Magnetic phase transitions in ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ and stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ graphite intercalation compounds

Pristine ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ and stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ graphite intercalation compounds (GICs) (0≤c≤1) approximate site-diluted three-dimensional (3D) and two-dimensional (2D) XY spin systems, respectively. We have studied the magnetic phase transitions of these two systems by using dc and ac magnetic susceptibilities. We find that the reduced critical temperature of stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GIC is almost the same as that of ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ for c>0.7. The effect of the dimensionality on the dilution with Mg ions becomes significant below c≊0.7. The percolation threshold for ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ is ${\mathit{c}}_{\mathit{p}}$≊0.36, close to the theoretical value (0.295) for the 2D triangular lattice with nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange interactions, and the percolation threshold for stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GIC is ${\mathit{c}}_{\mathit{p}}$≊0.5, close to the theoretical value (0.5) for the 2D triangular lattice with NN exchange interaction. We also find that the peak susceptibility of ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mg}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ at the Néel temperature drastically increases with decreasing Co concentration. This phenomenon is discussed in terms of recent scaling theory.