Theory of Mechanism of $\pi$-d Interaction in Iron-Phthalocyanine

TL;DR

This paper investigates the exchange interaction mechanism between d and π electrons in an iron-phthalocyanine compound, revealing a double Hund's exchange process that can lead to either ferromagnetic or antiferromagnetic coupling.

Contribution

It introduces a new understanding of the exchange interaction in Fe-Pc compounds, emphasizing the role of Hund's rule processes over super-exchange mechanisms.

Findings

No hybridization between d-orbitals and LUMO of π-orbitals.

The exchange interaction J can be ferromagnetic or antiferromagnetic depending on parameters.

J is estimated to be antiferromagnetic and around 100K.

Abstract

Transition metal-phtahalocyanine(Pc) compound, TPP[Fe(Pc)(CN)$_2$]$_2$, which is one of molecular conductors of charge transfer type with 3/4-filled conduction band consisting of LUMO of Pc molecules, shows characteristic features in transport and magnetic properties resulting from localized magnetic moments $S=1/2$ associated with Fe$^{+3}$ atoms. We construct an effective tight-binding model of this system and study the mechanism of exchange interaction, $J$, between $d$ and $\pi$ electrons based on both second order perturbation of transfer integrals between $d$ and $\pi$ orbitals and numerical diagonalization. It is found that there is no hybridization between $d$-orbitals and LUMO of $\pi$-orbitals and then super-exchange interaction in the Anderson model does not exist. Instead, processes associated with Hund's rule both on $d$ and $\pi$ orbitals, which may be called "the double Hund's exchange mechanism", turn out to play important roles and the sign of resultant $J$ can be either ferromagnetic or antiferromagnetic depending on model parameters because of competition among various processes. By taking account of magnetic anisotropy due to spin-orbit interactions and comparing with experimental results, it is indicated that $J$ is antiferromagnetic and of the order of 100K.