We combine several numerical and semianalytical methods to study the 5d double perovskites Sr2YIrO6 and Ba2YIrO6, which were recently proposed to exhibit excitonic magnetism. Starting from the density-functional theory and the constrained random-phase approximation, we construct effective multiband Hubbard models.
These are analyzed by means of static and dynamical mean-field theories and strong-coupling expansion. We find both materials to be insulators, but, contrary to the experimental claims, with a large spin gap of several hundreds of meV preventing the formation of an ordered state at low temperature.