The paper claims that replacing Co²⁺ with Zn²⁺ increases M_s due to Zn²⁺’s diamagnetic nature and preference for tetrahedral (T_d) sites, reducing the T_d sublattice magnetization (∑μ_T_d) and unbalancing the total moment. However, the reported M_s values for the Zn-series (Zn19, Zn32, Zn48) show a monotonic increase with Zn substitution (Table 2: 104 → 114 → 143 A m² kg⁻¹ at 5 K).
In contrast, the Neel model (eq. 4: μ_tot^Zn = 7 + 3x – 4y) predicts that M_s should peak and then decrease beyond a certain Zn²⁺ threshold (x ~ 0.5) due to the breakdown of superexchange interactions, as Zn²⁺ cannot participate in magnetic coupling. This is supported by literature.
Problem: The experimental data does not show this expected decrease, even at Zn48 (x = 0.48), which is close to the theoretical limit. This inconsistency suggests either:
Overestimation of M_s for Zn48 (143 A m² kg⁻¹), or Incorrect assumptions in the Neel model (e.g., ignoring surface spin canting or Zn²⁺ occupancy in octahedral sites).
The paper cites Mameli et al. (2016), who observed M_s peaking at Zn ~ 0.5 and then decreasing, aligning with theory. The authors’ data, however, shows no such peak, which is physically implausible for high Zn²⁺ content.
The authors use Mössbauer data (for Ni31 and Zn38) to validate the Neel model, but the calculated M_s values for these samples (red dots in Fig. 5b) fall below the experimental trendline. This discrepancy is handwaved as due to “spin canting” or “surface effects,” but no quantitative correction is applied.
Here are several critical questions and concerns regarding the methodology, data presentation, and interpretation:
1. Contradiction in Stoichiometry and Fe Valence: The ICP analysis shows an excess of iron (e.g., composition Zn₀.₄₈Co₀.₂₆Fe₂.₂₆O₄), which the authors attribute to the presence of Fe²⁺. However, Mössbauer spectrometry “does not provide evidence for the presence of Fe²⁺ ions”. How is this apparent contradiction reconciled? What is the charge compensation mechanism for the excess Fe³⁺ (e.g., cation vacancies), and how does this affect the assumed spin-only magnetic moments used in the Néel model?
2. Inconsistency in Anisotropy Equation: The text provides the equation for the anisotropy constant as Ka=μ0HKMs/2. However, this is dimensionally incorrect as written; Ms is in A m² kg⁻¹, not A m⁻¹. To obtain values in J m⁻³ (as reported in Table 2), one must multiply by the material’s density (ρ). Is the correct formula Ka=μ0HKMsρ/2? If so, why is the density factor omitted from the text?
3. Missing Data and Validation: The study’s key conclusion regarding the effect of cation distribution on magnetic properties relies heavily on the Ms(x,y) maps. However, the inversion degree (y) for the main samples is only estimated from the map, not measured directly. Mössbauer data are provided only for two additional samples (Ni31 and Zn38), not the main series. Why was the inversion degree not measured for the core samples (e.g., Zn48, Ni63) to validate the predictions of the model?
4. Size and Composition Data Omission: The text repeatedly states that particle size is constant across all samples, which is critical for isolating the effect of doping. However, Table 1, which presumably contains the crystallite sizes, TEM sizes, and exact compositions, is not included in the main text. Without access to this table, it is impossible to verify the claimed size uniformity or the exact compositions, which undermines the foundation of the analysis.