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

This study utilizes DFTB simulations to reveal that manganese atoms preferentially intercalate into and embed within NbSe $_2$ bilayers with a 0.68 eV diffusion barrier, exhibiting concentration-dependent inward migration that precedes clustering, thereby offering key insights into the stability and diffusion mechanisms of transition metal intercalation in 2D materials.

Original authors: Bruno Ipaves, Raphael B. de Oliveira, Guilherme da Silva Lopes Fabris, Matthias Batzill, Douglas S. Galvão

Published 2026-01-30

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CC BY 4.0

Original authors: Bruno Ipaves, Raphael B. de Oliveira, Guilherme da Silva Lopes Fabris, Matthias Batzill, Douglas S. Galvão

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a sandwich made of two very thin, flat slices of bread (the NbSe2 layers). In the world of tiny materials, these "slices" are actually sheets of atoms so thin they are essentially two-dimensional. Scientists want to stuff a special ingredient, Manganese (Mn) atoms, inside this sandwich to change how it behaves, much like adding a secret spice to a recipe.

This paper is a computer simulation study that acts like a high-tech "virtual kitchen" to figure out exactly how those Manganese atoms get inside the sandwich and where they like to sit.

Here is the breakdown of their findings using simple analogies:

1. The "Real Estate" Preference: Inside vs. On Top

The researchers asked: If a Manganese atom arrives at this atomic sandwich, does it want to sit on top of the crust (surface adsorption) or sneak inside between the layers (intercalation)?

Think of the Manganese atom as a guest at a party. The computer simulation showed that the guest strongly prefers to hide inside the house rather than stand on the porch.

The Result: The Manganese atoms are much more stable and comfortable when they are sandwiched between the layers or even embedded inside a single layer, rather than just sitting on the very top surface. It's like the guest feels safer and more "at home" in the living room than on the front step.

2. The "Doorway" Challenge: How Hard is it to Get In?

Once the guest is on the porch, how hard is it to get through the door and into the living room? The researchers calculated the "energy cost" (the effort required) to move the Manganese from the surface into the gap between the layers.

The Result: They found the "door" requires a push of 0.68 eV (a specific unit of energy).
The Analogy: This is like pushing a heavy door open. It's not impossible, and it's not a super-heavy vault door either. It's comparable to opening doors in other similar "houses" (materials). This means the Manganese atoms can naturally migrate inside without needing a broken window (defects) or a side entrance (edge sites); they can just walk right through the main door.

3. The "Crowded Room" Effect: How Many Guests Can Fit?

The team ran a time-lapse movie (called Molecular Dynamics) to see what happens when you add more and more Manganese guests to the system at a warm temperature (525 Kelvin, which is about the temperature used in real experiments).

One Guest: If there is only one Manganese atom, it sits on the surface but starts to wander toward the inside.
A Few Guests (4–8): As you add more, they start moving inside more noticeably, but they don't all get in yet.
The Sweet Spot (10 Guests): When they added 10 Manganese atoms, two of them successfully made it all the way inside the layers. This matched what real-world experiments had seen.
Too Many Guests (12): When they added 12, the room got too crowded. The atoms started bumping into each other and forming little clumps (clusters) on the surface, which stopped them from moving further inside.

The Takeaway: You need a certain "density" or crowd of Manganese atoms to successfully push them into the sandwich layers. If there are too few, they hesitate; if there are too many, they get stuck in a traffic jam on the surface.

Summary

In short, this study used a powerful computer model to confirm that:

Manganese atoms love being inside the NbSe2 layers more than on top.
They can walk through the layers without needing holes or cracks in the material.
You need a moderate crowd of Manganese atoms to successfully get them inside, but if the crowd gets too big, they start huddling together on the outside instead of going in.

These findings help scientists understand the "rules of the road" for moving atoms around in these tiny materials, which is a necessary step before they can build new types of electronic devices.

Technical Summary: Unraveling Mn Intercalation and Diffusion in NbSe2 Bilayers through DFTB Simulations

Problem Statement
While experimental studies have demonstrated the feasibility of intercalating manganese (Mn) guest atoms into niobium diselenide (NbSe2) layers to synthesize atomically engineered films, the microscopic mechanisms governing the atomic interactions, diffusion pathways, and stability of these systems remain incompletely understood. Specifically, the exact diffusion mechanism and the energetic preference for Mn atoms to reside on the surface versus within the interlayer or embedded positions require further elucidation to advance the design of transition metal dichalcogenide (TMD) based devices.

Methodology
The study employed Density Functional Tight Binding (DFTB) simulations using the DFTB+ code with Slater-Koster parametrization from the PTBP dataset. The computational approach included:

Structural Optimization: Rational optimization of bulk (3D) and bilayer (2D) NbSe2 structures, preserving symmetry with convergence criteria set to an energy threshold of $10^{-6}$ Ha and a force threshold of $10^{-3}$ Ha/Bohr. Long-range dispersion interactions were modeled via Lennard-Jones corrections.
Stability Analysis: Cohesive energy ( $E_{coh}$ ) calculations were performed to compare the stability of Mn in various configurations: surface adsorption (hollow, Nb-top, Se-top), intercalation between layers, and embedding within a single NbSe2 layer.
Diffusion Barriers: Nudged Elastic Band (NEB) calculations, implemented via the Atomic Simulation Environment (ASE) with the Improved Diameter Projection Path (IDPP) method, were used to determine energy barriers for Mn migration between sites.
Dynamic Behavior: Molecular Dynamics (MD) simulations were conducted using the velocity Verlet algorithm with a 1.0 fs time step. Systems were equilibrated and propagated for 20 ps at 525 K (250 °C) using a Nosé-Hoover thermostat to simulate experimental conditions. Simulations were performed for varying Mn concentrations (1, 4, 8, 10, and 12 atoms per supercell).

Key Results

Energetic Stability: Cohesive energy calculations indicate that Mn atoms prefer intercalated and embedded positions over surface adsorption. The embedded configuration was found to be the most stable ( $E_{coh} = -5.639$ eV), followed by the intercalated position ($-5.573$ eV). Surface adsorption sites (Se-top, hollow, Nb-top) exhibited lower stability, ranging from $-3.129$ eV to $-5.060$ eV.
Migration Barriers: NEB calculations revealed an energy barrier of 0.68 eV for the migration of Mn from a hollow surface site to an intercalated position, passing through an embedded state. This barrier is comparable to values reported for Mn on other substrates (e.g., graphene/Ge, GaAs), suggesting that Mn can migrate into the van der Waals gap without requiring defects or edge sites.
Concentration-Dependent Intercalation: MD simulations demonstrated that intercalation behavior is concentration-dependent. At low concentrations (1 Mn atom), Mn remained on the surface but showed a tendency to diffuse inward. As concentration increased to 10 Mn atoms, full intercalation of two atoms into the layers was observed, aligning with experimental findings. However, at higher concentrations (12 Mn atoms), clustering effects emerged, which limited further diffusion.
Discrepancy in Concentration: The simulations indicated that higher Mn concentrations are required to drive atoms into intercalation sites compared to experimental observations. The authors suggest this may imply the importance of defects in experimental settings or the existence of other intercalation sites with lower adsorption energies than the embedded sites modeled.

Significance and Claims
The paper claims to provide atomic-scale insights into the diffusion pathways and stability of Mn atoms within NbSe2 bilayers, offering a deeper understanding of heteroatom intercalation mechanisms in TMDs. The findings suggest that Mn embedding occurs spontaneously under suitable conditions and is energetically more favorable than surface adsorption. The study posits that intercalation serves as an effective strategy for tuning the electronic and magnetic properties of NbSe2, potentially enabling the design of new functional phases for TMD-based device applications, particularly in the context of spintronics. The results are presented as consistent with experimental observations regarding the lack of strong dependence on defects for intercalation, while also highlighting the role of concentration and potential defect-mediated pathways in real-world scenarios.

1. The "Real Estate" Preference: Inside vs. On Top

2. The "Doorway" Challenge: How Hard is it to Get In?

3. The "Crowded Room" Effect: How Many Guests Can Fit?

Summary

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