The distribution of cations at the A (tetrahedral) and B (octahedral) sublattices per the formula unit of the ferrite-spinel is: Fe3+[Ni2+Fe3+]O4, therefore, the number of Bohr magnetons is m(B)-m(A) = [2+5]-5 = 2 (muB). Experimentally found values are usually given in the range of 2.22-2.40 muB.

If you need to calculate the magnetic moment of a nanoparticle magnetized to saturation, you need to calculate the number of NiFe2O4 formula units (Nfu) contained in the particle and multiply by 2 (or 2.22-2.40 muB). Nfu = 8*V/auc3, where V = m/d is the particle volume, aec is the unit cell size of Nickel ferrite (0.834 nm), m is the particle mass, and d is the ferrite density (5.37 g/cm3).

If the value of the measured magnetic moment of the nanoparticle M in emu (=Gs*cm3) is known, then the magneton number (in muB) = M/muB, where muB = 9.27*10-21 emu.

The distribution of cations at the A (tetrahedral) and B (octahedral) sublattices per the formula unit of the ferrite-spinel is: Fe3+[Ni2+Fe3+]O4, therefore, the number of Bohr magnetons is m(B)-m(A) = [2+5]-5 = 2 (muB). Experimentally found values are usually given in the range of 2.22-2.40 muB.

If you need to calculate the magnetic moment of a nanoparticle magnetized to saturation, you need to calculate the number of NiFe2O4 formula units (Nfu) contained in the particle and multiply by 2 (or 2.22-2.40 muB). Nfu = 8*V/auc3, where V = m/d is the particle volume, aec is the unit cell size of Nickel ferrite (0.834 nm), m is the particle mass, and d is the ferrite density (5.37 g/cm3).

If the value of the measured magnetic moment of the nanoparticle M in emu (=Gs*cm3) is known, then the magneton number (in muB) = M/muB, where muB = 9.27*10-21 emu.

You have to assume the inversion degree of your material (if it is a normal ferrite or inverted one, or mixed). Then you just add up the moments of the atoms at A sublattice and the B atoms, separately. Then substract the two results.

For example in a Fe3O4 with a fully normal structure you have 16 Fe+3 atoms at B sites (with 5 muB theoretically) and 8 Fe+2 atoms at A sites (4 muB )Thus the net magnetic moment per unit cell should be

16x5 muB - 8x4 muB= 48 muB

this is to say a 6 muB per formula unit value.

Maybe this picture could help.

http://www.unizar.es/gfgoya/index_files/google0fef44f4db0f80b9.htm

In the normal spinels, the cation distribution is: Me2+[Fe3+2]O4. If for some reason, the distribution of cations has an another ordering, and the proportion of cations of higher valence in tetrahedra is i (it is a measure of the degree of spinel inversion), the structural formula of ferrite takes the form:

Me2+1-iFe3+i[Me2+iFe3+2-i]O4. Since pure Nickel ferrite is normally a inverted spinel (i=1), nickel cations are located in B-type sites, which suggests the calculation I proposed above.

Dr. G.F. Goya's just remark is relevant to a more General case. However, it should be noted that the magnetic moments of cations located inside each individual sublattice do not add up in all cases. Thus, it should be taken into account that in the case of significant “nonmagnetic” dilutions (substitutions by diamagnetic cations in one of the sublattices as in the case of normal zinc ferrite spinel) the unidirectional arrangement of magnetic moments in the other sublattice is disrupted due to the destruction of the antiferromagnetic interaction between opposite dissimilar sublattices, and antiparallel orientation of magnetic moments is established inside it.

Assuming that the magnetic cations at different sites (A and B) are antiparallel (Neel's model), theoretically, sum( M_i*C_i)_B - sum(M_j*C_j)A ;

(here M_i, C_i are the magnetic monuments and concentrations of the individual cations, and sum(C_i) = 2, sum(C_j) = 1).

Unfortunately it is not guaranteed that this simple model will work. In case of non-magnetic dilutions the orientations of the magnetic moments can get canted (or simply the linearity may be disrupted).

Such cases can be explained by YK model. YK model simply accounts the projections on any particular axis by the different cations.