The emergence of two-dimensional (2D) materials has revolutionised the landscape of condensed matter physics and material science. 2D materials exhibit extraordinary electronic and mechanical characteristics, offering unprecedented opportunities for exploring novel phenomena and engineering advanced functionalities in the limit of miniaturization. This thesis aims to contribute to expand the frontiers of knowledge in two main directions, (1) the rationalization of 2D magnetism and related phenomena from first principles and (2) the tailoring of magnetic properties in the limits of dimensionality. For this, first principles methods are used to simulate the most important 2D magnets in the field, namely FePS3 and the family of MPS3, CrI3 and the family of CrX3 and other new promising materials such as the CrSBr monolayer. This thesis aims to present an analysis of 2D magnetism from a fundamental perspective, that covers from its first origin in the formation of the electronic structure to the comprehension of the exchange mechanisms. The manifestation of magnetism in the atomic structure has been studied to understand magnetostriction in MPS3 and to underline the role of exchange interactions in the properties of 2D magnetic materials. Moreover, the distortions induced by magnetism in the crystal structure are employed to measure the magnetic order, providing a methodology to detect the still elusive antiferromagnetism. This thesis explores the possibility to tailor magnetic interaction via the design of new 2D materials, such as the Janus materials MPS3. The results presented exhibit the valuable possibilities offered by the Janus technique to induce SOC and symmetry breaking in 2D materials, affecting the magnetic anisotropy and DM interactions and thus, motivating the future exploration and synthesis of Janus 2D materials. Moreover, magnetic exchange interactions in 2D magnetic materials are rationalised from a different perspective based on the intrinsic competition of exchange interactions. In this extended perspective, individual exchange interactions can be seen as a complex magnetic system, where ferromagnetism and antiferromagnetism intrinsically coexist, forming different orbital pathways of interaction that mediate their intrinsic competition. The comprehension of 2D magnetism provided by this perspective is oriented in the last part of the thesis to practical applications, where the intrinsic competition of interactions in 2D magnets serves as a guideline to tailor 2D magnetism via external stimuli. The last chapters of this thesis illustrate how the intrinsic mechanisms can be rationally manipulated via the modification of the environmental screening or the distortion of the structures. As a proof of concept, this thesis introduces the concept of magnon straintronics in a 2D van der Waals magnet, that showcases the control of magnons manipulating the intrinsic competitions of exchange interactions in CrSBr and CrX3 using strain.
