Orbital-resolved superexchange and topological magnon bands in MXene Fe$_2$C

Abstract

Magnetic MXenes are promising candidates for future spintronics due to their intriguing properties. Nevertheless, the topological properties of magnon bands and superexchange mechanism remain relatively underexplored. In this work, we have calculated the spin wave dispersions for MXene Fe$_2$C using the linear spin wave method, with the exchange coupling parameters obtained from first-principles calculations. Owing to the staggered stacking of two Fe sub-lattices, the interlayer exchange coupling lifts the degeneracy of the ferromagnetic magnon modes. A Dirac point is identified in the magnon bands at the $K$ point. The topological properties of magnon bands, including Berry curvature, valley Chern number and edge states, are further computed by means of a two-band model. We also derive an effective Hamiltonian to explain the magnonic topology, which is protected by the $C_{3v}$ rotational symmetry. To understand the microscopic origin of the exchange couplings that govern the magnon bands, we then construct a refined model integrating perturbation theory and the tight-binding approach. The ferromagnetic superexchange coupling is mediated by the virtual hopping between the d orbitals of two distinct Fe sites via a pair of orthogonal p orbitals at the bridging C site. In detail, the intralayer exchange coupling is governed by the in-plane $p_x$ and $p_y$ orbitals, while the out-of-plane $p_z$ orbital is responsible for the interlayer exchange coupling. Our results establish a direct link between the orbital-resolved anisotropic superexchange and topological properties of the magnon bands in magnetic MXene Fe$_2$C, providing theoretical guidance for future spintronics applications.