Microscopic Origins and Stability of Ferromagnetism in Co3Sn2 S2

Based on the density functional theory, we examine the origin of ferromagnetism in the Weyl semimetal Co3Sn2S2 using different types of response theories. We argue that the magnetism of Co3Sn2S2 has a dual nature and bears certain aspects of both itineracy and localization. On the one hand, the magnetism is soft, where the local magnetic moments strongly depend on temperature and the angles formed by these moments at different Co sites of the kagome lattice, as expected for itinerant magnets. On the other hand, the picture of localized spins still remains adequate for the description of the local stability of the ferromagnetic (FM) order with respect to the transversal spin fluctuations. For the latter purposes, we employ two approaches, which provide quite different pictures for interatomic exchange interactions: the regular magnetic force theorem and a formally exact theory based on the calculation of the inverse response function. The exact theory predicts Co3Sn2S2 to be a three-dimensional ferromagnet with the strongest interaction operating between next-nearest neighbors in the adjacent kagome planes. The ligand states are found to play a very important role by additionally stabilizing the FM order. When the local moments decrease, the interplane interactions sharply decrease, first causing the FM order to become quasi-two-dimensional, and then making it unstable with respect to the spin-spiral order propagating perpendicular to the kagome plane. The latter instability is partly contributed by the states at the Fermi surface and may be relevant to the magnetic behavior of Co3Sn2S2 near the Curie temperature. Peculiarities of the half-metallic ferromagnetism in Co3Sn2S2 are also discussed. © 2022 American Physical Society. I.V.S. acknowledges useful communication with V. P. Antropov, drawing our attention to Refs. on validity of the Heisenberg model for transition metals, S. Okamoto on details of Ref., S. Streib on the relation between exchange parameters in MFT and the exact approach, and Y. Anahory, drawing our attention to the phenomenon of exchange bias in . The work was supported by the project RSF 20-62-46047 of the Russian Science Foundation in the part of conventional DFT calculations and the program AAAA-A18-118020190095-4 (Quantum) of the Russian Ministry of Science and Higher Education in the part of construction and analysis of microscopic models of interatomic exchange interactions.