Origin of second-order transverse magnetic anisotropy in Mn12-acetate

Thermodynamics of General Heisenberg Spin Tetramers Composed of Coupled Quantum Dimers

Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.

Thermodynamics and Magnetic Excitations in Quantum Spin Trimers: Applications for the Understanding of Molecular Magnets

Molecular magnets provide a playground of interesting phenomena and interactions that have direct applications for quantum computation and magnetic systems. A general understanding of the underlying geometries for molecular magnets therefore generates a consistent foundation for which further analysis and understanding can be established. Using a Heisenberg spin-spin exchange Hamiltonian, we investigate the evolution of magnetic excitations and thermodynamics of quantum spin isosceles trimers (two sides J and one side α J ) with increasing spin. For the thermodynamics, we produce exact general solutions for the energy eigenstates and spin decomposition, which can be used to determine the heat capacity and magnetic susceptibility quickly. We show how the thermodynamic properties change with α coupling parameters and how the underlying ground state governs the Schottky anomaly. Furthermore, we investigate the microscopic excitations by examining the inelastic neutron scattering excitations and structure factors. Here, we illustrate how the individual dimer subgeometry governs the ability for probing underlying excitations. Overall, we feel these calculations can help with the general analysis and characterization of molecular magnet systems.

Magnetic Anisotropy of Tetrahedral CoII Single-Ion Magnets: Solid-State Effects

This study reports the static and dynamic magnetic characterization of two mononuclear tetrahedral Co^II complexes, [Co{ⁱPr₂P(E)NP(E)ⁱPr₂}₂], where E = S (CoS₄) and Se (CoSe₄), which behave as single-ion magnets (SIMs). Low-temperature (15 K) single-crystal X-ray diffraction studies point out that the two complexes exhibit similar structural features in their first coordination sphere, but a disordered peripheral ⁱPr group is observed only in CoS₄. Although the latter complex crystallizes in an axial space group, the observed structural disorder leads to larger transverse magnetic anisotropy for the majority of the molecules compared to CoSe₄, as confirmed by electron paramagnetic resonance spectroscopy. Static magnetic characterization indicates that both CoS₄ and CoSe₄ show easy-axis anisotropy, with comparable D values (∼-30 cm^-1). Moreover, alternating-current susceptibility measurements on these Co^II complexes, magnetically diluted in their isostructural Zn^II analogues, highlight the role of dipolar magnetic coupling in the mechanism of magnetization reversal. In addition, our findings suggest that, despite their similar anisotropic features, CoS₄ and CoSe₄ relax magnetically via different processes. This work provides experimental evidence that solid-state effects may affect the magnetic behavior of SIMs.

The solvent effect in an axially symmetric FeIII4 single-molecule magnet

The axial symmetry of an Fe^III₄ SMM is broken by the interaction of the molecule with the disordered solvent molecules.

Interweaving spins with their environment: novel inorganic nanohybrids with controllable magnetic properties

We discuss the developments in the synthesis and characterization of magnetic nanohybrids made of molecular magnets and nanostructured materials.

Geometric-phase interference in a Mn12 single-molecule magnet with fourfold rotational symmetry

We study the magnetic relaxation rate Γ of the single-molecule magnet Mn(12)-tBuAc as a function of the magnetic field component H(T) transverse to the molecule's easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that Γ increases abruptly at certain values of H(T). These increases are observed just beyond values of H(T) at which a geometric-phase interference effect suppresses tunneling between two excited energy levels. The effect is washed out by rotating H(T) away from the spin's hard axis, thereby suppressing the interference effect. Detailed numerical calculations of Γ using the known spin Hamiltonian accurately reproduce the observed behavior. These results are the first experimental evidence for geometric-phase interference in a single-molecule magnet with true fourfold symmetry.

Magnetic dipolar ordering and quantum phase transition in an Fe8 molecular magnet

We show that a crystal of mesoscopic Fe(8) single-molecule magnets is an experimental realization of the quantum Ising model in a transverse field, with dipolar interactions. Quantum annealing has enabled us to explore the quantum and classical phase transitions between the paramagnetic and ferromagnetic phases, at thermodynamical equilibrium. The phase diagram and critical exponents that we obtain agree with expectations for the mean-field universality class.

Crystals in which some metal atoms are more equal than others: inequalities from crystal packing and their spectroscopic/magnetic consequences

Crystal structures of the heterometallic compounds CrCrFe(dpa)(4)Cl(2) (1), CrCrMn(dpa)(4)Cl(2) (2), and MoMoMn(dpa)(4)Cl(2) (3) (dpa = 2,2'-dipyridylamide) show disorder in the metal atom positions such that the linear M(A)[quadruple bond]M(A)···M(B) array for a given molecule in the crystal is oriented in one of two opposing directions. Despite the fact that the direct coordination sphere of the metals in the two crystallographically independent orientations is identical, subtle differences in some metal-ligand bond distances are observed in 1 and 3 due to differences in the orientation of a solvent molecule of crystallization. The Fe(II) and Mn(II) ions serve as sensitive local spectroscopic probes that have been interrogated by Mössbauer spectroscopy and high-field EPR spectroscopy, respectively. The subtle differences in the two independent Fe and Mn sites in 1 and 3 unexpectedly give rise to unusually large differences in the measured Fe quadrupole splitting (ΔE(Q)) in 1 and Mn zero-field splitting (D) in 3. Variable-temperature/single-crystal EPR spectroscopy has allowed us to determine that the temperature-dependent D tensors in 3 are oriented along the metal-metal axis and that they show significantly different dynamic behavior with temperature. The differences in ΔE(Q) and D are reproduced by density functional calculations on truncated models for 1 and 3 that lack the quadruply bonded M(A)[quadruple bond]M(A) groups, though the magnitude of the calculated effect is not as large as that observed experimentally. We suggest that the large observed differences in ΔE(Q) and D for the individual sites could be due to the influence of the strong diamagnetic anisotropy of the quadruply bonded M[quadruple bond]M unit.

Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case

Magnetic anisotropy is the capability of a system in a triplet or higher spin state to store magnetic information. Although the source of the magnetic anisotropy is the zero-field splitting of the ground state of the system, there is a difference between these two quantities that has to be fully rationalized before one makes comparisons. This is especially important for small spins such as triplets, where the magnetic anisotropy energy is only half of the zero-field splitting. Density functional calculations of magnetic anisotropy energies correspond to a high-field limit where the spins are aligned by the external magnetic field. Data are presented for the well-studied molecular magnet Mn(12)O(12) acetate. Both perturbative and self-consistent treatments, different quasirelativistic Hamiltonians (zeroth order regular approximation, Douglas-Kroll, effective core potentials) and exchange-correlation functionals are compared. It is shown that some effects usually considered minor, such as the inclusion of the exchange-correlation potential in the effective one-particle spin-orbit operator, lead to sizable differences when computing magnetic anisotropy energies. Higher-order contributions, that is, the difference between self-consistent and perturbative results, increase the magnetic anisotropy energy somewhat but do not introduce sizeable quartic terms or an in-plane anisotropy. In numerical experiments, on can switch off and on spin-orbit coupling at individual atomic sites. This procedure yields single-site contributions to the overall magnetic anisotropy energy that could be used as parameters in phenomenological spin Hamiltonians. If ferrimagnetic systems are treated with broken symmetry density functional methods where the Kohn-Sham reference function is not a spin eigenfunction, corrections are needed which depend on the size of the exchange couplings in the system and must therefore be evaluated case by case.

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.

The Drosophila of single-molecule magnetism: [Mn12O12(O2CR)16(H2O)4]

Single-molecule magnets (SMMs) are individual molecules that can function as nanoscale magnetic particles. The [Mn12O12(O2CR)16(H2O)4] (Mn12; R=Me, Et, etc.) family of SMMs was the first one discovered; it is also the one whose study has provided the majority of current knowledge on this interesting magnetic phenomenon, prompting its description here as the Drosophila of the field. This tutorial review will survey the various chemical studies that have been carried out to date on this family. This will include a discussion of methods that have been developed for their structural and redox transformation, and the effect of the latter on the magnetic and SMM properties.

Enhancing SMM properties in a family of [Mn6] clusters

The complex [Mn(6)O(2)(Et-sao)(6)(O(2)C(11)H(15))(2)(EtOH)(6)] has U(eff) = 80 K.

Fast magnetization tunneling in tetranickel(II) single-molecule magnets

A series of Ni(4) cubane complexes with the composition [Ni(hmp)(ROH)Cl](4) complexes 1-4 where R= -CH(3) (complex 1), -CH(2)CH(3) (complex 2), -CH(2)CH(2)(C(4)H(9)) (complex 3), -CH(2)CH(2)CH(2)(C(6)H(11)) (complex 4), hmp(-) is the anion of 2-hydroxymethylpyridine, t-Buhmp(-) is the anion of 4-tert-butyl-2-hydroxymethylpyridine, and dmb is 3,3-dimethyl-1-butanol] and [Ni(hmp)(dmb)Br](4) (complex 5) and [Ni(t-Buhmp)(dmb)Cl](4) (complex 6) were prepared. All six complexes were characterized by dc magnetic susceptibility data to be ferromagnetically coupled to give an S = 4 ground state with significant magnetoanisotropy (D approximately equal to -0.6 cm(-1)). Magnetization hysteresis measurements carried out on single crystals of complexes 1-6 establish the single-molecule magnet (SMM) behavior of these complexes. The exchange bias observed in the magnetization hysteresis loops of complexes 1 and 2 is dramatically decreased to zero in complex 3, where the bulky dmb ligand is employed. Fast tunneling of magnetization is observed for the high-symmetry (S(4) site symmetry) Ni(4) complexes in the crystal of complex 3, and the tunneling rate can even be enhanced by destroying the S(4) site symmetry, as is the case for complex 4, where there are two crystallographically different Ni(4) molecules, one with C(2) and the other with C(1) site symmetry. Magnetic ordering temperatures due to intermolecular dipolar and magnetic exchange interactions were determined by means of very low-temperature ac susceptibility measurements; complex 1 orders at 1100 mK, complex 3 at 290 mK, complex 4 at approximately 80 mK, and complex 6 at <50 mK. This confirms that bulkier ligands correspond to more isolated molecules, and therefore, magnetic ordering occurs at lower temperatures for those complexes with the bulkiest ligands.

Spectroscopic, Magnetochemical, and Crystallographic Study of Cesium Iron Phosphate Hexahydrate: Characterization of the Electronic Structure of the Iron(II) Hexa-aqua Cation in a Quasicubic Environment

Spectroscopic, magnetochemical, and crystallographic data are presented for CsFe(H2O)6PO4, a member of a little-known isomorphous series of salts that facilitates the study of hexa-aqua ions in a quasicubic environment. Above 120 K, the deviations from cubic symmetry are minimal, as shown by the first example of an iron(II) Mössbauer spectrum that exhibits no measurable quadrupole splitting. Two crystallographically distinct [Fe(OH2)6]2+ complexes are identified from inelastic neutron-scattering (INS) experiments conducted between 2 and 15 K. The data are modeled with the ligand-field Hamiltonian, H = lambdaLŝ + betaB(kL + 2ŝ) + Delta(tet){Lz2 - (1/3)L(L + 1)} + Delta(rhom){Lx2 - Ly2}, operating in the ground-term (5)T(2g) (Oh) basis. An excellent reproduction of INS, Mössbauer, HF-EPR, and magnetochemical data are obtained in the 2 and 15 K temperature regimes with the following parameters: lambda = -80 cm(-1); k = 0.8; site A Delta(tet) = 183 cm(-1), Delta(rhom)= 19 cm(-1); site B Delta(tet) = 181 cm(-1), Delta(rhom)= 12 cm(-1). The corresponding zero-field-splitting (ZFS) parameters of the conventional S = 2 spin Hamiltonian are as follows: site A D = 12.02 cm(-)(1), E = 2.123 cm(-1); site B D = 12.15 cm(-1), E = 1.37 cm(-1). A theoretical analysis of the variation of the energies of the low-lying states with respect to displacements along selected normal coordinates of the [Fe(OH2)6]2+, shows the zero-field splitting to be extremely sensitive to small structural perturbations of the complex. The expressions derived are discussed in the context of spin-Hamiltonian parameters reported for the [Fe(OH2)6]2+ cation in different crystalline environments.

The Properties of the [Mn12O12(O2CR)16(H2O)4] Single-Molecule Magnets in Truly Axial Symmetry: [Mn12O12(O2CCH2Br)16(H2O)4]·4CH2Cl2

Detailed studies are reported of a Mn(12) single-molecule magnet (SMM) in truly axial (tetragonal) symmetry. The complex is [Mn(12)O(12)(O(2)CCH(2)Br)(16)(H(2)O)(4)].4CH(2)Cl(2) (2.4CH(2)Cl(2) or Mn(12)-BrAc), obtained by the standard carboxylate substitution method. The complex has an S = 10 ground state, typical of the Mn(12) family, and displays frequency-dependent out-of-phase AC susceptibility signals and hysteresis in single-crystal magnetization vs applied DC field sweeps. Single-crystal high-frequency EPR spectra in frequencies up to 360 GHz exhibit narrow signals that are not overlapping multiplets, in contrast to [Mn(12)O(12)(O(2)CMe)(16)(H(2)O)(4)].2MeCO(2)H.4H(2)O (1 or Mn(12)-Ac), which also crystallizes in an axial (tetragonal) space group but which now is recognized to consist of a mixture of six hydrogen-bonded isomers in the crystal and thus gives multiple, inhomogeneously broadened EPR signals. Similarly, single-crystal (55)Mn NMR spectra on Mn(12)-BrAc display much sharper signals than a single crystal of Mn(12)-Ac, and this allows one Mn(III) signal to show an almost baseline-resolved quintet from quadrupolar splitting ((55)Mn, I = 5/2, 100%), allowing quadrupole coupling parameters (e(2)qQ) to be determined. In addition, it was found that crushing crystals of Mn(12)-BrAc into a microcrystalline powder causes severe broadening and shifts of the NMR resonances, emphasizing the superiority of single-crystal studies. The combined results establish that Mn(12)-BrAc is far superior to Mn(12)-Ac for the study of the intrinsic properties of the Mn(12) family of SMMs in axial symmetry, and for the search for new phenomena such as quantum interference effects caused by higher-order (>2nd-order) transverse terms in the spin Hamiltonian.