Hardening of Cobalt Ferrite Nanoparticles by Local Crystal Strain Release: Implications for Rare Earth Free Magnets

In this work, we demonstrate that the reduction of the local internal stress by a low-temperature solvent-mediated thermal treatment is an effective post-treatment tool for magnetic hardening of chemically synthesized nanoparticles. As a case study, we used nonstoichiometric cobalt ferrite particles of an average size of 32(8) nm synthesized by thermal decomposition, which were further subjected to solvent-mediated annealing at variable temperatures between 150 and 320 °C in an inert atmosphere. The postsynthesis treatment produces a 50% increase of the coercive field, without affecting neither the remanence ratio nor the spontaneous magnetization. As a consequence, the energy product and the magnetic energy storage capability, key features for applications as permanent magnets and magnetic hyperthermia, can be increased by ca. 70%. A deep structural, morphological, chemical, and magnetic characterization reveals that the mechanism governing the coercive field improvement is the reduction of the concomitant internal stresses induced by the low-temperature annealing postsynthesis treatment. Furthermore, we show that the medium where the mild annealing process occurs is essential to control the final properties of the nanoparticles because the classical annealing procedure (T > 350 °C) performed on a dried powder does not allow the release of the lattice stress, leading to the reduction of the initial coercive field. The strategy here proposed, therefore, constitutes a method to improve the magnetic properties of nanoparticles, which can be particularly appealing for those materials, as is the case of cobalt ferrite, currently investigated as building blocks for the development of rare-earth free permanent magnets.


S2
Energy Dispersive x-Ray Fluorescence (EDXRF) Table S1. Iron and cobalt (w/w) relative percentage obtained by Energy Dispersive X-Ray Fluorescence (EDXRF) for CFO before and after thermal annealing at different temperatures.

S3
The standard deviation (std) calculated from the strain maps obtained for (111)  x-Ray diffraction data

Mössbauer spectroscopy
57 Fe Mössbauer spectroscopy under intense magnetic field is a powerful tool to investigate magnetic structure of spinel ferrite, allowing a more reliable distinction between A-and B-site components than the zero field spectra, allowing to better determine all the hyperfine parameters, as mean isomer shift (), mean quadrupolar shift (2ε), and mean hyperfine field (B hyp ). The applied field is usually added to the A-site hyperfine field and subtracted from the B-site hyperfine field, B hyp , allowing less overlap between the two S4 components. Furthermore, such spectra can also give information about non-collinearity of the spin structure, mean canting angle (θ).
In the presence of an external magnetic field parallel to the γray direction, the relative areas of the absorption lines give information about the degree of alignment of the magnetization with the applied field. The modelling of the in-field Mössbauer spectrum allows one also the direct estimation of both the effective field (B eff ) and the angle (θ) of the two types of sites, for an inverse spinel structure, and then their respective hyperfine field B hyp can be calculated according to the relation: where B eff is the vectorial sum of the B hyp and the applied field, B app , and θ is the angle between the magnetic field at the nucleus and the γ-ray direction, respectively. For a thin absorber the relative area of the six lines is given by 3:p:1:1:p:3, where: In particular, the experimental results reveal the presence of an outer sub-spectrum (red line in figure 3) with symmetrical and narrow lines corresponding to Fe 3+ in A-sites according to the hyperfine parameters (Table   2), and an inner sub-spectrum (octahedral sites, blue line in the figure 3) with an asymmetric and complex shape. This complexity comes from the presence of Fe 2+ , which is characterized by a weak hyperfine field and large isomer shift compared with those of Fe 3+ . The description of this in-field sub-spectrum requires a model comprising several components of sextet splitting composed of Lorentzian lines ( Figure S3), considering the correlation between isomer shift, effective field, quadripolar shift and angle canting in each component (Table   S2).
The mean refined values of the hyperfine parameters correspond to those of Fe 3+ in A-sites of cobalt ferrite structure 2 . On the other hand, the <B hyf > of the iron species located in octahedral sites (51.2 T) are slightly lower than those of stoichiometric cobalt ferrite, and the mean value of the isomer shift of iron located in octahedral site ( 0.5 mm/s -1 ) is higher than that of Fe 3+ in cobalt ferrite NPs. 4,5 Therefore, the values of hyperfine parameters show the presence of iron ions at intermediate valence between Fe 3+ and Fe 2+ . 6 The nonzero intensity of lines 2 and 5 (i.e.,  0) in the spectra indicates the presence of a non-collinear magnetic structure, with some spins that are not aligned parallel or antiparallel to the external magnetic field. Figure S3. Mössbauer spectra measured at 12 K under 8 T magnetic field for samples CFO, CFO210 and CFO320. Grey dots and solid lines are experimental and simulated data. Black and red simulated lines are the total spectrum and sub-spectrum corresponding to A site, respectively; blue, green, pink and cyan simulated lines are the sub-spectrum corresponding to Fe 3+ , Fe 2+<x<3+ , Fe 2+ in B sites, respectively. Table S2. Mean isomer shift (δ), mean quadrupole shift (2ε), mean effective field (B eff ), mean hyperfine field (B hyf ), mean canting angle (ϑ) and relative amount of Fe in in the cavities evaluated from fitting Mössbauer spectra (recorded at 12 K applying an 8 T magnetic) of samples CFO, CFO210, and CFO320. Uncertainties on the last digit are given in parentheses. The error for canting angle has been assessed to be 10º. and CFO210-oven (red dots)

S8
The field dependence of remanent magnetization was measured using the IRM (Isothermal Remanent Magnetization) and DCD (Direct Current Demagnetization) protocols. According to the IRM protocol, the samples, in the demagnetized state, were cooled in a zero magnetic field down to 5 K. At this temperature, a small external field was applied for 10 s, then switched off, and finally, the remanence (M IRM ) was measured.
The process was repeated, increasing the field in steps up to 5 T. In a DCD measurement, the initial state was the magnetically saturated one. After cooling the sample at 5 K, an external field of -5 T was applied for 10 s, then it was turned off and the remanence (M DCD ) was measured. As in IRM, a small external field in the opposite direction to magnetization was applied for 10 s and then switched off. Finally, the remanent magnetization was measured. This was repeated increasing the field up to +5 T. The analysis of the remanent magnetization curves measured by IRM and DCD protocols ( Figure S3)