Two-dimensional systems with magnetic order are a key resource for next-generation spintronic and topological electronic devices. Many of them exhibit topological magnon spectra and host skyrmions providing thus a low energy alternative for classical information processing. Moreover, single molecular magnets have great potential as quantum information storage and processing units in future quantum computers. The Korringa-Kohn-Rostoker (KKR) and the Linearized Muffin-Tin Orbital (LMTO) Green's function techniques in conjunction with the torque method were successfully used in describing a large variety of metallic magnets. However, most of the novel 2D materials are challenging to study within the KKR or LMTO framework because of their dimensionality, geometry and chemical composition. To overcome this problem, we extended both the non-relativistic and the relativistic torque method to local orbital schemes employing non-orthogonal basis sets and implemented this formalism in the SIESTA code. [L. Oroszlány et al., Physical Review B 99, 224412 (2019); G. Martinez-Carracedo et al. arXiv:2309.02558]. The newly adapted method is ideally suited for investigation of low dimensional structures and hybrid organometallic compounds. Within this research project the PhD student will acquire a deep knowledge of the new code and investigate experimentally relevant quantities such as magnon spectra and devise effective magnetic model parameters suitable for large-scale spin dynamics simulations. Particular attention will be paid to the calculation of tensorial exchange interactions including anisotropies and the Dzyaloshinsky-Moriya interaction that makes possible to study chiral magnetic phenomena on ab initio level. Moreover, by using a Green’s function perturbation approach, we will attempt to calculate fourth-order spin-interactions proposed to play an important role in stabilizing complex non-collinear magnetic structures like magnetic skyrmions. Our aim is to study novel magnetic phenomena such as two-dimensional ferromagnetism in Cr based monolayers, single molecular magnetism in structures with Mn and Fe cores and magnetic topological systems such as Weyl magnons in antiferromagnetic insulators and in 2D van der Waals heterostuctures. One of the major objectives of the research is to understand how key properties of novel two-dimensional van der Waals magnets can be predicted to unlock their potential for applications as an MRAM device. The PhD work will be co-supervised by László Oroszlány (ELTE) and a strong collaboration with Prof. Jaime Ferrer and his group at the Oviedo University (Spain) is also foreseen.