First-principles determination of exchange interactions in delafossite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Y</mml:mi><mml:mi>Cu</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2.5</mml:mn></mml:msub></mml:math>

We perform a first-principles calculation within the local density approximation $(\mathrm{LDA})+\mathrm{U}$ approximation for the delafossite $\mathrm{Y}\mathrm{Cu}{\mathrm{O}}_{2.5}$, which up to now was considered as a sawtooth lattice. The magnetic interactions are mapped onto a Heisenberg model whose exchange interactions are fitted to first principles total energy calculations for different spin configurations. Four interactions appear to have a significant value. While interplane interactions can be safely neglected, interchain interactions are much smaller than intrachain ones, confirming the low-dimensional character of this system. Besides the nearest-neighbor intrachain antiferromagnetic interactions, we find two unexpected ferromagnetic interactions that can play an important role. The results are discussed in relation with recent experimental data.