Understanding Thermodynamic and Spectroscopic Properties of Tetragonal Mn12 Single-Molecule Magnets from Combined Density Functional Theory/Spin-Hamiltonian Calculations

Quantum Magnetism of the Iron Core in Ferritin Proteins-A Re-Evaluation of the Giant-Spin Model

The electron-electron, or zero-field interaction (ZFI) in the electron paramagnetic resonance (EPR) of high-spin transition ions in metalloproteins and coordination complexes, is commonly described by a simple spin Hamiltonian that is second-order in the spin S: H=D[Sz2-SS+1/3+E(Sx2-Sy2). Symmetry considerations, however, allow for fourth-order terms when S ≥ 2. In metalloprotein EPR studies, these terms have rarely been explored. Metal ions can cluster via non-metal bridges, as, for example, in iron-sulfur clusters, in which exchange interaction can result in higher system spin, and this would allow for sixth- and higher-order ZFI terms. For metalloproteins, these have thus far been completely ignored. Single-molecule magnets (SMMs) are multi-metal ion high spin complexes, in which the ZFI usually has a negative sign, thus affording a ground state level pair with maximal spin quantum number mS = ±S, giving rise to unusual magnetic properties at low temperatures. The description of EPR from SMMs is commonly cast in terms of the 'giant-spin model', which assumes a magnetically isolated system spin, and in which fourth-order, and recently, even sixth-order ZFI terms have been found to be required. A special version of the giant-spin model, adopted for scaling-up to system spins of order S ≈ 103-104, has been applied to the ubiquitous iron-storage protein ferritin, which has an internal core containing Fe3+ ions whose individual high spins couple in a way to create a superparamagnet at ambient temperature with very high system spin reminiscent to that of ferromagnetic nanoparticles. This scaled giant-spin model is critically evaluated; limitations and future possibilities are explicitly formulated.

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H̃=∑i Collapse

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Shadan Ghassemi Tabrizi Department of Chemistry, University of Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm, Germany

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Hubbard Trimer with Spin-Orbit Coupling: Hartree-Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian

We present unrestricted and generalized Hartree-Fock solutions (UHF and GHF, respectively) for the single-band Hubbard model of an equilateral triangle. Spin-orbit coupling (SOC) is treated self-consistently, and HF stability and properties of different spin structures are studied in detail. The GHF solution switches from noncollinear to collinear when crossing a high-symmetry point in parameter space (spanned by the amplitudes of spin-conserving and spin-dependent hopping, i.e., kinetic energy and SOC, respectively). The collinear GHF solution represents a simple example to disprove the notion that a collinear vector spin density in a Slater determinant necessarily entails a defined spin projection. Spin Hamiltonian parameters for the anisotropic interaction between three spin-1/2 centers are extracted from HF energies and subsequently compared to exact results from effective Hamiltonian theory. This provides an unambiguous benchmark for interpreting broken-symmetry mean-field solutions in terms of spin configurations and puts this semiclassical approach (frequently applied in broken-symmetry density functional theory) on a firmer basis.

Hyperfine tensors for a model system for the oxygen evolving complex of photosystem II: calculation of the anisotropy shift that occurs beyond the strong exchange limit

Broken-symmetry density functional calculations have been used to calculate effective ⁵⁵Mn hyperfine (A) tensors for a mixed-valence tetranuclear manganese complex, a model system for the S₂ state of the oxygen-evolving complex of photosystem II.

Quantum Monte Carlo simulations of a giant {Ni21Gd20} cage with a S = 91 spin ground state

The detailed analysis of magnetic interactions in a giant molecule is difficult both because the synthesis of such compounds is challenging and the number of energy levels increases exponentially with the magnitude and number of spins. Here, we isolated a {Ni₂₁Gd₂₀} nanocage with a large number of energy levels (≈5 × 10³⁰) and used quantum Monte Carlo (QMC) simulations to perform a detailed analysis of magnetic interactions. Based on magnetization measurements above 2 K, the QMC simulations predicted very weak ferromagnetic interactions that would give a record S = 91 spin ground state. Low-temperature measurements confirm the spin ground state but suggest a more complex picture due to the single ion anisotropy; this has also been modeled using the QMC approach. The high spin and large number of low-lying states lead to a large low-field magnetic entropy (14.1 J kg^-1 K^-1 for ΔH = 1 T at 1.1 K) for this material.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]₄ ('Ni₄ ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp^- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni₄ , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.

Magnetic Exchange Interactions in the Molecular Nanomagnet Mn_{12}

The discovery of magnetic bistability in Mn_{12} more than 20 years ago marked the birth of molecular magnetism, an extremely fertile interdisciplinary field and a powerful route to create tailored magnetic nanostructures. However, the difficulty to determine interactions in complex polycentric molecules often prevents their understanding. Mn_{12} is an outstanding example of this difficulty: although it is the forefather and most studied of all molecular nanomagnets, an unambiguous determination of even the leading magnetic exchange interactions is still lacking. Here we exploit four-dimensional inelastic neutron scattering to portray how individual spins fluctuate around the magnetic ground state, thus fixing the exchange couplings of Mn_{12} for the first time. Our results demonstrate the power of four-dimensional inelastic neutron scattering as an unrivaled tool to characterize magnetic clusters.