# Spin Molecular Orbital Coupling in Organometallic Complexes - A new approach

Speaker: Amie Khosla

Affiliation: University of Queensland

### Abstract

Spin-orbit coupling (SOC) is a relativistic effect that entangles orbital and spin degrees of freedom such that neither remain good quantum numbers. It splits otherwise degenerate sets of orbitals. The combination of SOC and strong electronic correlations can lead to a variety of novel phases such as topological Mott insulators and quantum spin liquids. To date much of this research has been largely focused on inorganic atomic crystals with partially filled d-orbitals, in particular transition metal oxides. In these systems the SOC is essentially atomic and increases with atomic number. Molecular crystals provide a novel playground for understanding the combined effect of strong SOC and electron correlations - due to the tunability of these organic and organometallic systems.

Calculating the exact form of the SOC is a difficult task. Thus SOC is often treated by only attributing its effects to the heaviest atoms in the molecule and assuming that the spherically symmetry of a single atom remains. In this work we present a new approach to determining the form of the SOC for organometallic systems and present the emergence of a Spin Molecular Orbital Coupling (SMOC) that is unlike what might be expected.

I will discuss my work on deriving the SOC Hamiltonians for all 32 Point Groups, starting with the simplest case of cyclic symmetry and moving on to the larger groups of higher symmetry. We invoke group theoretical techniques to derive the exact form of the SOC Hamiltonian. We make use of not only the geometric symmetry of the system but also time reversal symmetry. This method does not allow us to determine terms in the Hamiltonian are allowed to exist based on the symmetry alone, without the need for atomistic calculations.

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