  Quasi-one-dimensional iron chalcogenides possess various magnetic states
depending on the lattice distortion, electronic correlations, and presence of
defects. We present neutron diffraction and inelastic neutron scattering
experiments on the spin ladder compound BaFe$_{2-\delta}$S$_{1.5}$Se$_{1.5}$
with $\sim$6% iron vacancies. The data reveal that long-range magnetic order is
absent, while the characteristic magnetic excitations that correspond to both
the stripe- and block-type antiferromagnetic correlations are observed.
First-principles calculations support the existence of both stripe and
block-type antiferromagnetic short-range order in the experimental sample. The
disappearance of long-range magnetic order may be due to the competition
between these two magnetic orders, which is greatly enhanced for a certain
concentration of iron vacancies, which we calculate to be about 6%, consistent
with the measured iron vacancy concentration. Our results highlight how iron
vacancies in the iron-based spin ladder system strongly influence the magnetic
ground state.
