From Density Functional Theory to Spin Hamiltonians: Magnetism in $d^5$ Honeycomb Compound OsCl$_3$

TL;DR

The study tackles magnetism in a 2D honeycomb magnet with five d-electrons by combining DFT-derived t2g hopping/crystal-field parameters with a multi-orbital Hubbard-Kanamori model including spin-orbit coupling. Exact diagonalization on a two-site cluster yields a low-energy pseudospin Hamiltonian with bond-dependent Heisenberg, Kitaev, and Gamma exchanges, whose U and JH dependence is analyzed. A semiclassical Luttinger-Tisza treatment then reveals a zigzag antiferromagnetic ground state for OsCl3 that aligns with DFT findings, highlighting the preeminence of the Gamma term in driving order. The work provides a practical, first-principles-inspired route to extract magnetic exchange parameters in strongly correlated honeycomb magnets, enabling efficient exploration of Kitaev-like physics in real materials.

Abstract

Magnetism in strongly correlated honeycomb systems with $d^5$ electronic configuration has garnered significant attention due to its potential to realize the Kitaev spin liquid state, characterized by exotic properties. However, real materials exhibit not only Kitaev exchange interactions but also other magnetic exchanges, which may drive the transition from a spin liquid phase to a long-range ordered ground state. This work focuses on modelling the effective spin Hamiltonian for two-dimensional (2D) honeycomb magnetic systems with $d^5$ electronic configurations. The Hubbard-Kanamori (HK) Hamiltonian equipped with spin-orbit coupling and electron correlations is considered where onsite energies and hopping parameters, preserving the crystal symmetry, are extracted from the first principles Density functional theory (DFT) calculations. Exact diagonalization (ED) calculations for the HK Hamiltonian on a two-site cluster are performed to construct the effective magnetic Hamiltonian. The ground-state magnetic properties are explored using the semi-classical Luttinger-Tisza approach. As a representative case, the magnetic ground state of the $d^5$ honeycomb system OsCl$_3$ is investigated, and the variation of magnetic exchange parameters with respect to the correlation strength (U) and Hund's coupling ($J_H$) is analyzed. The magnetic ground state exhibits zigzag antiferromagnetic ordering for a chosen value of $U$ and $J_H$, consistent with DFT results. This study provides insight into the magnetism of OsCl$_3$ and offers a computationally efficient alternative to traditional energy-based methods for calculating exchange interactions for strongly correlated systems.

Figures (4)

• Figure 1: Crystal structure of OsCl$_3$: (a) Os atoms form a honeycomb network, with Cl ligands creating an octahedral environment. (b) Nearest-neighbour bonds X (red), Y (green), Z (blue), and the local coordinate system (x, y, z) defined by Cl ligands, forming an octahedral cage around Os. (c) Alternative viewpoint of the OsCl$_3$ structure.
• Figure 2: Electronic properties: (a) Non-spinpolarized electronic band structure and DOS, showing the dominance of the $d$-$t_{2g}$ bands of the Os atom near $E_F$. (b)$t_{2g}$ MLWFs obtained from Wannierization, oriented according to the local coordinate system.
• Figure 3: Variation of magnetic-exchange parameters with correlation parameter $U$ for first nearest-neighbour bonds: (a) Z-bond and (b) X and Y bonds, for $J_H/U = 0.18$.
• Figure 4: Semi-classical ground state obtained from Luttinger-Tisza method:(a) The magnetic ground state of OsCl$_3$. (b) The minimum energy distribution obtained from Luttinger-Tisza approach.