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

Abstract

A set of ∼9 nm CoFe₂O₄ nanoparticles substituted with Zn²⁺ and Ni²⁺ was prepared by thermal decomposition of metallic acetylacetonate precursors to correlate the effects of replacement of Co²⁺ 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 Co²⁺ by 48% of Zn²⁺ ions led to an increase in saturation magnetization of approximately 40% from ∼103 A m² kg⁻¹ to ∼143 A m² kg⁻¹, whereas the addition of Ni²⁺ at a similar percentage led to an ∼30% decrease in saturation magnetization to 68–72 A m² kg⁻¹. The results of calculations based on the two-sublattice Néel 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.

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Introduction

Spinel ferrites are materials with stoichiometry M²⁺Fe₂O₄ (M²⁺ = Co²⁺, Zn²⁺, Ni²⁺, Fe²⁺) 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. For these reasons, spinel ferrite nanoparticles (NPs) are suitable for many applications such as MRI contrast agents,^1–3 molecular detection and separation, drug delivery systems and hyperthermic therapy,^4,5 and design of rare-earth-free permanent magnets.^6–11

The spinel ferrite structure consists of a cubic close-packed (ccp) arrangement of oxygen atoms with tetrahedral (T_d) and octahedral [O_h] sites.^12–14 The cationic distribution is often reported as (M_1−δ²⁺Fe_δ³⁺)_Td[M_δ²⁺Fe_2−δ³⁺]_OhO₄, with δ 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 Néel'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 δ values in the range of 0.66 to 0.8;^13,16–19 its large magneto-crystalline anisotropy (K₁ = 290 kJ m⁻³ at room temperature²⁰) is due to the strong single-ion anisotropy of Co²⁺ in O_h-sites, arising from its non-quenched spin–orbit coupling.²¹ Ni²⁺ and Zn²⁺ exhibit lower anisotropy in comparison to Co²⁺, yet—owing to their different single-ion properties and site selectivity—they yield opposite effects on saturation magnetization, providing interesting perspectives. Ni²⁺ tends to occupy the O_h sites, while Zn²⁺ prefers T_d sites.^11,22,23 The selectivity for different sites leads to a change in the inversion degree of the spinel structure.

When Ni²⁺ substitutes Co²⁺, the inversion degree increases (i.e., the stoichiometric NiFe₂O₄ is the totally inverted spinel with δ = 1) while Zn²⁺ substitution leads to a lower value of δ.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 canting²⁵) as well as it is related to the particle size and synthesis method.²⁴ For example, Mameli et al.²⁶ studied the magnetic properties of ∼7 nm Zn-substituted CoFe₂O₄ NPs and reported a reduction of inversion degree to ∼0.4 when the Zn²⁺ content was ∼0.5. This led to a significant enhancement in saturation magnetisation up to 157 ± 3 A m² kg⁻¹, which is higher than the value measured for pure CoFe₂O₄. Andersen et al.²⁷ found metastable cation distributions in hydrothermally prepared Zn-substituted CoFe₂O₄ NPs leading to increased M_s in Zn-rich samples, which decreased after annealing to the thermodynamic distribution.

On the other hand, nanocrystals of NiFe₂O₄ and CoFe₂O₄ 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 reported values of ∼0.74, ∼0.78, and ∼0.44 for CoFe₂O₄, Ni_0.5Co_0.5Fe₂O₄, and NiFe₂O₄ NPs of ∼4.5 nm, respectively, significantly different from bulk.

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 CoFe₂O₄ NPs synthesized by the same method and with comparable morpho-structural features.

This study focuses on the comparative study of magnetic properties of M_xCo_1−xFe₂O₄ (M²⁺ = Ni²⁺, Zn²⁺) NPs with increasing Ni²⁺/Zn²⁺ content. The thermal decomposition of metallic acetylacetonates in high-temperature boiling solvent (TD) synthesis²⁹ has been used to have a fine control on morpho-structural features of NPs and the high value of M_s (see Fig. S1, ESI†). Furthermore, to the best of our knowledge, a few studies of the low-temperature magnetic properties of M_xCo_1−xFe₂O₄ are available in the literature^28,30,31 (see Fig. S1a, ESI†).^32–34 We prepared two sets of samples (hereafter referred to as “Ni-series” and “Zn-series”) which have an increasing M²⁺ 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.¹⁹ Therefore, 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 Néel 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 Mössbauer 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.

Experimental methods

Synthesis

For the synthesis of ∼9 nm CoFe₂O₄ 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 °C for 2 h, and then at 300 °C for 1 h (heating rates 5 °C min⁻¹); 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_xCo_1−xFe₂O₄ (M²⁺ = Ni²⁺, Zn²⁺), Co(acac)₂ was partially substituted with Ni(acac)₂ or Zn(acac)₂, so that the sum of all Co²⁺ and M²⁺ 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 M²⁺ 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.

Table 1 Sample acronyms, stoichiometry defined via ICP analysis, average XRPD (〈d〉_XRPD) and TEM (〈d〉_TEM) diameters

Sample	Stoichiometry	〈d〉XRPD, nm	〈d〉TEM, nm
CoRef	Co0.85Fe2.15O4	8.3(4)	9.0(1)
Ni22	Ni0.22Co0.71Fe2.07O4	8.0(4)	8.1(1)
Ni39	Ni0.39Co0.45Fe2.16O4	8.3(5)	8.5(1)
Ni63	Ni0.63Co0.23Fe2.14O4	8.3(5)	10.0(1)
Zn19	Zn0.19Co0.70Fe2.11O4	9.3(4)	8.4(2)
Zn32	Zn0.32Co0.47Fe2.22O4	9.0(1)	8.7(1)
Zn48	Zn0.48Co0.26Fe2.26O4	8.6(5)	9.3(2)

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Characterization techniques

X-ray powder diffraction (XRPD) was performed on NP powders using a Bruker D8 Advance diffractometer (solid state LynxEye detector, Cu Kα radiation, Bragg Brentano geometry, DIFFRACT plus software). The average sizes of crystallites were calculated using the Scherrer equation.³⁵ Transmission Electron Microscopy (TEM) images were acquired using a Philips CM200 microscope operating at 200 kV and equipped with a LaB₆ filament. The statistical analysis of particles’ sizes was performed using the ImageJ software.²⁸ Inductively 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 °C at 10 °C min⁻¹ under an O₂ atmosphere (20 mL min⁻¹). 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 ±5 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) M(H) = M_s(1 − a/H − b/H²) where a and b are free-fitting parameters, and H is the applied field.³⁶ The 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.^38,39 IRM curves are obtained starting from a demagnetized sample at μ₀H = 0 T and measuring the remanence corresponding to increasing fields μ₀H > 0; DCD curves are obtained in the same manner, but the measurement starts from μ₀H = 0 with a sample previously being saturated at μ₀H = −5 T. ⁵⁷Fe Mössbauer spectra were obtained at 12 K in an externally applied field of 8 T oriented parallel to the γ-beam using a ⁵⁷Co/Rh γ-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 δ are referred to those of α-Fe at 300 K.

Results and discussions

The XRPD patterns show the typical reflections of the spinel Fd3̄m 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.⁴⁰

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

TGA 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 CoFe₂O₄ particles by Gyergyek et al.⁴¹ made with the same approach, putting forward the lack of Co²⁺ as a consequence of the higher stability of Co²⁺-oleate, compared to Fe³⁺-oleate, and attributed the iron excess to the presence of Fe²⁺. 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 Mössbauer 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 Fe²⁺ 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 Ni²⁺ and Zn²⁺ 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

Table 2 Blocking and maximum temperatures from ZFC/FC (T_b, T_max), 5 K switching field (μ₀H_sw), 5 and 300 K magnetic saturation (M_s), reduced remanence (M_r/M_s), coercivity (μ₀H_C) and anisotropy constant (K_a). Uncertainties on the last digit indicated in parentheses

Sample	T b, K	T max, K	μ 0 H sw (5 K), T	M s (5 K), A m^2 kg^−1	M s (300 K), A m^2 kg^−1	M r /M s (5 K)	μ 0 H c (5 K), T	K a, 10^−5 J m^−3
CoRef	199(1)	289(1)	1.25(1)	103(2)	85(2)	0.60(3)	1.06(5)	11
Ni22	166(1)	252(1)	1.0(1)	73(1)	58(1)	0.67(1)	0.95(5)	5.7
Ni39	166(1)	228(1)	0.9(1)	68(3)	58(2)	0.68(4)	0.85(4)	4.5
Ni63	107(1)	157(1)	0.6(1)	72(2)	56(2)	0.64(2)	0.51(3)	3.1
Zn19	207(1)	285(1)	0.8(1)	104(3)	80(2)	0.56(3)	0.67(3)	7.1
Zn32	166(1)	228(1)	0.6(1)	114(4)	80(3)	0.56(4)	0.47(2)	5.3
Zn48	132(1)	201(1)	0.3(1)	143(5)	93(3)	0.49(4)	0.27(1)	4.3

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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 (χ_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 reversal. Both Ni²⁺ and Zn²⁺ have the same qualitative effect on the SFD, lowering their maximum position (μ₀H_sw) as shown in Table 2. The effect is more marked for Zn²⁺, since twice more Ni²⁺ is needed to have μ₀H_sw dropping to 0.6 T; the same applies to the width of the SFDs, showing that the substitution with Zn²⁺ narrows down the SFD more significantly than that with Ni²⁺.

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

Further evidence can be found in hysteresis loops at 5 K (Fig. 4), where the coercivity, μ₀H_c, monotonically decreases as the Zn²⁺/Ni²⁺ content increases; the μ₀H_c values of both series are similar to the corresponding μ₀H_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 μ₀H_K∼ μ₀H_irr, where μ₀H_irr is calculated as the field where the difference between the magnetizing and the demagnetizing branches of the hysteresis loop curve reaches 1%.⁴⁵ The K_a values are reported in Table 2, and their magnitude is similar to those reported in the literature.²⁸

Spinel ferrites have a cubic magneto-crystalline anisotropy with an expected reduced remanent magnetization (M_r/M_s) of ∼ 0.83–0.87,⁴⁶ but 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 ∼0.5, characteristic for uniaxial anisotropy.^40,42 In 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 Ni²⁺ cations, with lower single-ion anisotropy, compared to Co²⁺ 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 that for cobalt ferrite;¹³ that can result in an increase in cobalt occupying octahedral sites where it significantly contributes to anisotropy.⁴⁷ Alternatively, Ni²⁺ cations may lower the surface anisotropy term, thereby reducing this source of uniaxial anisotropy. At the same time, as expected, the introduction of Zn²⁺ 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 δm-plot:^48,49

δm = m_DCD(H) − 1 + 2m_IRM(H) (2)

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 Ni²⁺ and Zn²⁺ 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 Zn²⁺, 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.⁵³ In general, a system of randomly distributed NPs with average magnetic moment μ and average separation d, the dipole–dipole interaction energy among particles can be expressed as follows:

where ρ is the volume density of the material (estimated to be 5290 kg m⁻³ for all samples¹²), 〈V²〉 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 δm dip depth follow the same overall trend, confirming our interpretation. The small variation in M_s due to the introduction of Ni²⁺ 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.⁵² Both 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 δm plots, offering reliable means of assessing magnetic interactions among nanoparticles.

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

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.

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, Ni²⁺ 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 Ni²⁺ spin-only magnetic moment of 2μ_B is the lowest of all ions, and its selectivity drives it to O_h-sites, decreasing the term and explaining our observations. The moderate entity of the effect is in accordance with the literature.^28,32,56,57

Increasing Zn²⁺, instead, reveals a monotonic increase in M_s at 5 K, inducing an increase in M_s from ∼103 A m² kg⁻¹ for x = 0 to ∼143 A m² kg⁻¹ for x = 0.48 (Fig. 4 and Table 2). The Zn²⁺ diamagnetism and the selectivity for T_d-sites^27,58 make it decrease the term , unbalancing the sum of the moments and increasing saturation. However, the increase in saturation with Zn²⁺ content is limited to Zn²⁺ ∼ 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 ZnFe₂O₄,^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 Néel model, considering the well-known ion site selectivity of Ni²⁺ for O_h-sites⁵⁶ and of Zn²⁺ for T_d-sites²⁷ and the spin-only magnetic moment of our metal cations (Zn²⁺ = 0μ_B, Co²⁺ = 3μ_B, Ni²⁺ = 2μ_B, Fe³⁺ = 5μ_B).¹² For both series, an equation was written to express M_s as a function of the stoichiometric coefficient of M²⁺ (x) and the one of Co²⁺ in O_h-sites (y, corresponding to δ). For the Ni-series, the expression of the Bohr magneton magnetization per formula unit is (ESI,† Section S7)

μ^Ni_fu(x,y) = 7 − 5x − 4y, (4)

while for the Zn-series, the expression is

μ^Zn_fu(x,y) = 7 + 3x − 4y (5)

Note that the stoichiometric coefficient of Fe is kept to 2. Assuming that all the M²⁺ 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.

Fig. 5 (a) and (b) Low temperature magnetization maps calculated as a function of M²⁺ stoichiometric coefficient (x) and Co²⁺ inversion degree (y) for (a) Ni- and (b) Zn-series. Black dots represent the experimental saturations from hysteresis loops, while red dots represent M_s obtained from two additional samples with known composition and cationic distribution (Mössbauer spectroscopy data, see the ESI†). The black arrow indicates the verse of increasing magnetization. The (c) and (d) graphs compare the experimental and calculated magnetizations with respect to the composition for Ni- and Zn-series. Triangles indicate the maximal M_s value possible for two compositions with low M_s, as indicated on the map.

Considering CoRef, cobalt ferrite is a partially inverted spinel, meaning that a fraction of Co²⁺ is still in T_d-sites; far from the intention of giving an exact value of the cation distribution, the position of the point in the graph suggests y ∼ 0.66, which is close to literature values.^13,16–18

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 Co²⁺ and Ni²⁺ implies that with increasing substitution, if Ni²⁺ simply replaces Co²⁺ 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 ∼ 0.8). This is consistent with the almost identical saturation of CoRef and Zn19, and it is in accordance with the fact that Zn²⁺ being T_d-site selective, should occupy the fraction of T_d-sites which would be filled by Co²⁺ in CoFe₂O₄. 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 Zn²⁺ quantity in O_h-sites. Compared to other synthetic methods,^14,59–62 TD gives nanoparticles among those with the highest M_s values.^63,64 The differences are certainly related to the cationic distribution,⁴¹ size distribution, spin canting and surface layer.⁶⁵

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 Mössbauer 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.⁶⁵

Furthermore, 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 δ and thus providing a simple way to compare synthetic methods.

Conclusions

The magnetic properties of two sets of Ni²⁺ and Zn²⁺ doped cobalt ferrite NPs with equal size of ∼9 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 Zn²⁺ content. The highest value of saturation magnetisation of 143 ± 5 A m² kg⁻¹ at 5 K, which is 40% higher than in the CoRef sample, was found for a sample with the composition Zn_0.48Co_0.26Fe_2.26O₄. In contrast, Ni²⁺ substitution resulted in a decrease in both magnetization by ∼30% and anisotropy by ∼70% for the higher concentration of nickel.

A strong correlation was found between the results from the δm plot and the calculated dipolar energy. The obtained results suggest that Zn²⁺ 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.

Author contributions

The paper and ESI were written based on the contributions of all authors. P. M., D. P., F. C. and R. M. designed the 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 Mössbauer spectrometry. All authors contributed to the results discussion and revision of the article.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

P. M. and R. M. thank the Swedish Energy Agency (project number 46561-1) and the Swedish Research Council (VR). D. P. acknowledges project code PE0000021, Concession Decree No. 1561 of 11.10.2022 adopted by the “Ministero dell’Università e della Ricerca (MUR)”, according to attachment E of Decree No. 1561/2022, Project title “Network 4 Energy Sustainable Transition-NEST” in the frame of study of surface wettability properties, and REMAP, which has received funding from the European Commission PathFinder open programme under grant agreement No. 101046909.

Notes and references

1. N. Lee, D. Yoo, D. Ling, M. H. Cho, T. Hyeon and J. Cheon, Iron Oxide Based Nanoparticles for Multimodal Imaging and Magnetoresponsive Therapy, Chem. Rev., 2015, 115, 10637–10689.
2. J. Jang, H. Nah, J.-H. Lee, S. H. Moon, M. G. Kim and J. Cheon, Critical Enhancements of MRI Contrast and Hyperthermic Effects by Dopant-Controlled Magnetic Nanoparticles, Angew. Chem., Int. Ed., 2009, 48, 1234–1238.
3. S. H. Koenig and K. E. Kellar, Theory of 1/T 1 and 1/T 2 NMRD profiles of solutions of magnetic nanoparticles, Magn. Reson. Med., 1995, 34, 227–233.
4. M. Colombo, S. Carregal-Romero, M. F. Casula, L. Gutiérrez, M. P. Morales, I. B. Böhm, J. T. Heverhagen, D. Prosperi and W. J. Parak, Biological applications of magnetic nanoparticles, Chem. Soc. Rev., 2012, 41, 4306–4334.
5. N. Sanpo, C. C. Berndt, C. Wen and J. Wang, Transition metal-substituted cobalt ferrite nanoparticles for biomedical applications, Acta Biomater., 2013, 9, 5830–5837.
6. P. Maltoni, T. Sarkar, G. Barucca, G. Varvaro, D. Peddis and R. Mathieu, Exploring the magnetic properties and magnetic coupling in SrFe₁₂O₁₉/Co_1−xZn_xFe₂O₄ nanocomposites, J. Magn. Magn. Mater., 2021, 535, 168095.
7. M. Estrader, A. López-Ortega, S. Estradé, I. V. Golosovsky, G. Salazar-Alvarez, M. Vasilakaki, K. N. Trohidou, M. Varela, D. C. Stanley, M. Sinko, M. J. Pechan, D. J. Keavney, F. Peiró, S. Suriñach, M. D. Baró and J. Nogués, Robust antiferromagnetic coupling in hard-soft bi-magnetic core/shell nanoparticles, Nat. Commun., 2013, 4, 2960.
8. P. Shyam, M. Mørch, A. Z. Eikeland, J. Ahlburg, A. Mamakhel, M. Saura-Múzquiz and M. Christensen, Combined characterization approaches to investigate magnetostructural effects in exchange-spring ferrite nanocomposite magnets, Mater. Chem. Front., 2022, 6, 2422–2437.
9. B. Muzzi, M. Albino, M. Petrecca, C. Innocenti, C. de, J. Fernández, G. Bertoni, C. Marquina, M. R. Ibarra and C. Sangregorio, 3d Metal Doping of Core@Shell Wüstite@ferrite Nanoparticles as a Promising Route toward Room Temperature Exchange Bias Magnets, Small, 2022, 18, 1–11.
10. R. Sharma, P. Thakur, P. Sharma and V. Sharma, Ferrimagnetic Ni2+ doped Mg-Zn spinel ferrite nanoparticles for high density information storage, J. Alloys Compd., 2017, 704, 7–17.
11. P. Maltoni, M. Baričić, G. Barucca, M. C. Spadaro, J. Arbiol, N. Yaacoub, D. Peddis and R. Mathieu, Tunable particle-agglomeration and magnetic coupling in bi-magnetic nanocomposites, Phys. Chem. Chem. Phys., 2023, 25, 27817–27828.
12. B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2008.
13. F. G. da Silva, J. Depeyrot, A. F. C. Campos, R. Aquino, D. Fiorani and D. Peddis, Structural and Magnetic Properties of Spinel Ferrite Nanoparticles, J. Nanosci. Nanotechnol., 2019, 19, 4888–4902.
14. S. S. Jadhav, S. E. Shirsath, S. M. Patange and K. M. Jadhav, Effect of Zn substitution on magnetic properties of nanocrystalline cobalt ferrite, J. Appl. Phys., 2010, 108, 093920.
15. A. Feirweather, F. F. Roberts and A. J. E. Welch, Ferrites, Rep. Prog. Phys., 1952, 15, 142–172.
16. D. Carta, M. F. Casula, A. Falqui, D. Loche, G. Mountjoy, C. Sangregorio and A. Corrias, A Structural and Magnetic Investigation of the Inversion Degree in Ferrite Nanocrystals MFe₂O₄ (M = Mn, Co, Ni), J. Phys. Chem. C, 2009, 113, 8606–8615.
17. A. S. Vaingankar, B. V. Khasbardar and R. N. Patil, X-ray spectroscopic study of cobalt ferrite, J. Phys. F: Met. Phys., 1980, 10, 1615–1619.
18. D. Carta, G. Mountjoy, G. Navarra, M. F. Casula, D. Loche, S. Marras and A. Corrias, X-ray Absorption Investigation of the Formation of Cobalt Ferrite Nanoparticles in an Aerogel Silica Matrix, J. Phys. Chem. C, 2008, 112, 19791.
19. H. L. Andersen, M. Saura-Múzquiz, C. Granados-Miralles, E. Canévet, N. Lock and M. Christensen, Crystalline and magnetic structure-property relationship in spinel ferrite nanoparticles, Nanoscale, 2018, 10, 14902–14914.
20. J. M. D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, Cambridge, 2010.
21. S. Chikazumi and C. D. Graham, Magnetocrystalline anisotropy, Physics of Ferromagnetism, International series of monographs on physics, Oxford University Press, New York, 2nd edn, 1997, ch. 12, pp. 270–272.
22. G. Varvaro, A. Omelyanchik and D. Peddis, Tailored Functional Oxide Nanomaterials, Wiley, 2022, pp. 405–437.
23. G. F. Dionne, Magnetic Oxides, Springer US, Boston, MA, 2009, vol. 8.
24. K. R. Sanchez-Lievanos, J. L. Stair and K. E. Knowles, Cation Distribution in Spinel Ferrite Nanocrystals: Characterization, Impact on their Physical Properties, and Opportunities for Synthetic Control, Inorg. Chem., 2021, 60, 4291–4305.
25. D. Peddis, in Magnetic Nanoparticle Assemblies, ed. K. N. Trohidou, Pan Stanford, Singapore, 2014, vol. 7, pp. 159–198.
26. V. Mameli, A. Musinu, A. Ardu, G. Ennas, D. Peddis, D. Niznansky, C. Sangregorio, C. Innocenti, N. T. K. Thanh and C. Cannas, Studying the effect of Zn-substitution on the magnetic and hyperthermic properties of cobalt ferrite nanoparticles, Nanoscale, 2016, 8, 10124–10137.
27. H. L. Andersen, C. Granados-Miralles, M. Saura-Múzquiz, M. Stingaciu, J. Larsen, F. Søndergaard-Pedersen, J. V. Ahlburg, L. Keller, C. Frandsen and M. Christensen, Enhanced intrinsic saturation magnetization of Zn_xCo_1−xFe₂O₄ nanocrystallites with metastable spinel inversion, Mater. Chem. Front., 2019, 3, 668–679.
28. G. Muscas, N. Yaacoub, G. Concas, F. Sayed, R. Sayed Hassan, J. M. Greneche, C. Cannas, A. Musinu, V. Foglietti, S. Casciardi, C. Sangregorio and D. Peddis, Evolution of the magnetic structure with chemical composition in spinel iron oxide nanoparticles, Nanoscale, 2015, 7, 13576–13585.
29. S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang and G. Li, Monodisperse MFe₂O₄ (M = Fe, Co, Mn) Nanoparticles, J. Am. Chem. Soc., 2004, 126, 273–279.
30. U. B. Sontu, N. G. Rao, F. C. Chou and V. M. Ramana Reddy, Temperature dependent and applied field strength dependent magnetic study of cobalt nickel ferrite nano particles: Synthesized by an environmentally benign method, J. Magn. Magn. Mater., 2018, 452, 398–406.
31. N. B. Velhal, N. D. Patil, A. R. Shelke, N. G. Deshpande and V. R. Puri, Structural, dielectric and magnetic properties of nickel substituted cobalt ferrite nanoparticles: Effect of nickel concentration, AIP Adv., 2015, 5, 097166.
32. T. Orlando, M. Albino, F. Orsini, C. Innocenti, M. Basini, P. Arosio, C. Sangregorio, M. Corti and A. Lascialfari, On the magnetic anisotropy and nuclear relaxivity effects of Co and Ni doping in iron oxide nanoparticles, J. Appl. Phys., 2016, 119, 134301.
33. A. B. Nawale, N. S. Kanhe, S. A. Raut, S. V. Bhoraskar, A. K. Das and V. L. Mathe, Investigation of structural, optical and magnetic properties of thermal plasma synthesized Ni-Co spinel ferrite nanoparticles, Ceram. Int., 2017, 43, 6637–6647.
34. G. Datt, M. Sen Bishwas, M. Manivel Raja and A. C. Abhyankar, Observation of magnetic anomalies in one-step solvothermally synthesized nickel-cobalt ferrite nanoparticles, Nanoscale, 2016, 8, 5200–5213.
35. J. I. Langford and A. J. C. Wilson, Scherrer after sixty years: A survey and some new results in the determination of crystallite size, J. Appl. Crystallogr., 2016, 11, 1536–1545.
36. A. H. Morrish, The Physical Principles of Magnetism, IEEE Press, Piscataway, 1965, vol. 1.
37. G. Concas, F. Congiu, G. Muscas and D. Peddis, Determination of Blocking Temperature in Magnetization and Mössbauer Time Scale: A Functional Form Approach, J. Phys. Chem. C, 2017, 121, 16541–16548.
38. D. Peddis, P. E. Jönsson, S. Laureti and G. Varvaro, in Frontiers of Nanoscience, ed. C. Binns, Elsevier B.V, Oxford, UK, 2014, vol. 6, pp. 129–188.
39. E. P. Wohlfarth, Relations between Different Modes of Acquisition of the Remanent Magnetization of Ferromagnetic Particles, J. Appl. Phys., 1958, 29, 595–596.
40. D. Peddis, C. Cannas, A. Musinu, A. Ardu, F. Orru, D. Fiorani, S. Laureti, D. Rinaldi, G. Muscas, G. Concas, G. Piccaluga, F. Orrù, D. Fiorani, S. Laureti, D. Rinaldi, G. Muscas, G. Concas and G. Piccaluga, Beyond the Effect of Particle Size: Influence of CoFe2O4 Nanoparticle Arrangements on Magnetic Properties, Chem. Mater., 2013, 25, 2005–2013.
41. S. Gyergyek, D. Makovec, A. Kodre, I. Arčon, M. Jagodič and M. Drofenik, Influence of synthesis method on structural and magnetic properties of cobalt ferrite nanoparticles, J. Nanopart. Res., 2010, 12, 1263–1273.
42. M. Albino, E. Fantechi, C. Innocenti, A. López-Ortega, V. Bonanni, G. Campo, F. Pineider, M. Gurioli, P. Arosio, T. Orlando, G. Bertoni, C. de Julián Fernández, A. Lascialfari and C. Sangregorio, Role of Zn²⁺ Substitution on the Magnetic, Hyperthermic, and Relaxometric Properties of Cobalt Ferrite Nanoparticles, J. Phys. Chem. C, 2019, 123, 6148–6157.
43. S. Mørup, M. F. Hansen and C. Fradsen, Magnetic Nanoparticles, Amsterdam, 2011.
44. R. H. Kodama, A. E. Berkowitz, E. J. McNiff and S. Foner, Surface spin disorder in ferrite nanoparticles, Phys. Rev. Lett., 1996, 77, 394–397.
45. D. Peddis, F. Orrù, A. Ardu, C. Cannas, A. Musinu and G. Piccaluga, Interparticle Interactions and Magnetic Anisotropy in Cobalt Ferrite Nanoparticles: Influence of Molecular Coating, Chem. Mater., 2012, 24, 1062–1071.
46. S. E. Peschany and N. A. Usov, Theoretical hysteresis loops for single-domain particles with cubic anisotropy, J. Magn. Magn. Mater., 1997, 174, 247–260.
47. M. Tachiki, Origin of the Magnetic Anisotropy Energy of Cobalt Ferrite, Prog. Theor. Phys., 1960, 23, 1055–1072.
48. P. E. Kelly, K. O’Grady, P. I. Mayo and R. W. Chantrell, Switching mechanisms in cobalt-phosphorus thin films, IEEE Trans. Magn., 1989, 25, 3881–3883.
49. J. García-Otero, M. Porto and J. Rivas, Henkel plots of single-domain ferromagnetic particles, J. Appl. Phys., 2000, 87, 7376–7381.
50. C. Binns, Nanomagnetism: Fundamentals and Applications, Elsevier, 2014.
51. J. A. De Toro, M. Vasilakaki, S. S. Lee, M. S. Andersson, P. S. Normile, N. Yaacoub, P. Murray, E. H. Sánchez, P. Muñiz, D. Peddis, R. Mathieu, K. Liu, J. Geshev, K. N. Trohidou and J. Nogués, Remanence Plots as a Probe of Spin Disorder in Magnetic Nanoparticles, Chem. Mater., 2017, 29, 8258–8268.
52. A. Omelyanchik, S. Villa, M. Vasilakaki, G. Singh, A. M. Ferretti, A. Ponti, F. Canepa, G. Margaris, K. N. Trohidou and D. Peddis, Interplay between inter- and intraparticle interactions in bi-magnetic core/shell nanoparticles, Nanoscale Adv., 2021, 3, 6912–6924.
53. A. V. Ambarov, V. S. Zverev and E. A. Elfimova, Influence of field amplitude and dipolar interactions on the dynamic response of immobilized magnetic nanoparticles: Perpendicular mutual alignment of an alternating magnetic field and the easy axes, Phys. Rev. E, 2023, 107, 24601.
54. G. Muscas, M. Cobianchi, A. Lascialfari, C. Cannas, A. Musinu, A. Omelyanchik, V. Rodionova, D. Fiorani, V. Mameli and D. Peddis, Magnetic Interactions Versus Magnetic Anisotropy in Spinel Ferrite Nanoparticles, IEEE Magn. Lett., 2019, 10, 1–5.
55. E. H. Sánchez, M. Vasilakaki, S. S. Lee, P. S. Normile, M. S. Andersson, R. Mathieu, A. López-Ortega, B. P. Pichon, D. Peddis, C. Binns, P. Nordblad, K. Trohidou, J. Nogués and J. A. De Toro, Crossover From Individual to Collective Magnetism in Dense Nanoparticle Systems: Local Anisotropy Versus Dipolar Interactions, Small, 2022, 18, 2106762.
56. C. Yang, Y. Hu, X. Li, J. Li, L. Wang and H. Li, Tuning of magnetic properties and hyperfine interaction by the substitution of Ni²⁺ for cobalt ferrite nanoparticles, J. Mater. Sci.: Mater. Electron., 2019, 30, 19647–19653.
57. A. Omelyanchik, G. Singh, M. Volochaev, A. Sokolov, V. Rodionova and D. Peddis, Tunable magnetic properties of Ni-doped CoFe2O4 nanoparticles prepared by the sol–gel citrate self-combustion method, J. Magn. Magn. Mater., 2019, 476, 387–391.
58. S. Amiri and H. Shokrollahi, The role of cobalt ferrite magnetic nanoparticles in medical science, Mater. Sci. Eng., C, 2013, 33, 1–8.
59. G. Barrera, M. Coisson, F. Celegato, S. Raghuvanshi, F. Mazaleyrat, S. N. Kane and P. Tiberto, Cation distribution effect on static and dynamic magnetic properties of Co1-xZnxFe2O4 ferrite powders, J. Magn. Magn. Mater., 2018, 456, 372–380.
60. A. Omelyanchik, K. Levada, S. Pshenichnikov, M. Abdolrahim, M. Baricic, A. Kapitunova, A. Galieva, S. Sukhikh, L. Astakhova, S. Antipov, B. Fabiano, D. Peddis and V. Rodionova, Green Synthesis of Co-Zn Spinel Ferrite Nanoparticles: Magnetic and Intrinsic Antimicrobial Properties, Materials, 2020, 13, 5014.
61. D. D. Andhare, S. R. Patade, J. S. Kounsalye and K. M. Jadhav, Effect of Zn doping on structural, magnetic and optical properties of cobalt ferrite nanoparticles synthesized via. Co-precipitation method, Phys. B, 2020, 583, 412051.
62. M. Stefanescu, M. Bozdog, C. Muntean, O. Stefanescu and T. Vlase, Synthesis and magnetic properties of Co_1−xZn_xFe₂O₄ (x = 0 ÷ 1) nanopowders by thermal decomposition of Co(II), Zn(II) and Fe(III) carboxylates, J. Magn. Magn. Mater., 2015, 393, 92–98.
63. G. Muscas, S. Jovanović, M. Vukomanović, M. Spreitzer and D. Peddis, Zn-doped cobalt ferrite: Tuning the interactions by chemical composition, J. Alloys Compd., 2019, 796, 203–209.
64. R. Topkaya, A. Baykal and A. Demir, Yafet–Kittel-type magnetic order in Zn-substituted cobalt ferrite nanoparticles with uniaxial anisotropy, J. Nanopart. Res., 2013, 15, 1359.
65. C. R. Vestal and Z. J. Zhang, Effects of Surface Coordination Chemistry on the Magnetic Properties of MnFe₂O₄ Spinel Ferrite Nanoparticles, J. Am. Chem. Soc., 2003, 125, 9828–9833.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp06029b

‡ Present affiliations: Laboratoire Interfaces Traitements Organisation et Dynamique des Systèmes, Université Paris Cité, CNRS UMR-7886, Rue Jean Antoine de Baïf, 75013 Paris, France and Dipartimento di Scienze, Università degli Studi Roma TRE, Via della Vasca Navale, 84-00146 Roma, Italy.

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