First-principles study of the magnetic anisotropic exchange interactions and magnetoelastic coupling in Fe-based kagome metals

Anisotropic magnetic exchange interactions induced by spin-orbit coupling have been less explored than their isotropic part and, when they were, they were nearly always limited to the Dzyaloshinskii-Moriya interaction (DMI) and single-site anisotropy. In our work, we address the full magnetic exchange interaction matrix using density functional theory, including all terms allowed by the crystal symmetry of Fe-based kagome metal. To this end, we propose an accurate but computationally inexpensive protocol to obtain the anisotropic magnetic exchange interactions, whereby only the spin quantization axis is rotated and other parameters remain fixed, reducing computational noise. We observe a smooth trigonometric energy dependence on the rotation angle and extract magnetic interaction parameters from the trigonometric equation fitting obtained from our mathematical expression for the Fe-based kagome metal. We also investigated how the chemical composition and crystal structure affect DMI and other anisotropic terms in the Fe-based kagome structure. Our simple protocol for robust calculations of nonzero anisotropic magnetic interactions, which naturally cancel our systematic errors, can be readily applied to other materials. In the second part, we calculate zone-center phonon frequencies and show how they depend on the presence of magnetism and on the pattern of magnetic ordering.