| Spinel ferrites with a general molecular formula(A)[B]2O4 are the important magnetic materials, which are used to many fields, such as electron devices, magnetic recording medium, medical biology, etc. In each spinel unit cell, there are 24 metal cations occupying the interstitial positions formed by oxygen anions with a face-centered-cubic close-packed structure. There are two types of interstitial sites: the tetrahedral(8a) or(A) sites, and the octahedral(16d) or [B] sites. Therefore, the available space of an(A) site is smaller than that of a [B] site, and the ratio of the anions charge density around an(A) site to that of a [B] site is 2/3. The metal cations can be Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, etc.For typical materials with compositions MFe2O4(M=Fe, Co, Ni, Cu), all cation magnetic moments at the [B] sites(or the(A) sites) are parallel to each other, whereas the cation magnetic moments at the(A) sites are antiparallel to those at the [B] sites. In the traditional theory, the magnetic structures of spinel ferrites were explained by super-exchange interaction model. Recently, American researchers proposed that the cations on the octahedral and tetrahedral sites coupled antiferromagnetically via the magnetic superexchange interaction, while the divalent and trivalent cations on the octahedral sites coupled ferromagnetically through the magnetic double exchange interaction. Fe cations can approximately be considered as Fe3+ cations, which equally occupy the(A) and [B] sites. Therefore, the Fe cation magnetic moments in the(A) sites just offset those in the [B] sites. Meanwhile, M cations can be seen as M2+ cations, which all occupy the [B] sites. When M=Fe, Co, Ni, Cu, the observed magnetic moments per formula are 4.2, 3.3, 2.3, 1.3 mB, which are slightly higher than the magnetic moments of Fe2+, Co2+, Ni2+ and Cu2+ cations. The magnetic moments of Fe2+, Co2+, Ni2+ and Cu2+ cations are 4, 3, 2, 1 mB, respectively. For M=Mn, the observed magnetic moment is 4.6 mB, which is slightly lower than the magnetic moments of Mn2+ cations(5 mB). For M=Cr, the observed magnetic moment is 2 mB, which is only half of the Cr2+ magnetic moments(4 mB). So far, there have no satisfactory explanation for the differences of magnetic structure between Mn(or Cr) and Fe(Co, Ni, Cu) doped spinel ferrites, which become a puzzle to the magnetism for a long time. Consequently, magnetic structures of Cr-doped spinel ferrites are not introduced in classical physics of ferromagnetism.According to Hund’s rules, our group firstly propose that the magnetic moment directions of Cr cations(with the numbers of 3d electrons nd￡4), will be antiparallel to those of Fe, Co, Ni, Cu cations(with nd35) whether at the(A) sites or at the [B] sites of the spinel ferrites, and estimate the cation distributions of Crx M1-x Fe2O4(M=Fe, Co, 0.0≤x≤1.0) spinel ferrites by quantum-mechanical potential barrier model(QMPB model) and the magnetic moments of the samples at 10 K.Three series of samples with chemical compositions Crx Ni1-x Fe2O4(0.0≤x≤0.3), Mnx Co1-x Fe2O4(0.0≤x≤0.3), Cox Ni1-x Fe2O4(0.0≤x≤0.3) were prepared by the chemical co-precipitation method. The samples were characterized by X-ray diffraction spectra, Field emission scanning electron microscope pictures, X-ray energy dispersive spectra and Physical property measurement system. On the basis of QMPB model and 3d electron spin directions constrained by Hund’s rules, we studied the cation distributions of these materials. The main results of this study were as follow:(1) All samples had a single-phase cubic spinel structure with space group Fd3 m. The lattice parameter in three series of samples increased with doping level x. The average crystallite sizes of all samples are larger than 100 nm, so that the influence of surface effects on the magnetization of all samples can be ignored. The particle diameters of Crx Ni1-x Fe2O4 and Mnx Co1-x Fe2O4 samples were between 0.3 and 4.5 mm, and all samples were polycrystalline materials. There was a little difference between the experiment compositions and the nominal compositions of the samples.(2) The trend in the magnetic moments of Crx Ni1-x Fe2O4 samples was compared with that of Cox Ni1-x Fe2O4 samples, and we found an interesting phenomenon. There are two different trends in the magnetic moments with increasing x, in spite of the fact that the magnetic moments of Cr2+ and Co2+ cations are higher than that of Ni2+ cations. The magnetic moments of samples decreased when Cr substituted for Ni, but increased when Co substituted for Ni, which can be explained by the magnetic moments of Cr cations being antiparallel to those of Fe, Co, Ni cations in the(A) or [B] sublattices proposed by our group.(3) For Mn Fe2O4, the observed magnetic moment was about 4.6 mB, which was slightly lower than the magnetic moment of Mn2+ ions(5 mB). According to the traditional theory, about 80 percent of Mn ions enter the(A) sites. However, on basis of the experimental results, most of Mn ions enter the [B] sites proposed by some researchers. We assumed that the magnetic moment of the Mn3+(3d4, the same as the 3d electron numbers of Cr3+) cations is antiparallel to that of the Mn2+(3d5), Fe2+ and Fe3+ cations in Mnx Co1-x Fe2O4(0.0≤x≤0.3) samples, which was similar to the study of Cr cation magnetic moment directions. We fitted the magnetic moments at 10 K of the samples by quantum mechanical potential barrier model, and obtained that the cation distributions of Mn ions at the(A) and [B] sites were similar to those of Co and Ni ions, namely, most of Mn ions enter the [B] sites.(4) The magnetic structure that the magnetic moment of the Mn3+ cations are antiparallel to that of the Mn2+ cations in a given sublattice can not be explained using the double-exchange model. Therefore, we proposed an O2 p electron itineration mechanism in oxides:(i) For oxides, taking into account the ionicity, there exist a part of monovalence oxygen ions with 2p hole in the outer orbit.(ii) In a given sublattice, a 2p electron of an oxygen ion could hop to a 2p hole in an adjacent oxygen ion mediated by the metal cations. The spin direction of the 2p electron remained constant during the hopping process, which could become an itinerant electron. When an itinerant electron arrived at Cr3+, Cr2+, Mn3+ cations(with nd￡4), the itinerant electron spin direction was the same as the major spin direction of the cations. When it arrived at Mn2+, Fe, Co, Ni cations(with nd35), the itinerant electron spin direction was antiparallel to the major spin direction of the cations. Therefore, the magnetic moment directions of Cr3+, Cr2+, Mn3+ cations were antiparallel to those of Mn2+, Fe, Co, Ni cations.(iii) Due to the fact that the two O2 p electrons in the outer orbit of an oxygen anion had opposite spin directions, each of them became an itinerant electron in two different sublattices, resulting in the cation magnetic moments at the(A) sites being antiparallel to those at the [B] sites in MFe2O4(M=Fe, Co, Ni, Cu) spinel ferrites.Applying the O2 p electron itineration mechanism to instead of the super-exchange interaction and the double exchange interaction, not only the magnetic structures of ferrites MFe2O4(M =Fe, Co, Ni, Cu) can be explained, but also the magnetic structures of the Cr(Mn) doped spinel ferrites can be explained. Meanwhile, a clear physic picture for the causes of these magnetic structures is given on the basis of the atomic shell structure theory, which is easier to understand. |
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