Effective Hamiltonians from Spin Adapted Configuration Interaction

TL;DR

This paper introduces a generalized method for deriving effective Hamiltonians to analyze magnetic interactions in multi-site systems with high local spins, using angular momentum graphical techniques and ab initio data.

Contribution

It presents a new, non-recursive extraction procedure applicable to systems with multiple high-spin sites, extending previous two-site methods and incorporating symmetry considerations.

Findings

Derived closed-form expressions for chains of equal spins.

Successfully applied the method to a complex Mn cubane system.

Extended the approach to non-sequential coupling schemes.

Abstract

A generalised extraction procedure for magnetic interactions using effective Hamiltonians is presented that is applicable to systems with more than two sites featuring local spins $S_i \geq 1$. To this end, closed, non-recursive expressions pertaining to chains of arbitrary equal spins are derived with the graphical method of angular momentum. The method is illustrated by extracting magnetic couplings from ab initio calculations on a [CaMn$_3$$^{(IV)}$O$_4$] cubane. An extension to non-sequential coupling schemes proves conducive to expressing additional symmetries of certain spin Hamiltonians.