Interpretation and Quantification of Magnetic interaction through Spin Topology

摘要

This work develops a formalism to quantify the interaction among unpaired spins from the ground state spin topology. Magnetic systems where the spins are coupled through direct exchange and superexchange are chosen as references. Starting from a general Hamiltonian, an effective Hamiltonian is obtained in terms of spin density which is utilized to compute exchange coupling constants in magnetic systems executing direct exchange, The high-spin-low-spin energy gap, required to extract the coupling constant, is obtained through the broken symmetry approach within the framework of density functional theory. On the other hand, a perturbative approach is adopted to address the superexchange process. Spin transfer in between the sites in the exchange pathway is found to govern the magnetic nature of a molecule executing superexchange. The metal-ligand magnetic interaction is estimated using the second order perturbation energy for ligand to metal charge transfer and spin densities on the concerned sites. Using the present formalism, the total coupling constant in a superexchange process is also partitioned into the contributions from metal-ligand and metal-metal interactions. Sign and magnitude of the exchange coupling constants, derived through the present formalism, are found to be in parity with those obtained using the well-known spin projection technique. Moreover, in all of the cases, the ground state spin topology is found to complement the sign of coupling constants. Thus, the spin topology turns into a simple and logical means to interpret the nature of exchange interaction. The spin density representation in the present case resembles McConnell's spin density Hamiltonian and in turn validates it.