizes in the monoclinic space group C2/c, with cell dimensions at -160 degrees C of a = 17.0852(4) A, b = 20.8781(5) A, c = 14.835(3) A, beta = 90.5485(8) degrees, and Z = 4. This neutral complex also has a mixed-valence Mn2(III)Mn2(II) composition and is best described as having four manganese ions arranged in a bent chain. A mu2-oxygen atom of the 6-me-hmp(-) anion bridges between the manganese ions; the Cl(-) ligands are terminal. Variable-field magnetization and high-frequency and -field EPR (HFEPR) data indicate that complex 2-4H2O has a S = 9 ground state whereas complex 3.4H(2)O has S = 0 ground state. Fine structure patterns are seen in the HFEPR spectra, and in the case of 2.4H(2)O it was possible to simulate the fine structure assuming S = 9 with the parameters g = 1.999, axial zero-field splitting of D/k(B) = -0.498 K, quartic longitudinal zero-field splitting of B4(omicron)/k(B) = 1.72 x 10(-5) K, and rhombic zero-field splitting of E/k(B) = 0.124 K. Complex 2-4H2O exhibits a frequency-dependent out-of-phase AC magnetic susceptibility signal, clearly indicating that this complex functions as a SMM. The AC susceptibility data for complex 2-4H2O were measured in the 0.05-4.0 K range and when fit to the Arrhenius law, gave an activation energy of DeltaE = 15.8 K for the reversal of magnetization. This DeltaE value is to be compared to the potential-energy barrier height of U/k(B) = absolute value DSz(2) = 40.3 K calculated for 2-4H2O.

Magnetic-field-dependent heat capacity of the single-molecule magnet [Mn(12)O(12)(O(2)CEt)(16)(H(2)O)(3)].

Accurate heat capacities of the single-molecule magnet [Mn(12)O(12)(O(2)CEt)(16)(H(2)O)(3)] were measured from 0.3 to 311 K by adiabatic calorimetry without an external magnetic field. Heat-capacity anomalies were separated by assuming several contributions including lattice vibration, magnetic anisotropy, and hyperfine splitting. Among them, a tiny thermal anomaly between 1 and 2 K is attributable to the presence of Jahn-Teller isomers. The heat capacities of the polycrystalline sample were also measured with applied magnetic fields from 0 to 9 T in the 2-20 K temperature region by the relaxation method. With an applied magnetic field of up to 2 T, a steplike heat-capacity anomaly was observed around the blocking temperature T(B) approximately 3.5 K. The magnitude of the anomaly reached a maximum at 0.7 T. With a further increase in the magnetic field, the step was decreasing, and finally it disappeared above 3 T. The step at T(B) under 0.7 T can be roughly accounted for by assuming that a conversion between the up-spin and down-spin states is allowed above T(B) by phonon-assisted quantum tunneling, while it is less effective below T(B). Excess heat capacity under a magnetic field revealed a large heat-capacity hump around 14 K and 2 T, which would be attributed to a thermal excitation from the S = 9 ground state to the spin manifold with different S values, where S is the total spin quantum number.

Distribution of tunnel splittings in Mn(12) acetate.

In magnetic fields applied parallel to the anisotropy axis, the relaxation of the magnetization of Mn(12)-acetate measured for different sweep rates collapses onto a single scaled curve. The form of the scaling implies that the dominant symmetry-breaking process responsible for tunneling is a locally varying second-order transverse anisotropy, forbidden by tetragonal symmetry in the perfect crystal, which gives rise to a broad distribution of tunnel splittings in a real crystal of Mn(12) acetate. Different forms applied to even- and odd-numbered steps provide a clear distinction between even resonances (associated with crystal anisotropy) and odd resonances (which require a transverse magnetic field).