5 Application of this equation confirms the ferromagnetic order in bulk LCMN sample. The obtained parameters are Curie constant (C ∼ 0.0196) and paramagnetic Curie temperature ( θ$_{w}$ ∼ + 270 K). In contrast, the inverse of dc susceptibility ( χ − $^{1}$) for Mn 0 . 5 Ru 0 . 5 Co 2 O 4 spinel oxide at high temperatures is fitted with a typical equation: In general, this equation is applicable for ferrimagnet [12]. The obtained parameters ( θ 1 ∼ -1320 K, C$_{eff}$ ∼ 0.076, ξ ∼ 200850, θ 2 ∼ + 112 K), in particular the positive value of θ 2 (slightly larger than T$_{C}$ ∼ 100 K) and a high negative value of θ 1 , clearly indicate the ferrimagnetic order in Mn 0 . 5 Ru 0 . 5 Co 2 O 4 spinel oxide. Similar ( χ − 1 dc (T))character was also noted in many other ferrimagnetic materials [12, 13]. Now, we analyze the temperature dependence of the inverse of dc susceptibility data for mechanical millled nanoparticle samples. As shown in Fig. 3, the data are well fitted with a simple Curie-Weiss law (equation (1)) above 330 K. The fit parameters of Curie-Weiss law (C and θ$_{w}$ ) are shown in Table I. On the other hand, the hyperbolic shape of χ − 1 (T) curves (with down curvature) above the Curie temperature of the samples suggests that milled samples belong to the class of either ferrimagnet or double exchange ferromagnet [14]. We noted that the χ − 1 (T) curves of the present nanoparticle samples are identical to the ferromagnetic MnCr 2 O 4 nanoparticle samples [13]. To clarify the ferrimagnetic nature of the nanoparticle (NP) samples, we have fitted the χ − 1 (T) data in the temperature range 330 K-400 K using equation (2). We followed a non-linear curve fitting method. Initially, the parameters ( θ 1 , C$_{eff}$, ξ and θ 2 ) were allowed to take initial values and iterated 10 times. As soon as the fitted curve comes close to the experimental curve, we start to restrict the parameters one by one. Finally, best fit curve was obtained by allowing all parameters to vary, except θ 2 keeping constant. The experimental data in the paramagnetic state of the samples fitted with equation (2) are shown in Fig. 3. The fit on susceptibility data in the paramagnetic regime according to equation (2) is excellent. The fit parameters are shown in Table I. A comparative fits applying equation (1) and (2) for mh98 and mh200 samples suggests that equation (1) may be well valid at higher temperature, but equation (2) is more appropriate to describe the magnetic behaviour over a wide temperature range above T$_{C}$. We noted using equation (1) that the paramagnetic Curie temperature ( θ$_{w}$ ) systematically decreases as the material transforms from bulk polycrystalline phase to nanocrystalline (NC) 1 /χ = ( T − θ 1 ) /C$_{eff}$ − ξ/ ( T − θ 2 ) (2)