Mechanical control of magnetic exchange and response in GdRu$_2$Si$_2$: A computational study

We present a systematic computational study of the effect of uniaxial strain on the magnetic properties of GdRu$_2$Si$_2$, a centrosymmetric material known to host a field-induced skyrmion lattice (SkL). Using first-principles density functional theory, we first demonstrate the pronounced sensitivity of the exchange and anisotropy to specific structural distortions. These DFT-derived interactions are then integrated into a classical spin model to construct comprehensive magnetic phase diagrams under both compressive and tensile strain. Our key finding is that compressive strain ($\sim 2\%$) acts as an effective tuning parameter, substantially expanding the stability region of the $\vec Q_{100}$-driven topologically nontrivial phases. This results from the shifts in the critical magnetic fields and enhancement of the energy scale of the favored magnetic wave vector. In contrast, tensile strain induces a different magnetic ground-state by promoting a different magnetic ordering vector, $\vec Q_{110}$, leading to entirely distinct phase behavior. This work not only provides a quantitative understanding of the structural-magnetic coupling in GdRu$_2$Si$_2$ but also establishes strain engineering as a powerful approach to control and optimize topologically non-trivial magnetic phases in centrosymmetric magnets.