  Using complementary polarized and unpolarized single-crystal neutron
diffraction, we have investigated the temperature-dependent magnetic structures
of Eu$_{0.5}$Ca$_{0.5}$Fe$_{2}$As$_{2}$. Upon 50 \% dilution of the Eu sites
with isovalent Ca$^{2+}$, the Eu sublattice is found to be still long-range
ordered below $\mathit{T_{Eu}}$ = 10 K, in the A-typed antiferromagnetic (AFM)
structure. The moment size of Eu$^{2+}$ spins is estimated to be as large as
6.74(4) $\mu_{B}$ at 2.5 K. The Fe sublattice undergoes a spin-density-wave
transition at $\mathit{T_{SDW}}$ = 192(2) K and displays an in-plane AFM
structure above $\mathit{T_{Eu}}$. However, at 2.5 K, the Fe$^{2+}$ moments are
found to be ordered in a canted AFM structure with a canting angle of
14(4){\deg} out of the $\mathit{ab}$ plane. The spin reorientation of Fe below
the AFM ordering temperature of Eu provides a direct evidence of a strong
interplay between the two magnetic sublattices in
Eu$_{0.5}$Ca$_{0.5}$Fe$_{2}$As$_{2}$.
