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We performed muon spin rotation/relaxation measurements to investigate themagnetic behavior of $T^{\prime}$-type Eu$_2$CuO$_4$ (ECO), which is the parentcompound of electron-doped cuprate superconductors, and the effects ofoxygen-reduction annealing on its magnetism. In as-sintered (AS) ECO, weclarified the development of magnetic correlations upon cooling below$T_\mathrm{N1}$ (= 265 K) as well as the coexistence of a dominant fluctuatingspin state and partially ordered spin state in the temperature range between$\sim$150 K and $T_\mathrm{N1}$. Upon further cooling, uniform long-rangemagnetic order was observed below $T_\mathrm{N2} = 110$ K, which is close tothe ordering temperature of 115 K in $T^{\prime}$-type La$_2$CuO$_4$ (LCO)[Phys. Rev. B {\bf 82}, 180508(R) (2010)]. For oxygen-reduction-annealed ECO, asimilar ordering sequence with the same $T_\mathrm{N2}$ was observed butwithout the partially ordered spin state. Therefore, the fluctuating spin stateover a wide temperature range and a $T_\mathrm{N2}$ less than the N{\'e}eltemperature ($T_\mathrm{N2} \approx T_\mathrm{N1}$) in $T$-type LCO are commonfeatures of the $T^{\prime}$-type parent $R_2$CuO$_4$ ($R$CO, $R$: rare-earthion). The origin of the partially ordered spin state in AS ECO is discussedfrom the viewpoint of chemical defect. Furthermore, we discuss the roles ofelectron doping and repairing defect in the observed effect of annealing on themagnetism of $T^{\prime}$-type $R$CO.

Magnetism behavior of $T^{\prime}$-type Eu$_2$CuO$_4$ revealed by muon spin rotation/relaxation measurements