  We study the evolution of magnetic excitations in the disordered
two-dimensional antiferromagnet Sr2Ir1-xRuxO4. A gigantic magnetic gap greater
than 40 meV opens at x = 0.27 and increases with Ru concentration, rendering
the dispersive magnetic excitations in Sr2IrO4 almost momentum independent. Up
to a Ru concentration of x = 0.77, both experiments and first-principles
calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap
arises from the local interaction anisotropy in the proximity of the Ru
disorder. Under the coherent potential approximation, we reproduce the
experimental magnetic excitations using the disordered Heisenberg
antiferromagnetic model with suppressed next-nearest neighbor ferromagnetic
coupling.
