In this study, we utilized quantum-mechanical calculations to explore the electronic structure of binary and ternary Fe-Al-based systems with noncollinear magnetic configurations. Our findings indicate that the ground state of systems, such as Fe₉Al₇, Fe₉Al₆B, Fe₉Al₆Ga, and Fe₉Ga₆, is not ferromagnetic, but rather exhibits a spin spiral structure in the [111] direction. We analyzed the effects of different types of exchange-correlation potentials, aluminum concentration, relaxation of interatomic distances, substituting atom positions, and spin wave orientations on magnetic properties. Various exchange-correlation potentials consistently demonstrated the dependency of the total energy on the spin spiral q-vector, with the generalized gradient approximation closely matching experimental observations. In the Fe₉Al₇ unit cell, a spin spiral structure prevails at 43.75% atomic Al, while other compositions favor ferromagnetism. The system can support spin spiral vectors in the [001], [110], and [111] directions, with [111] being the most energetically favorable. The equilibrium state is highly sensitive to the position and type of sp-elements within the unit cell. Overall, our results show that spin spiral structures with the [111] q-vector are energetically favored when the average magnetic moment is approximately 1 μB per Fe atom, which is consistent with Mössbauer data

The research focuses on the explanation of a phenomenon observed in the spectra of electron-nuclear resonance (ENDOR) pertaining to nitrogen atoms adjacent to the boron vacancy (V_B^-) defect in hexagonal boron nitride (hBN). The phenomenon is manifested as a shift of the ENDOR spectrum lines with respect to the nitrogen Larmor frequency. It is hypothesized that these shifts are indicative of a substantial hyperfine interaction between the V_B^- defect and the ¹⁴N nuclei in hBN. A calculation utilizing second-order perturbation theory was executed to determine the positions of the ENDOR spectrum lines, resulting in the formulation of correction equations. The values obtained from the perturbation theory corrections align well with the experimental results. The extent of nuclear state admixture into electron states was found to be around 0.04-0.07%.