Chemical engineering of cationic distribution in spinel ferrite nanoparticles: the eﬀect on the magnetic properties †

A set of B 9 nm CoFe 2 O 4 nanoparticles substituted with Zn 2+ and Ni 2+ was prepared by thermal decomposition of metallic acetylacetonate precursors to correlate the eﬀects of replacement of Co 2+ with the resulting magnetic properties. Due to the distinct selectivity of these cations for the spinel ferrite crystal sites, we show that it is possible to tailor the magnetic anisotropy, saturation magnetization, and interparticle interactions of the nanoparticles during the synthesis stage. This approach unlocks new possibilities for enhancing the performance of spinel ferrite nanoparticles in specific applications. Particularly, our study shows that the replacement of Co 2+ by 48% of Zn 2+ ions led to an increase in saturation magnetization of approximately 40% from B 103 A m 2 kg (cid:2) 1 to B 143 A m 2 kg (cid:2) 1 , whereas the addition of Ni 2+ at a similar percentage led to an B 30% decrease in saturation magnetization to 68–72 A m 2 kg (cid:2) 1 . The results of calculations based on the two-sublattice Ne´el model of magnetization match the experimental findings, demonstrating the model’s effectiveness in the strategic design of spinel ferrite nanoparticles with targeted magnetic properties through doping/ inversion degree engineering.


Introduction
Spinel ferrites are materials with stoichiometry M 2+ Fe 2 O 4 (M 2+ = Co 2+ , Zn 2+ , Ni 2+ , Fe 2+ ) that have been intensely studied for their chemical flexibility, enabling the inclusion of a wide range of transition metal cations, thus providing an easy way to tune their magnetic properties.3][14] The cationic distribution is often reported as (M 1Àd 2+ Fe d ] O h O 4 , with d as the inversion degree, with a value between 0 (in normal spinel and 1 (in inverse spinel).The magnetization of spinel ferrites can be described by Ne ´el's model for antiferro-and ferrimagnetic materials, 12,13,15 where the total magnetic moment is the vectorial sum of the magnetic sublattice's magnetizations, corresponding to O h and T d sites in spinel ferrites: Since the metallic cations have different magnetic properties and site selectivity within the lattice, such spinel structures offer the possibility to easily modify the saturation magnetization (M s ), magneto-crystalline anisotropy, and interparticle magnetic interactions.Specifically, cobalt ferrite is a relatively highly anisotropic material with d values in the range of 0.66 to 0.8; 13,[16][17][18][19] its large magneto-crystalline anisotropy (K 1 = 290 kJ m À3 at room temperature 20 ) is due to the strong single-ion anisotropy of Co 2+ in O h -sites, arising from its nonquenched spin-orbit coupling. 21Ni 2+ and Zn 2+ exhibit lower anisotropy in comparison to Co 2+ , yet-owing to their different single-ion properties and site selectivity-they yield opposite effects on saturation magnetization, providing interesting perspectives.Ni 2+ tends to occupy the O h sites, while Zn 2+ prefers T d sites. 11,22,23The selectivity for different sites leads to a change in the inversion degree of the spinel structure.
When Ni 2+ substitutes Co 2+ , the inversion degree increases (i.e., the stoichiometric NiFe 2 O 4 is the totally inverted spinel with d = 1) while Zn 2+ substitution leads to a lower value of d. 24 This ability to control the inversion degree by chemical engineering provides an additional degree of freedom in designing the magnetic properties of spinel ferrite NPs.
At the nanoscale, the magnetic structure of spinel ferrites is due to the complex interplay between cationic distribution and surface magnetic disorder (i.e., spin canting 25 ) as well as it is related to the particle size and synthesis method. 24For example, Mameli et al. 26 studied the magnetic properties of B7 nm Zn-substituted CoFe 2 O 4 NPs and reported a reduction of inversion degree to B0.4 when the Zn 2+ content was B0.5.This led to a significant enhancement in saturation magnetisation up to 157 AE 3 A m 2 kg À1 , which is higher than the value measured for pure CoFe 2 O 4 .Andersen et al. 27 found metastable cation distributions in hydrothermally prepared Zn-substituted CoFe 2 O 4 NPs leading to increased M s in Zn-rich samples, which decreased after annealing to the thermodynamic distribution.
On the other hand, nanocrystals of NiFe 2 O 4 and CoFe 2 O 4 may exhibit weak interdependence between particle size and inversion degree.For example, in their study, Carta et al. 16 demonstrated that 6-9 nm NPs (including cobalt and nickel ferrites) prepared by the sol-gel method show the same inversion degree values as bulk analogues (0.68 and 1.0, respectively).On the other hand, Muscas et al. 28  In this framework, comparative studies of nanostructure spinel ferrites, which go beyond the effect of synthesis methods and morpho structural features, appear to be very important.To the best of our knowledge, no prior studies have directly compared Zn-and Ni-substituted CoFe 2 O 4 NPs synthesized by the same method and with comparable morpho-structural features.
This study focuses on the comparative study of magnetic properties of M x Co 1Àx Fe 2 O 4 (M 2+ = Ni 2+ , Zn 2+ ) NPs with increasing Ni 2+ /Zn 2+ content.The thermal decomposition of metallic acetylacetonates in high-temperature boiling solvent (TD) synthesis 29 has been used to have a fine control on morphostructural features of NPs and the high value of M s (see Fig. S1, ESI †).][34] We prepared two sets of samples (hereafter referred to as ''Ni-series'' and ''Zn-series'') which have an increasing M 2+ substitution with respect to the cobalt-ferrite reference sample.The NPs have comparable size and shape distributions, thus avoiding any possible size effects on the magnetic properties owing to changes in the inversion degree. 19Therefore, this system can be considered as a model that allows us to establish direct correlations between the magnetic structure (i.e., cationic distribution) and magnetic properties.Herein, we present a thorough investigation, conducted at both low temperature and room temperature, on the magnetic anisotropy, saturation magnetization, and interparticle interactions.Inversion/doping content maps of the low temperature M s were plotted by considering a spin-only two-sublattice Ne ´el model of magnetization.The usefulness of the maps is demonstrated by predicting M s for 2 samples for the Ni-and Zn-series with known composition and cationic distribution from in-field Mo ¨ssbauer spectrometry.The potential interest of this study is related to the possibility of controlling the magnetic structure at the nanoscale, opening interesting perspectives to improve materials' performance for targeted technological applications.

Synthesis
For the synthesis of B9 nm CoFe 2 O 4 NPs, Fe(acac) 3 (2 mmol), Co(acac) 2 (1 mmol), oleic acid (OLAC, 6 mmol), oleylamine (OLAM, 6 mmol), 1,2-hexadecanediol (HDD, 10 mmol) and dibenzylether (DBE, 20 mL) were employed according to the method described by Sun et al. 29 All chemicals were stirred under an inert nitrogen atmosphere at 200 1C for 2 h, and then at 300 1C for 1 h (heating rates 5 1C min À1 ); at the end of the thermal program, the product was cooled at room temperature by removing the heating mantle.Eventually, the sample was washed in ethanol using a centrifuge (10 min, 4000 rpm) three times, and stored in a few mL of toluene.To synthesize M x Co 1Àx Fe 2 O 4 (M 2+ = Ni 2+ , Zn 2+ ), Co(acac) 2 was partially substituted with Ni(acac) 2 or Zn(acac) 2 , so that the sum of all Co 2+ and M 2+ acetylacetonates is kept to 1 mmol.The resulting stoichiometries in the final product were analysed by inductively coupled plasma atomic emission spectroscopy (ICP-AES), and each sample was named after its M 2+ stoichiometric coefficient, x (e.g., Zn19 or Ni63).The samples were all compared with a reference no-substituted sample, CoRef.See the used acronyms of samples in Table 1.

Characterization techniques
X-ray powder diffraction (XRPD) was performed on NP powders using a Bruker D8 Advance diffractometer (solid state LynxEye detector, Cu Ka radiation, Bragg Brentano geometry, DIFFRACT plus software).The average sizes of crystallites were calculated using the Scherrer equation. 35Transmission Electron Microscopy (TEM) images were acquired using a Philips CM200 microscope operating at 200 kV and equipped with a LaB 6 filament.The statistical analysis of particles' sizes was performed using the ImageJ software. 28Inductively Coupled Plasma -Atomic Emission Spectroscopy (ICP-AES) measurements were performed using an iCAP 6300 DUP ICP-AES spectrometer (ThermoScientific) to check the composition of each sample.Thermo-gravimetric Analysis (TGA) was performed on a LabsysEvo 1600 DTA/TGA (Setaram): a few mg of powder was placed in an alumina crucible and heated from 30 to 1000 1C at 10 1C min À1 under an O 2 atmosphere (20 mL min À1 ).The magnetization was normalized considering the weight loss measured by TGA, due to decomposition of the organic part.DC magnetization measurements were performed using a SQUID magnetometer (Quantum Design MPMS XL).The field dependence of magnetization loops was measured at 5 and 300 K in the range of AE5 T. The saturation magnetization (M s ) of each sample was obtained by fitting the high field values with the Law of Approach to Saturation (LAS) where a and b are free-fitting parameters, and H is the applied field. 36The temperature dependence of magnetization has been investigated using Zero Field Cooled (ZFC) and Field Cooled (FC) protocols under 2.5 mT fields from 5 to 300 K, and T max and T b were estimated by following the procedure reported in ref. 37. Remanent magnetization was measured by means of Isothermal Remanent Magnetization (IRM) and Direct Current Demagnetization (DCD) protocols. 38,39IRM curves are obtained starting from a demagnetized sample at m 0 H = 0 T and measuring the remanence corresponding to increasing fields m 0 H 4 0; DCD curves are obtained in the same manner, but the measurement starts from m 0 H = 0 with a sample previously being saturated at m 0 H = À5 T. 57 Fe Mo ¨ssbauer spectra were obtained at 12 K in an externally applied field of 8 T oriented parallel to the g-beam using a 57 Co/Rh g-ray source mounted on an electromagnetic transducer with a triangular velocity form.The hyperfine structure was modelled by a least-squares fitting procedure involving Zeeman sextets composed of Lorentzian lines using MOSSFIT (made-home software).The isomer shift values d are referred to those of a-Fe at 300 K.

Results and discussions
The XRPD patterns show the typical reflections of the spinel Fd% 3m cubic phase for all the samples, without any secondary phase (Fig. 1 and Fig. S2, ESI †).The crystallite size obtained by the Scherrer equation and estimated from the analysis of the TEM pictures were found in agreement (Table 1), suggesting the high crystallinity of the samples.TEM images confirm the spherical morphology and the low polydispersity of the particles (ESI, † Section S3; Table 1).It should be emphasized that the size is constant within experimental errors of different samples, allowing the investigation of magnetic properties beyond the effect of NPs' size. 40A was performed to determine the organic content (ESI, † Section S4) and the magnetization measurements were normalised considering only the inorganic content.The ICP analysis revealed an excess of iron with respect to the stoichiometric Co : Fe 1 : 2 ratio (Table 1 and ESI, † Section S5) expected for cobalt ferrite.This phenomenon was already observed for CoFe 2 O 4 particles by Gyergyek et al. 41 made with the same approach, putting forward the lack of Co 2+ as a consequence of the higher stability of Co 2+ -oleate, compared to Fe 3+ -oleate, and attributed the iron excess to the presence of Fe 2+ .This agrees with other studies, that do not exclude the formation of Fe 2+29,42 .We left out the possibility that the Fe 2+/3+ excess formed oxide impurities, as we did not identify any, neither structurally nor magnetically, as also observed by Mo ¨ssbauer spectrometry.Note that, based on the mean value of isomer shift, the recorded spectra on all studied samples do not provide evidence for the presence of Fe 2+ ions (Table S4 and Fig. S10, ESI †).
The temperature dependence of magnetization recorded by ZFC/FC protocols (Fig. S6, ESI †) shows a clear dependence: the average blocking temperature and temperature of M ZFC maximum (i.e., T b and T max ) decrease with an increase in Ni 2+ and Zn 2+ contents, suggesting a dominating effect of the magnetic anisotropy, even if an effect due to interparticle interactions can be present (ESI, † Section S6 and Table 2). 11

Magnetic anisotropy
The decrease in magnetic anisotropy is also confirmed by the shift in the maximum irreversible susceptibility obtained by the differentiated DCD curves at 5 K (w irr = dM DCD /dH) (Fig. 2), which is directly correlated with the distribution of coercive fields (i.e., switching fields distribution, SFD).All the SFDs have a single peak shape, indicating a homogeneous magnetization This journal is © the Owner Societies 2024 reversal.Both Ni 2+ and Zn 2+ have the same qualitative effect on the SFD, lowering their maximum position (m 0 H sw ) as shown in Table 2.The effect is more marked for Zn 2+ , since twice more Ni 2+ is needed to have m 0 H sw dropping to 0.6 T; the same applies to the width of the SFDs, showing that the substitution with Zn 2+ narrows down the SFD more significantly than that with Ni 2+ .
Further evidence can be found in hysteresis loops at 5 K (Fig. 4), where the coercivity, m 0 H c , monotonically decreases as the Zn 2+ /Ni 2+ content increases; the m 0 H c values of both series are similar to the corresponding m 0 H sw .(Table 2).An estimation of the NPs' magnetic anisotropy was obtained by: 43 where H K is the anisotropy field of the material.Kodama et al. 44 pointed out that m 0 H K B m 0 H irr , where m 0 H irr is calculated as the field where the difference between the magnetizing and the demagnetizing branches of the hysteresis loop curve reaches 1%. 45The K a values are reported in Table 2, and their magnitude is similar to those reported in the literature. 28pinel ferrites have a cubic magneto-crystalline anisotropy with an expected reduced remanent magnetization (M r /M s ) of B 0.83-0.87, 46but this feature is usually suppressed in small NPs by the surface and shape contributions, resulting in a uniaxial effective anisotropy; this is confirmed by the low M r /M s value of B0.5, characteristic for uniaxial anisotropy. 40,42n our case, the undoped cobalt ferrite sample CoRef possesses a M r /M s value of approximately 0.6, confirming the presence of competing uniaxial and cubic anisotropy contributions.Interestingly, the substitution with Ni 2+ cations, with lower singleion anisotropy, compared to Co 2+ initially leads to an increase in M r /M s , while one would expect a reduction due to the decrease in a cubic magneto-crystalline term.This can be attributed to the change in cationic distribution.In fact, the inversion degree for nickel ferrite is expected to be higher than Table 2 Blocking and maximum temperatures from ZFC/FC (T b , T max ), 5 K switching field (m 0 H sw ), 5 and 300 K magnetic saturation (M s ), reduced remanence (M r /M s ), coercivity (m 0 H C ) and anisotropy constant (K a ).Uncertainties on the last digit indicated in parentheses  that for cobalt ferrite; 13 that can result in an increase in cobalt occupying octahedral sites where it significantly contributes to anisotropy. 47Alternatively, Ni 2+ cations may lower the surface anisotropy term, thereby reducing this source of uniaxial anisotropy.At the same time, as expected, the introduction of Zn 2+ led to the formation of a pronounced uniaxial anisotropy, with M r /M s tending to be 0.5. 42

Magnetic interparticle interactions
To study NPs' magnetic interparticle interactions, normalized IRM and DCD magnetizations can be compared by means of the Kelly equation, providing the so-called dm-plot: 48,49 dm = m DCD (H) The prevalence of either dipolar or superexchange interactions can be evaluated on the basis of the negative/positive dips, respectively, 50 although some contribution of the intraparticle effect can be present 51,52 Since the NPs are physically separated by an OLAC layer, only dipolar interactions are expected.The increase of Ni 2+ and Zn 2+ substitution shifts the average reversal field (i.e., the peak position) to lower values-in agreement with the coercivities and SFD peaks.In the case of Zn 2+ , the substitution also causes a remarkable increase in peak depth, indicating an increase in interaction strength.A semi-quantitative estimation of the magnetic dipolar interactions can be obtained by calculating the dipolar energy. 53In general, a system of randomly distributed NPs with average magnetic moment m and average separation d, the dipole-dipole interaction energy among particles can be expressed as follows: where r is the volume density of the material (estimated to be 5290 kg m À3 for all samples 12 ), hV 2 i is the average volume calculated by considering all particles as spherical, and d is the average center-to-center distance of two nanoparticles covered with a single layer of OLAC molecules 2 nm long. 45,54,55Fig. 3c  and d show that E dip and dm dip depth follow the same overall trend, confirming our interpretation.The small variation in M s due to the introduction of Ni 2+ is expected to be reflected in small variations in the dipolar interactions, which are indeed observed.This is in agreement with literature comparing cobalt and nickel ferrites. 52Both trends of interactions measured in the case of the Zn-series are qualitatively matching.The accordance between the two methods lends robustness to the measure of the dip depth in dm plots, offering reliable means of assessing magnetic interactions among nanoparticles.

Saturation magnetization
Finally, it is quite interesting to discuss the trend of M s with respect to the chemical composition of the samples (ESI, † Section S7).In the case of the Ni-series, Ni 2+ induces a steep decrease in M s followed by an almost constant trend, leaving little room for property tuning (Fig. 4 and Table 2).The Ni 2+ spin-only magnetic moment of 2m B is the lowest of all ions, and its selectivity drives it to O h -sites, decreasing the P m O h term and explaining our observations.The moderate entity of the effect is in accordance with the literature. 28,32,56,57ncreasing Zn 2+ , instead, reveals a monotonic increase in M s at 5 K, inducing an increase in M s from B103 A m 2 kg À1 for x = 0 to B143 A m 2 kg À1 for x = 0.48 (Fig. 4 and Table 2).The Zn 2+ diamagnetism and the selectivity for T d -sites 27,58 make it decrease the term P m T d , unbalancing the sum of the moments and increasing saturation.However, the increase in saturation with Zn 2+ content is limited to Zn 2+ B 0.5: 26,42 due to its diamagnetic nature, it cannot participate in super-exchange interactions, interrupting the magnetic superexchange coupling and weakening the magnetic structure of the material.Above this threshold, the magnetic behaviour converges to that of ZnFe 2 O 4 , 59,60 a normal antiferromagnetic spinel (T N = 10 K), 13 and thus M s decreases.Our results are in qualitative agreement with this explanation and with other results obtained by TD. 26,42 The M s values can be estimated using the two-sublattice Ne ´el model, considering the well-known ion site selectivity of Ni 2+ for O h -sites 56 and of Zn 2+ for T d -sites 27 and the spin-only magnetic moment of our metal cations (Zn 2+ = 0m B , Co 2+ = 3m B , Ni 2+ = 2m B , Fe 3+ = 5m B ). 12 For both series, an equation was written to express M s as a function of the stoichiometric coefficient of M 2+ (x) and the one of Co 2+ in O h -sites (y, corresponding to d).For the Ni-series, the expression of the Bohr magneton magnetization per formula unit is (ESI, † Section S7) while for the Zn-series, the expression is m Zn fu (x,y) = 7 + 3x À 4y (5)   Note that the stoichiometric coefficient of Fe is kept to 2. Assuming that all the M 2+ cations occupy their preferential sites, the functions can be plotted as M s (x,y) maps (Fig. 5), allowing us to easily predict M s for different x and y.Reciprocally, an estimate of the cationic distribution (i.e., y) can be obtained if M s and x are known.The excluded grey areas are present because x + y cannot be greater than 1.][18] The calculation explains a small change in magnetic saturation for the Ni-series after Ni22, with the points arranged between two iso-composition lines.The common O h -site selectivity of Co 2+ and Ni 2+ implies that with increasing substitution, if Ni 2+ simply replaces Co 2+ at O h sites, the magnetization will reduce slowly due to the small difference in spin-only magnetic moment between the two cations.
Turning now to the Zn series, Zn19 lies almost on the same iso-magnetization line of CoRef, thus suggesting an increase in the relative cobalt fraction in O h -sites (y B 0.8).This is consistent with the almost identical saturation of CoRef and Zn19, and it is in accordance with the fact that Zn 2+ being T dsite selective, should occupy the fraction of T d -sites which would be filled by Co 2+ in CoFe 2 O 4 .Zn32 and Zn48 experimental values are lower than the value predicted for their composition, lying on the composition limit line.This discrepancy may reflect spin canting, size effects, and a small Zn 2+ quantity in O h -sites.Compared to other synthetic methods, 14,[59][60][61][62] TD gives nanoparticles among those with the highest M s values. 63,64The differences are certainly related to the cationic distribution, 41 size distribution, spin canting and surface layer.To confirm the usefulness of the M s (x,y) maps, the cationic distribution of samples of similar composition (Ni31 and Zn38) has been determined by Mo ¨ssbauer spectrometry at 12 K and under an intense magnetic field of 8 T (ESI, † Section S8), yielding y = 0.54 and 0.62, respectively.
Combining x and y values yields M s which is found to be close to the expected values (see ESI †).Yet, the obtained values are smaller, as mentioned earlier.This stems from structural features (defects, surface contributions) and the possible effect of the ligand on the magnetic moments on the surface. 65urthermore, by examining Fig. S1 (ESI †), we note that only the samples obtained by this TD synthesis come close to the spin-only M s , while other synthesis methods provide M s much lower than any values predicted by the map, regardless of the particle size.As shown in Fig. S1 (ESI †), M s depends greatly on the synthesis methods for a given x.M s (x,y) maps may be used to give a quick graphical estimate of whether these differences stem from different d and thus providing a simple way to compare synthetic methods.

Conclusions
The magnetic properties of two sets of Ni 2+ and Zn 2+ doped cobalt ferrite NPs with equal size of B9 nm were investigated to evaluate the influence of cation distribution over chemical composition on the saturation magnetization, magnetic anisotropy and interparticle interactions.Specifically, we observed up to 40% enhancement of saturation magnetization and decreased magnetic anisotropy in samples with greater Zn 2+ content.The highest value of saturation magnetisation of 143 AE 5 A m 2 kg À1 at 5 K, which is 40% higher than in the CoRef sample, was found for a sample with the composition Zn 0.48 -Co 0.26 Fe 2.26 O 4 .In contrast, Ni 2+ substitution resulted in a decrease in both magnetization by B30% and anisotropy by B70% for the higher concentration of nickel.
A strong correlation was found between the results from the dm plot and the calculated dipolar energy.The obtained results suggest that Zn 2+ substitution strongly affects the dipolar interparticle interaction intensity due to the increasing saturation magnetization and decreasing magnetocrystalline anisotropy.
Moreover, the inversion/doping content maps developed in this study provide a simple method to both visualize substitution impacts and predict M s values from knowledge of only cation distributions or compositions.Our demonstration of accurate modelling of experimental data highlights the utility of these maps for the rational design of spinel ferrite nanoparticles tailored to further application needs.experiments; R. M., A. O. and D. P. coordinated the data analysis and discussion.M. B. and P. M. synthesized the nanoparticles and characterized them by XRPD and magnetometry techniques.G. B. performed structural characterisation by TEM.N. Y. performed Mo ¨ssbauer spectrometry.All authors contributed to the results discussion and revision of the article.

Fig. 1
Fig. 1 (a) XRPD pattern and (b) TEM pictures and size distribution histogram of sample Ni22.

Fig. 2
Fig. 2 (a) and (b) DCD remanence plots and (c) and (d) switching field distributions (SFD) for the Zn and the Ni-series.

Fig. 3
Fig. 3 (a) and (b) interaction dm plots of Ni-series and Zn-series, and (c) and (d) interaction dipolar energy values compared with dm profile depth.

Fig. 4
Fig. 4 (a) and (b) 5 K isothermal magnetization plots for Ni and Zn-series; (c) coercivity and (d) reduced remanent magnetization (M r /M s ) for all samples.