Unraveling Mn intercalation and diffusion in NbSe$_2$ bilayers through DFTB simulations

Understanding transition metal atoms’ intercalation and diffusion behavior in two-dimensional (2D) materials is essential for advancing their potential in spintronics and other emerging technologies. In this study, we used density functional tight binding (DFTB) simulations to investigate the atomic-scale mechanisms of manganese (Mn) intercalation into NbSe$_2$ bilayers. Our results show that Mn prefers intercalated and embedded positions rather than surface adsorption, as cohesive energy calculations indicate enhanced stability in these configurations. Nudged elastic band (NEB) calculations revealed an energy barrier of 0.68 eV for the migration of Mn into the interlayer, comparable to other substrates, suggesting accessible diffusion pathways. Molecular dynamics (MD) simulations further demonstrated an intercalation concentration-dependent behavior. Mn atoms initially adsorb on the surface and gradually diffuse inward, resulting in an effective intercalation at higher Mn densities before clustering effects emerge. These results provide helpful insights into the diffusion pathways and stability of Mn atoms within NbSe$_2$ bilayers, consistent with experimental observations and offering a deeper understanding of heteroatom intercalation mechanisms in transition metal dichalcogenides.

💡 Research Summary

In this work the authors employ density‑functional‑tight‑binding (DFTB) simulations to investigate how manganese (Mn) atoms intercalate and diffuse within a NbSe₂ bilayer, a representative transition‑metal dichalcogenide (TMD). The study proceeds in four logical stages. First, the computational protocol is validated: using the DFTB+ code together with the recently developed PTBP Slater‑Koster parameters, bulk (3‑D) NbSe₂ and a vacuum‑separated bilayer are fully relaxed. The resulting lattice constants (a ≈ 3.607 Å, c ≈ 13.44 Å) match experimental reports, confirming that the chosen tight‑binding description faithfully reproduces the host material.

Second, five plausible Mn adsorption sites are examined on a 4 × 4 supercell: three surface sites (hollow, Nb‑top, Se‑top) and two insertion sites (intercalated between the two layers, and embedded within a single layer at an interstitial position). Cohesive energies are computed via a standard expression that subtracts the energies of the isolated NbSe₂ sheet and isolated Mn atoms from the total energy of the Mn‑doped system. The embedded configuration (E_coh = −5.639 eV) and the intercalated configuration (E_coh = −5.573 eV) are markedly more stable than any surface adsorption site (ranging from −3.129 eV to −5.060 eV). This thermodynamic analysis demonstrates that Mn prefers to reside inside the van‑der‑Waals gap or within the chalcogen layer rather than staying on the exterior surface.

Third, the kinetic barrier for Mn migration from a surface hollow site into the interlayer space is quantified using the nudged elastic band (NEB) method as implemented in the Atomic Simulation Environment (ASE). Three intermediate images are generated and refined with the improved initial guess (IDPP) scheme. The calculated maximum energy along the minimum‑energy path is 0.68 eV. This value is comparable to previously reported Mn diffusion barriers in other heterostructures (e.g., Mn/graphene/Ge(001) or Mn/graphene/GaAs(001) with barriers of 0.1–0.5 eV, and Mn diffusion in GaAs with 0.7–0.8 eV). Consequently, Mn can penetrate the van‑der‑Waals gap without the assistance of defects or edge sites, provided a modest thermal activation (the simulations are performed at 525 K, the experimental growth temperature).

Fourth, molecular dynamics (MD) simulations are carried out to capture the collective, concentration‑dependent behavior. Using a velocity‑Verlet integrator with a 1 fs timestep and a Nosé‑Hoover thermostat, the system is equilibrated and then propagated for 20 ps at 525 K. Five Mn loadings are examined: 1, 4, 8, 10, and 12 Mn atoms per supercell. At the lowest loading, Mn remains on the surface but shows a gradual tendency to move inward. With 4 and 8 atoms, partial inward migration is observed, yet full intercalation is not achieved within the simulation window. At 10 atoms, two Mn atoms successfully reach the interlayer region, reproducing the experimental observation of Mn intercalation in NbSe₂ films. When the concentration is increased to 12 atoms, clustering of Mn occurs, which hinders further diffusion. This concentration‑dependent trend suggests that while thermal energy is sufficient to overcome the 0.68 eV barrier, a critical surface coverage is required to drive the atoms into the gap; excess Mn, however, leads to aggregation rather than additional intercalation.

Overall, the paper delivers three key insights: (i) Mn is thermodynamically favored to occupy intercalated or embedded sites within NbSe₂ bilayers; (ii) the diffusion barrier of 0.68 eV is modest, indicating that Mn can migrate into the van‑der‑Waals gap under realistic growth temperatures without needing defect‑mediated pathways; and (iii) a sufficient Mn surface concentration is essential for efficient intercalation, whereas over‑saturation promotes clustering. These findings have direct implications for engineering magnetic and electronic properties of NbSe₂ via transition‑metal doping, guiding the design of spintronic devices and tailored van‑der‑Waals heterostructures.