Low-field magnetization of magnetic random-mixture graphite intercalation compounds

We have measured the temperature dependence of low-field SQUID magnetization for random-mixture graphite intercalation compounds (GICs), stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Ni}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs, stage-2 ${\mathrm{Ni}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs, and stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs. For stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Ni}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs (0≤c≤1), stage-2 ${\mathrm{Ni}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs (0.8≤c≤1), and stage-2 ${\mathrm{Co}}_{\mathit{c}}$${\mathrm{Mn}}_{1\mathrm{-}\mathit{c}}$${\mathrm{Cl}}_2$ GICs (0.9≤c≤1) where ferromagnetic intraplanar exchange interactions are dominant within each island in the magnetic intercalate layers, the zero-field-cooled (ZFC) magnetization of these compounds deviates downward from the field-cooled (FC) magnetization below a critical temperature ${\mathit{T}}_{\mathit{c}}$, and shows a broad peak at a temperature ${\mathit{T}}_{\max }$(<${\mathit{T}}_{\mathit{c}}$). This irreversible effect of magnetization indicates that a cluster glass phase appears below ${\mathit{T}}_{\mathit{c}}$. The ferromagnetic spin order is established within each island, forming a ferromagnetic cluster. The spin directions of these ferromagnetic clusters are frozen because of frustrated interisland interactions consisting of both the dipole-dipole interaction between ferromagnetic clusters and antiferromagnetic interplanar exchange interaction between different intercalate layers. The broad peak of ZFC arises as a result of a competition between thermal energy and these frustrated interisland interactions.