Within this project we investigate the magnetic properties of the new generation low-dimensional copper oxides in order to elucidate the mechanisms which lead to formation of the non-trivial magnetic orders: spin spirals, skyrmions, non-collinear magnetism – objects of the spintronics and nanoelectronics interests. For this purpose we utilize the modern first principle methods of investigations based on density functional theory with taking the many-body correlations effects into account. In the framework of the project the most fundamental effects such as spin-orbit coupling, hybridization of the atomic states, which plays crucial role in formation of magnetic order, will be taken into consideration. Also, the significant part of our study will contain modeling the spectra of elastic and inelastic neutron scattering, and simulation of experimentally observable thermodynamic characteristics on the basis of the quantum Monte Carlo (QMC) methods, which will allow to connect the theory and experiment. The obtained results will help to understand the nature of the magnetic interactions, which lead to formation of the mentioned magnetic orders, the conditions of occurrence, and methods of controlling of them.​