Interlayer RKKY interaction in ferromagnet/tilted Weyl semimetal/ferromagnet trilayer system

Abstract

We have investigated the interlayer RKKY interaction in ferromagnet/Weyl semimetal/ferromagnet (FM/WSM/FM) trilayer system in the presence of the tilting effect of Weyl cones. Our investigation focuses on the influence of the unique features of WSMs: anisotropy dispersion, tilt effect, intervalley transitions, and Fermi arc states. Due to the separation of Weyl nodes, the RKKY behaviors, such as spin model, decaying rate, and oscillation period, heavily depend on the stacked direction of FMs, exhibiting strong magnetic anisotropy. Tilt of Weyl cones can increase the RKKY amplitude, change spin model, switch the antiferromagnetism and ferromagnetism, and more importantly generate the noncollinear Dzyaloshinskii-Moriya or spin-frustrated terms. Intervalley transition generates extra oscillation with period determined by separated distance between Weyl nodes, which together with Fermi-energy-induced oscillation leads to an interesting battering pattern. These signatures are significantly different from the interlayer RKKY interaction with single-node topological insulators or impurity RKKY case reported in previous literatures. More importantly, we find that the interlayer RKKY interaction decays more slowly with the spacer thickness than one reported extensively in WSMs doped with magnetic impurities, which is explained by providing a general formula. In addition, we discuss the effect from Weyl Fermi arcs. Compared to the bulk contributions, a more slowly decaying rate is found at the edges of ferromagnetic layer if the edges are parallel to the line connecting two Weyl nodes. Our research suggests that trilayer FM/WSM/FM is a more powerful platform to understand the WSM magnetic property and to extract the parameters of WSM materials by measuring the RKKY interaction.