Manifestation of finite temperature size effects in nanogranular magnetic graphite

Abstract

In addition to the double phase transition (with the Curie temperatures TC=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 TL∝ℏ2/L2 and is well fitted by the periodic function ML(T)∝sin[M(T)Λ(T)/L] with M(T) being the bulk magnetization and Λ(T)∝ℏ/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 TC) and proximity mediated interactions between neighboring grains (through potential barriers U created by thin layers of nonMG) with energy Jt=exp(−d/ξ)J≃5.8 meV (which defines the intergranular Curie temperature TCt) with d≃1.5 nm and ξ∝ℏ/U≃2 nm being the intergranular distance and characteristic length, respectively.