Quantum mechanical method for estimating ionicity of spinel ferrites

Study of magnetic ordering in the perovskite manganites Pr0.6Sr0.4CrxMn1-xO3

“…Taking into account the requirement that a portion of the O ions be O 1-anions, our group investigated the magnetic structure and cation distributions for several series of spinel ferrites [34][35][36][37][38][39][40][41][42][43] using a quantum mechanical potential barrier model, in which the second and third ionization energies of the cations were used to calculate the probabilities presented different cations. 44 In the process of these research, we also developed an O2p itinerant electron model, 34 and found that using these models to replace the SE and DE models, the magnetic structures of not only Co, Ni, Cu doped spinel ferrites could be explained, but also those of the Cr, [36][37][38][39]42 Mn 34,40 and Ti 41 doped spinel ferrites, for which there have been many ongoing disputes regarding the cation distributions.…”

Study of the magnetic structure and the cation distributions in MnCo spinel ferrites

“…(i) There is certain probability of 2p electrons with opposite spin directions being found in the outer orbit of the oxygen anions, taking into account the ionicity [24,27]. The O2p electrons serve as the intermedium for itinerant 3d electrons passing between cations.…”

“…x s s-10 K (Am 2 /kg) s s-300 K (Am 2 /kg) μ exp (μ B /formula) On the basis of the MOIF model, we estimated the cation distributions in the samples Cr x Fe 3 À x O 4 (0.0rx r1.0) [17], Cr x Co 1 À x Fe 2 O 4 (0.0 rx r1.0) [18], Cu x1 Cr x2 Fe 3 À x1 À x2 O 4 (0.0 rx 1 r0.284 with 1.04 Zx 2 Z0.656) [19], Cr x Ni 1 À x Fe 2 O 4 (0.0 rx r0.3) [20] and Ni 0.68 À 0.8x Ti x Fe 2.32 À 0.2x O 4 (0 r xr0.312) [21], by fitting the magnetic moments of the samples measured at 10 K, using the QMPB method [22][23][24][25]. In the fitting process, there are four important factors that affect the cation distributions in spinel ferrites doped with magnetic cations: (i) the cation ionization energy and the distance between neighboring cations and anions; (ii) the Pauli repulsion energy of the electron cloud between neighboring cations and anions; (iii) the tendency toward charge density balance, and (iv) the ionicity of the oxides.…”

“…Therefore, we obtain that the magnetic moments of Cr 3 þ , Cr 2 þ , Mn 3 þ , Mn 2 þ , Fe 3 þ , Fe 2 þ , Co 3 þ , Co 2 þ , Ni 3 þ and Ni 2 þ are À 3, À 4, À 4, 5, 5, 4, 4, 3, 3 and 2 μ B , respectively, as shown in Table 3. Consequently, we can calculate the average magnetic moments per formula in samples of According to the above mentioned QMPB method [22][23][24][25], and following the methods of Ref. [17][18][19][20][21], the probability ratios R A1 , R A2 , R A4 , R A5 and R A6 for the (A) sites, and R B1 and R B2 for the [B] sites can be derived using the following formulas: Table 3 Cation data used in the fitting process, including the second and third ionization energies, V(M 2 þ ) and V(M 3 þ ), effective radii r of the divalent cations with coordination number 6, ionicities f i , the magnetic moments of divalent and trivalent cations, m 2 and m 3 .…”

“…On the basis of a new magnetic ordering model (MOIF model) proposed by our group [17][18][19][20], we have successfully fitted the magnetic moments per formula of samples of Cr x Fe 3 À x O 4 (0.0r xr1.0) [17], Cr x Co 1 À x Fe 2 O 4 (0.0rx r1.0) [18], Cu x1 Cr x2 Fe 3 À x1 À x2 O 4 (0.0 rx 1 r0.284 with 1.04 Zx 2 Z0.656) [19], Cr x Ni 1 À x Fe 2 O 4 (0.0rx r0.3) [20] and Ni 0.68 À 0.8x Ti x Fe 2.32 À 0.2x O 4 (0 rx r0.312) [21] using the quantum mechanical potential barrier model (QMPB method) also earlier proposed by our group [22][23][24][25]. In the fitting process, we assumed that the magnetic moments of Cr 2 þ , Cr 3 þ and Mn 3 þ cations (number of 3d electrons, n d r4) were antiparallel to those of the Fe, Co, Ni, Cu cations and Mn 2 þ cations (n d Z5) whether at the (A) sites or the [B] sites, due to the fact that the spin directions of 3d electrons in the cations are constrained by Hund's rules.…”