Dzyaloshinskii-Moriya interaction and chiral magnetism in 3$d$-5$d$ zig-zag chains: Tight-binding model and ab initio calculations

TL;DR

This study combines first-principles calculations and a minimal tight-binding model to analyze the Dzyaloshinskii-Moriya interaction in 3d-5d zig-zag chains, revealing how electronic structure influences chiral magnetic order.

Contribution

It introduces a minimal tight-binding model that captures key features of DMI in 3d-5d chains, validated by ab initio calculations, providing new insights into the electronic origins of chiral magnetism.

Findings

DMI significantly influences magnetic structure energetics.

The tight-binding model reproduces key features of ab initio results.

Hybridization, bandwidth, and energy differences determine DMI sign and strength.

Abstract

We investigate the chiral magnetic order in free-standing planar 3$d$-5$d$ bi-atomic metallic chains (3$d$: Fe, Co; 5$d$: Ir, Pt, Au) using first-principles calculations based on density functional theory. We found that the antisymmetric exchange interaction, commonly known as Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. We used the full-potential linearized augmented plane wave method and performed self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction (SOI) in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and 4 orbitals that contains all essential features: the spin-canting between the magnetic $3d$ atoms, the spin-orbit interaction at the $5d$ atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We found that spin-canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the $5d$ atom. We show that, the sign and strength of the hybridization, the bonding or antibonding character between $d$-orbitals of the magnetic and non-magnetic sites, the bandwidth and the energy difference between states occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.