  Establishing the physical mechanism governing exchange interactions is
fundamental for exploring exotic phases such as the quantum spin liquids (QSLs)
in real materials. In this work, we address exchange interactions in
Sr2CuTe$_{1-x}$W$_{x}$O, a series of double perovskites that realize the
spin-1/2 square lattice and were suggested to harbor a QSL ground state arising
from random distribution of non-magnetic ions. Our {\it ab initio}
multi-reference configuration interaction calculations show that replacing Te
atoms with W atoms changes the dominant couplings from nearest to next-nearest
neighbor explained by the crucial role of unoccupied states of non-magnetic
ions in the super-superexchange mechanism. Combined with spin-wave theory
simulations, our calculated exchange couplings provide an excellent description
of the inelastic neutron scattering spectra of the end compounds, as well as
explain the magnetic excitations in Sr2CuTe$_{0.5}$W$_{0.5}$O as emerging from
the bond-disordered exchange couplings. Our results provide crucial
understanding of the role of non-magnetic cations in exchange interactions
paving the way to further exploration of QSL phases in bond-disordered
materials.
