Estimate of the cation distribution for Ti-doped Ni_0.68Fe_2.32O₄spinel ferrites by fitting magnetic moments at 10 K

Abstract

Ti-doped Ni 0.68 Fe 2.32 O 4 spinel ferrite samples with nominal composition Ni 0.68À0.8x Ti x Fe 2.32À0.2x O 4 (0 x 0.312) were prepared using conventional ceramic methods. The samples exhibited a single-phase cubic spinel structure. When the doping level had values x > 0.15, a transition temperature, T N , was found, below which the magnetization of the samples decreased with decreasing measurement temperature. This phenomenon indicates that an additional antiferromagnetic structure arises in the traditional spinel phase of ferrites resulted from Ti doping. Therefore, Ti ions appear in the form of Ti 3þ and Ti 2þ cations that have magnetic moments, rather than as Ti 4þ cations without magnetic moment as assumed by many researchers. The dependence of the magnetic moments on the Ti doping level x at 10 K was fitted successfully using our quantum-mechanical potential barrier model proposed earlier. In the fitting process, we assumed that the magnetic moments of the Ti cations were opposite to the direction of the Fe and Ni moments. According to the fitted results, the Ti 2þ cations at the [B] sites constitute about 81% of the total Ti content x for all samples, which is close to the content of the Ni 2þ cations at the [B] sites (77%).

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.…”