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.

We describe how previously known methods for determining the number of decimation classes of density $\delta$ binary vectors can be extended to nonnegative integer vectors, where the vectors are indexed by a finite abelian group $G$ of size $\ell$ and exponent $\ell^*$ such that $\delta$ is relatively prime to $\ell^*$. We extend the previously discovered theory of multipliers for arbitrary subsets of finite abelian groups, to arbitrary multisubsets of finite abelian groups. Moreover, this developed theory provides information on the number of distinct translates fixed by each member of the multiplier group as well as sufficient conditions for each member of the multiplier group to be translate fixing.

Angle-resolved Raman spectroscopy (ARRS) is an effective method to analyze the symmetry of phonons and other excitations in molecules and solid-state crystals. While there are several configurations of ARRS instruments, the measurement system detailed here utilizes two pairs of linear polarizers and superachromatic half-wave plates. After the orientations of the linear polarizers are set to fixed angles, the two half-wave plates rotate independently, through motorized control, enabling 2D linear polarization mapping. Described within is a protocol to achieve high quality ARRS measurements leveraging phonons from easily accessible test materials [molybdenum disulfide (MoS_2), sapphire (Al_2O_3) and silicon] to validate the system and operation. Quantitative polarized Raman data strongly depends on the quality of sample surface and the optics: the order of placement, alignment, and any distortion caused by their coatings. This study identifies the impact of commonly used edge filters on the polarization response of materials with an anisotropic response as emulated by the T_2g phonon in the Si(100). We detect and model the significant distortion of the T_2g phonon polarization response originating from our dichroic edge filters, the results of which are broadly applicable to optics in any Raman instrument. This ARRS setup also enables helicity-resolved Raman measurements by replacing the first half-wave plate with a superachromatic quarter-wave plate; this configuration is also validated using the Raman response of the aforementioned test materials. This paper aims to increase the quality and reproducibility of polarized Raman measurements through both instrumental considerations and methodology.