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Magnetic frustration is a route that can lead to the emergence of novelground states, including spin liquids and spin ices. Such frustration can beintroduced through either the geometry of lattice structures or by incompatibleexchange interactions. Identifying suitable strategies to control the degree ofmagnetic frustration in real systems is an active field of research. In thisstudy, we devise a design principle for the tuning of frustrated magnetism onthe square lattice through the manipulation of nearest (NN) and next-nearestneighbor (NNN) antiferromagnetic (AF) exchange interactions. By studying themagnon excitations in epitaxially-strained La$_2$NiO$_4$ films using resonantinelastic x-ray scattering (RIXS) we show that, in contrast to the cuprates,the dispersion peaks at the AF zone boundary. This indicates the presence of anAF-NNN spin interaction. Using first principles simulations and an effectivespin-model, we demonstrate the AF-NNN coupling to be a consequence of thetwo-orbital nature of La$_2$NiO$_4$. Our results demonstrate that compressivestrain can enhance this coupling, providing a design principle for thetunability of frustrated magnetism on a square lattice.

Strain-Tuned Magnetic Frustration in a Square Lattice $J_1$-$J_2$ Material