Experimental evidence for the magnetic moment directions of Cr2+ and Cr3+ cations in the spinel ferrites Cux1Crx2Fe3−x1−x2O4

Magnetic moment directions and distributions of cations in Cr (Co) substituted spinel ferrites Ni0.7Fe2.3O4

“…As in our previous work, [16][17][18][19][20][21][22] the cation distributions for all the samples were estimated by fitting the dependence of the magnetic moments measured at 10 K on the doping level, using the quantum mechanical potential barrier model proposed by our group. [26][27][28][29] In the fitting process, the following factors were taken into account:…”

“…If we consider all samples in a series, we have only two independent fitting parameters, if we assume that V BA (M 2+ ) varies lineally with the doping level, [16][17][18][19][20][21][22] as shown in Fig. 6.…”

“…The results indicate that the distributions of the Cr cations at the (A) and [B] sites are very close to those obtained using neutron diffraction and are very close to those of Fe cations. For the three series of samples in this work and the samples M x N 1−x Fe 2 O 4 (M, N = Cr, Mn, Fe, Co, and Ni) in our previous work, [16][17][18][19][20][21][22] we have found that the pattern followed by the fitting parameter V BA (M 2+ ) is similar to that of the third ionization energy of the M cation, whether the initial value of V BA (M 2+ ) was assumed to be proportional to the second or third ionization energy of the M cation.…”

“…6,7 The influence of Cr-doping on the crystal structure and physical properties of spinel ferrites have been reported in many studies, but the Cr ion distributions have been disputed. [8][9][10][11][12][13][14][15] Pervaiz et al 8 In order to explain these discrepancies, our group proposed an O2p itinerant electron model, [16][17][18][19][20][21][22][23] which contains three factors: (i) There are O2p holes in the outer orbits of oxygen anions. 24 In a given sublattice, an O2p electron with constant spin direction can hop to the O2p hole of an adjacent oxygen anion with a metal cation acting as intermediary.…”

“…(iii) The two oxygen O2p electrons which have opposite spin directions become itinerant electrons in the two different sublattices (involving the (A) or [B] sites). Using these premises, our group has successfully fitted the magnetic moments, measured at 10 K, of ferrite samples of Cr x Fe 3−x O 4 (0.0 ≤ x ≤ 1.0), 16 Cr x Ni 1−x Fe 2 O 4 (0.0 ≤ x ≤ 0.3), 17 Cr x Co 1−x Fe 2 O 4 (0.0 ≤ x ≤ 1.0), 18 Cu x1 Cr x2 Fe 3−x1−x2 O 4 (0.0 ≤ x 1 ≤ 0.284 with 1.04 ≤ x 2 ≤ 0.656), 19 Ni 0.68−0.8x Ti x Fe 2.32−0.2x O 4 (0 ≤ x ≤ 0.312), 20 and Mn x Co 1−x Fe 2 O 4 (0.0 ≤ x ≤ 0.3) 21 and estimated the cation distributions for all samples, using the quantum mechanical potential barrier model (QMPB) also proposed by our group. [26][27][28][29] In the fitting process, only one independent fitting parameters, V BA (M 2+ ), was used for a given sample.…”