Manifestation of finite temperature size effects in nanogranular magnetic graphite

In addition to the double phase transition (with the Curie temperatures T_C =300 K and TCt =144 K), a low-temperature anomaly in the dependence of the magnetization is observed in the bulk magnetic graphite (MG) (with an average granular size of L≃10 nm), which is attributed to the manifestation of the size effects below the quantum temperature T _L∞h²/L² and is well fitted by the periodic function M_L (T) sin [M (T) (T) /L] with M (T) being the bulk magnetization and (T) /T the thermal de Broglie wavelength. The best fits of the high-temperature data (using the mean-field Curie-Weiss and Bloch expressions) produced reasonable estimates for the model parameters, such as defects mediated effective spin exchange energy J≃12 meV (which defines the intragranular Curie temperature T_C) and proximity mediated interactions between neighboring grains (through potential barriers U created by thin layers of nonMG) with energy J_t =exp (-d/) J≃5.8 meV (which defines the intergranular Curie temperature TCt) with d≃1.5 nm and /U≃2 nm being the intergranular distance and characteristic length, respectively.