A combined Quantum Monte Carlo and DFT study of the strain response and magnetic properties of two-dimensional (2D) 1T-VSe$_2$ with charge density wave

Two-dimensional (2D) 1T-VSe$_2$ has prompted significant interest due to the discrepancies regarding alleged ferromagnetism (FM) at room temperature, charge density wave (CDW) states and the interplay between the two. We employed a combined Diffusion Monte Carlo (DMC) and density functional theory (DFT) approach to accurately investigate the magnetic properties and response of strain of monolayer 1T-VSe$_2$. Our calculations show the delicate competition between various phases, revealing critical insights into the relationship between their energetic and structural properties. We went on to perform Classical Monte Carlo simulations informed by our DMC and DFT results, and found the magnetic transition temperature ($T_c$) of the undistorted (non-CDW) FM phase to be 228 K and the distorted (CDW) phase to be 68 K. Additionally, we studied the response of biaxial strain on the energetic stability and magnetic properties of various phases of 2D 1T-VSe$_2$ and found that small amounts of strain can enhance the $T_c$, suggesting a promising route for engineering and enhancing magnetic behavior. Finally, we synthesized 1T-VSe$_2$ and performed Raman spectroscopy measurements, which were in close agreement with our calculated results. Our work emphasizes the role of highly accurate DMC methods in advancing the understanding of monolayer 1T-VSe$_2$ and provides a robust framework for future studies of 2D magnetic materials.