phase and then, to amorphous (AMP) phase. The θ$_{w}$ values remained positive for bulk as well as mh25, mh61 and mh98 samples, where as θ$_{w}$ becomes negative for mh146 and mh200 samples. The negative value of θ$_{w}$ indicates the introduction of antiferromagnetic exchange interactions in the material as the particle size and crystalline phase changed. As discussed in earlier report [11], the magnetic dynamics of the present material strongly depends on the structural phase transformation, rather than the particle size effects. The θ 1 (obtained using equation (2)) also follows the pattern of θ$_{w}$ , showing positive values only for mh25 and mh61 samples. The spin glass like feature in amorphous (mh146) sample clearly proves the the reduction of ferromagnetic (FM) exchange interactions or development of antiferromag- netic (AFM) exchange interactions in nanocrystalline and amorphous samples, because spin glass like feature needs sufficient amount of both magnetic disorder and competition between FM/AFM interactions. On the other hand, θ 2 is always positive and change is not drastic (within 9 K considering all milled samples). The positive value of θ 2 suggested the retain- ing of a strong double exchange ferromagnetic interactions [14] both in nanocrystalline and amorphous phase of La 0 . 67 Ca 0 . 33 MnO 3 nanoparticles [11]. At the same time, application of equation (2) suggests the ferrimagnetic character of mechanical milled nanoparticle LCMN samples. Similar magnetic behaviour was also observed in ferrimagnetic MnCr 2 O 4 nanopar- ticles [13]. Some reports [15, 16] also attempted to explain the magnetization data in the paramagnetic regime of ferromagnetic nanomaterials by following a simple Curie-Weiss law (equation (1)), but those data seem to be more appropriate to the ferrimagnetic description (equation (2)). 

The validity of ferrimagnetic equation (2) in our milled samples can be examined by con- sidering the core-shell spin structure of nanoparticles, already proposed in earlier work [11]. The existence of strong ferromagnetic order, even in the nanocrystalline and amorphous phase, is essentially due to ferromagnetic ordered core spins. On the other hand, magnetic disorder is confined mainly in the shell part for nanocrystalline particles (NCR NP) and also introduces in the core part for amorphous nanoparticles (AMP NP). The shell spins may not be typical antiparallel with respect to core, but effective spin moment of shell is obviously low in comparison with ferromagnetic core and schematically shown in Fig.4. Similar magnetic modulation was previously proposed for antiferromagnetic nanoparticle [4] and later applied for ferromagnetic manganite nanoparticles [17]. This allows us to consider the magnetic contributions form shell and core of a nanoparticle equivalent to two unequal 

