Monometallic Ni(II) and Co(II) complexes with large magnetic anisotropy are studied using correlated wave function based ab initio calculations. Based on the effective Hamiltonian theory, we propose a scheme to extract both the parameters of the zero-field splitting (ZFS) tensor and the magnetic anisotropy axes. Contrarily to the usual theoretical procedure of extraction, the method presented here determines the sign and the magnitude of the ZFS parameters in any circumstances. While the energy levels provide enough information to extract the ZFS parameters in Ni(II) complexes, additional information contained in the wave functions must be used to extract the ZFS parameters of Co(II) complexes. The effective Hamiltonian procedure also enables us to confirm the validity of the standard model Hamiltonian to produce the magnetic anisotropy of monometallic complexes. The calculated ZFS parameters are in good agreement with high-field, high-frequency electron paramagnetic resonance spectroscopy and frequency domain magnetic resonance spectroscopy data. A methodological analysis of the results shows that the ligand-to-metal charge transfer configurations must be introduced in the reference space to obtain quantitative agreement with the experimental estimates of the ZFS parameters.

The magnetic anisotropy of the [Ni2(en)4Cl2](2+) (en = ethylenediamine) complex has been studied using wave function based computational schemes. The spin-orbit state interaction methodology provides accurate ab initio energies and wave functions that are used to interpret the anisotropy in bimetallic complexes. The extraction of the anisotropic spin Hamiltonian is performed using the effective Hamiltonian theory. This procedure which has successfully been applied to mononuclear complexes enables one to solve the weak exchange limit. It is shown that the standard coupled spin Hamiltonian only describes a part of the anisotropy of the molecule. Important higher order terms such as the biquadratic anisotropic exchange should be included in the model for an appropriate description of the anisotropy.

This paper analyzes the different contributions to the magnetic coupling in systems with more than one unpaired electron per center. While in S=12 spin systems the Heisenberg Hamiltonian involving only bilinear exchange interactions is reliable for the description of the magnetic states, biquadratic exchange interactions must be sometimes introduced for S=1 (or higher) spin systems to account for isotropic deviations to Heisenberg behavior. The analysis establishes that the excited atomic states, the so-called non-Hund states, are responsible for the main contribution to the deviations. The kinetic exchange contribution and the spin, hole, and particle polarizations increase the magnetic coupling but essentially maintain the Heisenberg pattern. The importance of the different contributions has been studied for a series of Ni(2) compounds with a polarizable double azido bridge. The coupling between two Fe(3+) ions in the molecular crystal Na(3)FeS(3), which is known experimentally to present large deviations to Heisenberg behavior, has also been investigated.

Herein we evaluate the influence of an electric field on the coupling of two delocalized electrons in the mixed-valence polyoxometalate (POM) [GeV14 O40 ](8-) (in short V14 ) by using both a t-J model Hamiltonian and DFT calculations. In absence of an electric field the compound is paramagnetic, because the two electrons are localized on different parts of the POM. When an electric field is applied, an abrupt change of the magnetic coupling between the two delocalized electrons can be induced. Indeed, the field forces the two electrons to localize on nearest-neighbors metal centers, leading to a very strong antiferromagnetic coupling. Both theoretical approaches have led to similar results, emphasizing that the sharp spin transition induced by the electric field in the V14 system is a robust phenomenon, intramolecular in nature, and barely influenced by small changes on the external structure.

We have reanalyzed the microscopic origin of the isotropic deviations that are observed from the energy spacings predicted by the HDVV Hamiltonian. Usually, a biquadratic spin operator is added to the HDVV Hamiltonian to account for such deviations. It is shown here that this operator cannot describe the effect of the excited atomic non-Hund states which brought the most important contribution to the deviations. For systems containing more than two magnetic centers, non-Hund states cause additional interactions that are of the same order of magnitude as the biquadratic exchange and should have significant effects on the macroscopic properties of extended systems. 71.27+a The magnetic interactions between S=1/2 sites can accurately be parametrized with the standard Heisenberg-Dirac-van Vleck (HDVV) Hamiltonian [1]. Usually this Hamiltonian is extrapolated to systems with higher spin moments and the interaction between such magnetic sites gives rise to an energy spectrum with a regular spacing between the different levels, the so-called Landé pattern: E(S − 1) − E(S) = SJ, where J parametrizes the strength of the magnetic coupling between magnetic centers. However, in some cases significant deviations from this regular pattern are observed and extra terms must be added to the HDVV Hamiltonian. One of the most commonly applied extensions of the HDVV Hamiltonian is the addition of the biquadratic exchange term:where ij are couples of interacting sites, J eff is the effective bilinear exchange and λ eff the biquadratic exchange. Numerous theoretical and experimental studies have established that the biquadratic interaction significantly affects the magnetic properties of both ferromagnets and antiferromagnets [2,3]. For instance, the ferromagnetic phase transition [4] changes character from first-order to second-order for a critical value λ eff c . The spontaneous magnetization, the exchange energy and the spin-correlation function exhibit discontinuous jumps at λ eff = λ eff c and unstable behavior for λ eff > λ eff c . One may also quote that from spin wave theory, both ferromagnetic and antiferromagnetic spin structures change abruptly to canted ones [5] for a critical value of λ eff . More recently, the phase diagram of the S=1 model given in equation 1 has been precisely studied in triangular lattice in a magnetic field, with emphasis on the quadrupolar phases[6] as well as in spin one chains where the open question of the existence of a ferroquadrupolar phase between the dimerized and the ferromagnetic phases is adressed [7].The theoretical explanation of the appearance of a bi-quadratic exchange was initially given by Anderson [8] and Kittel [9]. The analysis of its physical content was performed based on a Hubbard Hamiltonian applied to a dimer of magnetic sites [10]. The microscopic origin of the isotropic non-Heisenberg behavior is here reanalyzed. A magnetic Hamiltonian is extracted at the fourth-order of perturbation from a Hubbard Hamiltonian of a trimer of magnetic sites. In comparison to previous w...

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The variational energies of broken-symmetry single determinants are frequently used (especially in the Kohn-Sham density functional theory) to determine the magnetic coupling between open-shell metal ions in molecular complexes or periodic lattices. Most applications extract the information from the solutions of m(s)(max) and m(s)(min) eigenvalues of S(z) magnetic spin momentum, assuming that a mapping of these energies on the energies of an Ising Hamiltonian is grounded. This approach is unable to predict the possible importance of deviations from the simplest form of the Heisenberg Hamiltonians. For systems involving s=1 magnetic centers, it cannot provide an estimate of neither the biquadratic exchange integral nor the three-body operator interaction that has recently been proven to be of the same order of magnitude [Phys. Rev. B 70, 132412 (2007)]. The present work shows that one may use other broken-symmetry solutions of intermediate values of m(s) to evaluate the amplitude of these additional terms. The here-derived equations rely on the assumption that an extended Hubbard-type Hamiltonian rules the interactions between the magnetic electrons. Numerical illustrations on a model problem of two O(2) molecules and a fragment of the La(2)NiO(4) lattice are reported. The results obtained using a variable percentage of Fock exchange in the BLYP functional are compared to those provided by elaborate wave function calculations. The relevant percentage of Fock exchange is system dependent but a mean value of 30% leads to acceptable amplitudes of the effective exchange interaction.

We compute the temperature-dependent spin-wave spectrum and the magnetization for a spin system using the unified decoupling procedure for the high-order Green's functions for the exchange coupling and anisotropy, both in the classical and quantum case. Our approach allows us to establish a clear crossover between quantum-mechanical and classical methods by developing the classical analog of the quantum Green's function technique. The results are compared with the classical spectral density method and numerical modeling based on the stochastic Landau-Lifshitz equation and the Monte Carlo technique. As far as the critical temperature is concerned, there is a full agreement between the classical Green's functions technique and the classical spectral density method. However, the former method turns out to be more straightforward and more convenient than the latter because it avoids any a priori assumptions about the system's spectral density. The temperature-dependent exchange stiffness as a function of magnetization is investigated within different approaches.