Mathematical Modeling and Simulation of Exchange Coupling Constant (J) and Zero-Field Splitting Parameters (D)

Abstract

The study of low-dimensional magnets entails an in-depth inspection of the quantum chemical origin of magnetism. The microscopic spin Hamiltonian (SH) provides the necessary theoretical underpinning of spin and orbital angular momentum and their interaction, which contributes to the overall magnetic nature of molecular nanomagnets. This chapter reviews different mathematical models and computational methodologies involved in the evaluation of two particular SH parameters, which are the isotropic exchange coupling constant ( J ) and the zero-field splitting (D) parameter. The interaction among spins through different exchange mechanisms is quantified in terms of the exchange coupling constant ( J ), which dictates the overall ground spin state. In addition to the ground spin state, it is also important to evaluate the energy barrier for magnetization reversal, often called the magnetic anisotropy energy (MAE) barrier. High MAE causing slow magnetic relaxation in nanomagnetic systems increases their suitability for technological applications. The MAE can be quantified in terms of zero-field splitting (ZFS) parameters, D and E, defined as axial and rhombic anisotropy parameters. The chapter describes effective spin Hamiltonians along with an overview of the state-of-the-art computational methods based on density functional theory (DFT) and wave function theory (WFT), which are used for estimation of the exchange coupling constant and ZFS parameters.