Reduction of Magnetic Interaction Due to Clustering in Doped Transition-Metal Dichalcogenides: A Case Study of Mn-, V-, and Fe-Doped WSe 2 .

Using Hubbard-U-corrected density functional theory calculations, lattice Monte Carlo simulations, and spin Monte Carlo simulations, we investigate the impact of dopant clustering on the magnetic properties of WSe 2 doped with period four transition metals. We use manganese (Mn) and iron (Fe) as candidate n-type dopants and vanadium (V) as the candidate p-type dopant, substituting the tungsten (W) atom in WSe 2 . Specifically, we determine the strength of the exchange interaction in Fe-, Mn-, and V-doped WSe 2 in the presence of clustering. We show that the clusters of dopants are energetically more stable than discretely doped systems. Further, we show that in the presence of dopant clustering, the magnetic exchange interaction significantly reduces because the magnetic order in clustered WSe 2 becomes more itinerant. Finally, we show that the clustering of the dopant atoms has a detrimental effect on the magnetic interaction, and to obtain an optimal Curie temperature, it is important to control the distribution of the dopant atoms.