Estimation of cation distribution in spinel ferrites Co1+Fe2−O4 (0.0 ⩽x⩽ 2.0) using the magnetic moments measured at 10 K

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

“…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.…”

“…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.…”

Nanocrystalline Zn1− Co0.5Ni0.5 Fe2O4 ferrites: Fabrication via co-precipitation route with enhanced magnetic and electrical properties

“…retentivity, coercivity, saturation magnetization and magnetic moment. The magnetic moment is calculated by using the following relation [33]. However the CoFe 2 O 4 adopts the inverse spinel structure i.e.…”

Magnetic moments of Ti cations in Ti-doped Ni0.68Fe2.32O4 spinel ferrites

“…It can be seen that the l cal is lower than l obs , which is similar to the case of NiFe 2 O 4 as mentioned in the above paragraph. The reason why there is a difference between l cal and l obs is that the actual cation distribution in spinel ferrites [18][19][20] is more complicated than that in the conventional model [5,14]. This question will be studied in the future.…”