Raman scattering from spin fluctuations in ${\mathrm{Pr}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$, ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$, and ${\mathrm{Sm}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$

Antiferromagnetic excitations in single crystals of ${\mathrm{Pr}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$, ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$, and ${\mathrm{Sm}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ were investigated as a function of Ce concentration using Raman scattering at room temperature. The introduction of electrons by Ce doping significantly broadens the two-magnon peak in the ${\mathit{B}}_{1\mathit{g}}$ mode, indicating that zone-boundary magnons become damped with increasing Ce concentration. The existence of broad spin-pair-excitation spectra in the ${\mathit{B}}_{1\mathit{g}}$ and ${\mathit{B}}_{2\mathit{g}}$ modes at x=0.15 suggests that the short-range spin fluctuations persist in these electron-doped superconductors. The energy of the spin-pair-excitation peak in ${\mathrm{Pr}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ is not affected by doping up to x=0.2. This is similar in behavior to the ${\mathrm{Sm}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ system up to x=0.17. The absence of softening of the short-wavelength magnons in these systems is in marked contrast to the magnon softening behavior in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$. The Raman spectra in ${\mathrm{Pr}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ make no distinction between the superconducting and the metallic regions. The highly damped magnetic-excitation spectra support the picture that the spin-spin correlation length in the present systems decreases gradually with increasing Ce concentration.