Molecular magnetism in the multi-configurational self-consistent field method

Abstract

We develop a structured theoretical framework used in our recent articles (2019 Eur. Phys. J. B 92 93 and 2020 Phys. Rev. B 101 094427) to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic susceptibility of the molecular magnet Ni4Mo12. The theoretical background is based on the molecular orbital theory in conjunction with the multi-configurational self-consistent field method and results in a post-Hartree–Fock scheme for constructing the corresponding energy spectrum. Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete coupling parameters accounting for the relevant spectroscopic magnetic excitations, magnetization and magnetic susceptibility. The explicit expressions of the eigenenergies of the ensuing Hamiltonian are determined and the physical origin of broadening and splitting of experimentally observed peaks in the magnetic spectra is discussed. To demonstrate the efficiency of our method we compute the spectral properties of a spin-one magnetic dimer. The present approach may be applied to a variety of magnetic units based on transition metals and rare Earth elements.

An Exchange Mechanism for the Magnetic Behavior of Er3+ Complexes

“…To study the experimentally observed magnetic properties of the compounds Na [Er(W O ) ] [ 9 ] and [(Pc)Er{Pc{N(C H ) } }] [ 24 ], we rely on the method proposed in Reference [ 25 ]. Here, we assume that a single molecule hosts no more than three unpaired valence electrons in its ground state with all non-bonding orbitals being fully occupied.…”

“…Under the considered assumptions and the introduced effective spin coupling scheme, the spin–sigma Hamiltonian reads (see e.g., Reference [ 25 ]) where is the intramolecular exchange parameter between the spin centers, the effective three components’ spin operator and the spin-like operator are associated to the i -th magnetic center. The operator in the field dependent term satisfies the relation where , with , is the -th component of the i -th spin operator and …”

“…Notice that, for all , s and m , is the -th component of the effective g -factor, say , and are the corresponding spectroscopic and field parameters, respectively. Moreover, we would like to point out that the model parameters, related to Hamiltonian ( 1 ), account for the contribution of all electrons occupying core molecular orbitals and that, due to the lack of exchange bridges, the value of the g -factor does not depend directly on any of the three good spin quantum numbers as the general case described in Reference [ 25 ] suggests. For more details about the physics behind all model parameters, the reader may consult Reference [ 25 ].…”

“…We demonstrate that the effective energy barrier to magnetization reversal satisfies the inequality meV, which agrees very well with the experimental value of meV [ 9 ], explaining the slow magnetic relaxation. The model further suggests an abrupt change in the ground state from a non-fully polarized spin ground state in the absence of an external magnetic field to a fully spin polarized one that does not result from the decreased spin rotational degeneracy caused by the relevant Zeeman interactions, but rather orbital ones that affect the system’s energy indirectly due to the used multi-configurational basis, see Reference [ 25 ].…”

“…In this paper, we study to what extent an effective spin exchange Hamiltonian may rationalize the magnetic properties of Er single ion magnets. To this end, we adapt a recently proposed spin–sigma model [ 25 ] and focus on the erbium-based molecular magnets, Na [Er(W O ) ] and [(Pc)Er{Pc{N(C H ) } }] . The proposed model is developed within the multi-configurational self-consistent field method, and was successfully used to characterize the magnetism of the molecular magnet, Ni Mo [ 26 , 27 ], and the magnetic spectrum of the trimeric compounds, A Cu (PO ) A=(Ca, Sr, Pb) [ 28 ].…”