Thickness-dependent anisotropic Gilbert damping in heterostructures of ferromagnets and two-dimensional ferroelectric bismuth monolayers

The Gilbert damping parameter, which describes magnetization dynamics, is crucial for the performance of modern spintronic devices, affecting factors such as the switching speed and critical current density of magnetoresistive random access memory. Thus, the ability to engineer it on demand is pivotal for developing spintronic applications. In this paper, we systematically examine the Gilbert damping parameter of Fe films in contact with a black phosphoruslike bismuth monolayer using first-principles calculations. In these Bi/Fe heterostructures, we obtain a significantly enhanced Gilbert damping owing to strong interfacial spin-orbit couplings (SOCs). Interestingly, we find nonmonotonic thickness-dependent Gilbert damping anisotropy and attribute that to the competition between the interfacial SOC and the intrinsically anisotropic SOC of Fe films. We further demonstrate that these SOC effects lead to anisotropic band structures, which are responsible for the anisotropic Gilbert damping. In this paper, we provide a deep understanding of the anisotropic Gilbert damping and open avenues for exploring it in ferromagnetic heterostructures.