Coupled hard–soft spinel ferrite-based core–shell nanoarchitectures: magnetic properties and heating abilities

Bi-magnetic core–shell spinel ferrite-based nanoparticles with different CoFe2O4 core size, chemical nature of the shell (MnFe2O4 and spinel iron oxide), and shell thickness were prepared using an efficient solvothermal approach to exploit the magnetic coupling between a hard and a soft ferrimagnetic phase for magnetic heat induction. The magnetic behavior, together with morphology, stoichiometry, cation distribution, and spin canting, were investigated to identify the key parameters affecting the heat release. General trends in the heating abilities, as a function of the core size, the nature and the thickness of the shell, were hypothesized based on this systematic fundamental study and confirmed by experiments conducted on the water-based ferrofluids.


SAMPLES CHARACTERIZATION
. Particle diameter determined by different techniques: DTEM, SD_DTEM, and σ_DTEM are the numberweighted median diameter, standard deviation and distribution width obtained from TEM image analysis. DTEM_V is the volume-weighted particle diameter calculated from the number-weighted data, DXRD R is the particle diameter obtained from the Rietveld analysis of the XRD patterns, DXRD SPA is the particle diameter obtained from the single peaks analysis of the XRD patterns with the Scherrer equation as described in reference 1 , DMAG O is the particle diameter obtained from the analysis of the magnetization isotherms in generalized Langevin scaling by using Octave, while DMAG M is obtained by MINORIM software.    LOW-TEMPERATURE MÖSSBAUER SPECTROSCOPY. The in-field measurements were done in a perpendicular arrangement of the external magnetic field with respect to the γ-beam and are useful to get information about the cationic distribution and the canting phenomena in the spinel structure.

Sample
Indeed, the angle θ between the magnetic moment ( ⃗) and the applied magnetic field has been estimated thanks to the following equation: where Bhf is the hyperfine field (Bhf 0T ), Beff the total effective magnetic field at the nucleus (Bhf 6T ), Bapp the external applied magnetic field, and α is the angle between Beff and Bapp. The angle θ corresponds to the canting angle of the magnetic moment for the octahedral sites, whereas for the tetrahedral ones the canting angle is equal to π-θ. This is because of the relative arrangement of the hyperfine and applied fields vectors that are parallel or antiparallel aligned for tetrahedral or octahedral sites, respectively. 2 Figure 3S. Low temperature 57 Fe Mössbauer spectra with no external magnetic field (upper side) and in the presence of external magnetic field (lower side) of the samples CoB (left), CoB@Mn (middle), and CoB@Fe (right). Octahedral sites are represented in blue, tetrahedral in red. For CoB@Fe, the external field increases up to 6 T.  Table 2S. 57 Fe Mössbauer parameters of the samples obtained from the spectra recorded at low temperature (4 K) and with a 6 T magnetic field applied: values of the isomer shift (δ), effective field at 0 T (Beff 0T = Bhf) and 6 T (Beff 6T ), relative area (A), canting angles (α) and chemical formula calculated from site occupancy corrected by ICP-OES data. Without the external magnetic field, the spectra showed the overlapping of two sextets associated with the octahedral and tetrahedral sites of the spinel structure. The in-field measurements allowed us to split these two subspectra and to calculate the occupancy in the two sublattices. For instance, from the relative areas of the  [3][4][5][6][7][8][9] Similar results were found for the sample CoA and CoC, whose inversion degrees are equal to 0.65 and 0.74, respectively. For the sample CoA@Fe, it was found from relative areas that 37% of Fe cations are located in tetrahedral positions and 63% in octahedral positions. The comparison of these data with the core ones allowed to estimate the cation distribution of the shell. Taking into account the iron fraction in the core calculated from ICP-OES measurements (0.10) and the site occupancy of the core, we estimated the amount of Fe in the shell, which corresponds to 38% and 62% for tetrahedral and octahedral sites respectively. Consequently, the ratio Fe(Oh)/Fe(Td) is 1.65. This result is in agreement with the theoretical maghemite ratio, which value is 1.67, while for stoichiometric magnetite is 2. 10 The same behaviour is revealed in the samples CoB@Fe and CoC@Fe2, whose Fe(Oh)/Fe(Td) ratios are equal to 1.71 and 1.74, respectively. The increased Fe(Oh)/Fe(Td) ratio with the NPs size is in line with the RT Mössbauer data that suggested a lower degree of oxidation for the larger sample, CoC@Fe2. 1 By using the same procedure, Fe content in CoB@Mn shell was estimated, and the inversion degree was found equal to 0.46. Consequently, the formula of the shell can be written as (Mn0.43Fe0.55)[Mn0.46Fe1.52]O4. Similar behaviour was observed for sample CoC@Mn, with an inversion degree of 0.44. This result is in good agreement with the theoretical value of inversion degree for nanosized manganese ferrite. 11 The chemical formula of the different samples with site occupancies are reported in Table 2S. By using Eq. 1S, it is also possible to calculate the canting angles. For sample CoA, the values for the tetrahedral and octahedral sites are 19° and 0°, respectively. Within the experimental error, we can consider that the magnetic moments of both sublattices are not canted being the angles calculated from the cosine's equation (Eq. 1S), and therefore small changes in the cosθ lead to significant changes on the angle values. The same results were found for samples CoB and CoC, which canting angle values for tetrahedral and octahedral sites are equal to 19°-10° and 25°-0°, respectively (Table 2S). Spin canting has not also been revealed in the core-shell samples. The sample CoB@Fe was measured at different magnetic fields (from 1 to 6 T) to gather information on the spin saturation process (Figure 3S, right). Even with the external magnetic field of 1 T, the splitting of the two sextets was observed. At 0 T the octahedral sites have a larger hyperfine field than tetrahedral ones, while at 6 T an inversion occurred ( Figure 3S). This is due to the antiparallel direction of the octahedral hyperfine field with respect to the externally applied field. The increase of the hyperfine field in the tetrahedral sites (or decrease in octahedral sites), when a magnetic field of 1 T is applied, is equal to 0.3 T. When a 2 T field is applied, the Bhf changes by 1.5 T for Td and 1.7 T for Oh sites, while it changes of about 1 T for all the subsequent increase of external magnetic field up to 6 T. The different behaviour observed below and above 2 T is probably caused by the unsaturated magnetic moment, that requires a field of such strength to be saturated, as it can be revealed from the field dependence of the magnetization at low temperature (Figure 3). Figure 5S. ZFC (full circles) and FC (empty circles) curves, normalized for the magnetization at Tmax of the ZFC curve, of core-shell samples and respective cores recorded at low external magnetic field (10 mT).  Figure 6S) show a furcation at a specific temperature (Tdiff), with a maximum on the ZFC curve (Tmax), that is proportional to the blocking temperature of the largest particles and the mean value, respectively. Tb is the blocking temperature calculated with the first derivative of the difference curve (MFC-MZFC) as the temperature at which 50% of the nanoparticles are in the superparamagnetic state. 12,13 Both Tmax and Tb increases with the size of cobalt ferrite, as predicted by the Stoner-Wohlfarth model, 14 and are in a good agreement with the previously reported values for cobalt ferrite of similar size. [15][16][17][18] The saturation of the low-temperature part of the FC curve extends to higher temperatures for larger particles; it is a typical signature of enhancement of inter-particle interactions due to the increase of the mean magnetic moments per particle and reform of effective magnetic anisotropy. 19 ZFC curves ( Figure 5S) of core-shell samples show a dominant maximum (Tmax), associated with majority particle population, also confirmed by a single energy barrier distribution (-d(MFC-MZFC)/dT) 20 centred at a specific temperature (Tb). Both Tmax and Tb values increase in the core-shell samples compared to the cores, due to the increased particle magnetic volume. The difference Tdiff -Tmax is generally lower in the core-shell samples than in the cores, suggesting a decrease in the energy barrier distribution dispersity, because of the homogeneous growth on the shells around the seeds that induces a narrower size distribution.

DC MAGNETOMETRY
Nevertheless, also the increase of interparticle interactions in the core-shell systems can affect Tdiff, as also evidenced by the flatness of the FC curves. In particular, spinel iron oxide coated core-shells show a more pronounced FC saturation, typical for strongly interacting systems (e.g. superspin glass). [21][22][23] Magnetization isotherms of cobalt ferrite samples show no hysteretic behaviour at 300 K ( Figure 6S), typical for particles in the superparamagnetic state. A large hysteresis is instead present at 10 K for cobalt ferrite samples. Coercive field increases with increases the particle size, in agreement with the Stoner-Wohlfarth model, 14  For the real system of the superparamagnetic NPs with a size distribution, the magnetization, M of the NPs in the magnetic field, H can be written as a weighted sum of the Langevin functions: where f (μ) corresponds to the unimodal log-normal distribution of the magnetic moments, μ expressed as: where σ is the distribution width, μ0 and μm are the median and mean magnetic moment, respectively ( Table  3S). The second term in the equation (Eq. 2S) corresponds to an additional linear contribution to the magnetization, which can originate from some diamagnetic or paramagnetic components of the sample. The parameters of f (μ) were obtained from the refinement of the magnetization isotherm measured above TB in the Matlab/Octave software. The median magnetic size, dmag of the particle was calculated from the μ0 using the expression:

Eq. 5S
where a and μuc are the lattice parameter and the magnetic moment of the unit cell of the spinel phase (calculated assuming site occupancy estimated from LT 57 Fe Mössbauer spectroscopy), respectively (Table  3S). For comparison, magnetic moments ( ) and magnetic diameters (DMAG) have been calculated also by MINORIM software, which uses a non-regularized method. 24 The parameters used for the calculation of magnetic diameters are reported in Table 3S. where is equal to 0.5 and 0.64 for uniaxial (K2_uni) and cubic (K2_cub) anisotropy, respectively.

= 25
Eq. 8S 5 Eq. 6S and Eq. 7S depend on saturation magnetization and coercive field or anisotropy field, respectively, and give an approximated value of anisotropy constant assuming collinear orientation with respect to the magnetic field. Eq. 8S derives from the energy barrier equation, and it depends on blocking temperature (Tb) estimated from -d(MFC-MZFC)/dT curves, and particle volume anisotropy constant K3 was calculated by using <DMAG>, <DXRD>, and <DTEM> values. The results are reported in Table 4S.

DETAILS ON MAGNETIC FLUID HYPERTHERMIA Theoretical Calculation of SAR
The equations for the calculation of SAR are as follows: = P is the lost power, expressed as follows: Eq. 9S χ'' is the out-of-phase component of the susceptibility, expressed as follows: Eq. 10S 0 is the actual susceptibility, while τ the effective relaxation time, expressed in Eq. 11S and 14S, respectively.
is the susceptibility calculation parameter, and ξ is the Langevin parameter, expressed in Eq. 12S and 13S, respectively.

AC MAGNETOMETRY ON POWDERED SAMPLES
AC magnetometry was used to measure the temperature dependence of the in-phase (χ') and out-of-phase (χ'') component of the magnetic susceptibility at different frequencies (0.1-1000 Hz) for the core (Figure 9S) and core-shell samples ( Figure 10S) and the Néel relaxation time estimated by the Vogel-Fulcher equation (Eq. 17S,) is reported in Table 5S. The Néel relaxation times of core-shell samples are slower than those of the respective cores, due to the increased particle volume that dominates the overall decrease of effective anisotropy.

Eq. 17S
Where τ0 is the characteristic relaxation time, Eb the energy barrier against magnetization reversal, T the absolute temperature, and T0 the temperature value accounting for the strength of magnetic interactions.
As an example, the calculation for the CoA sample is reported. The Vogel-Fulcher equation (Eq. 17S) has been written in the logarithmic form (Eq. 18S):

INTERCALATION PROCESS
The hydrophobic nanoparticles were made hydrophilic by an intercalation process with CTAB, as described in the main article. The concentration of the colloidal dispersion was 3.4 mg • mL -1 . The presence of CTAB molecules was verified by FT-IR, as shown as an example in Figure 12S.   To the best of our knowledge, in the literature the role of dipolar interactions in bimagnetic spinel ferrite-base core-shell nanoparticles in the heat release is not studied, due to the intrinsic complex nature of the system. 29,30,[39][40][41][42][43][44][45][31][32][33][34][35][36][37][38] Indeed, to investigate the role of dipolar interactions it would be necessary to have no changes in composition, size, morphology, etc. of the primary nanoparticles, but only differences in the aggregates/agglomerates in terms of size (number of primary NPs) and shape (random or controlled clustering such as chain-like alignment). In our work, the samples differ for several features (core size, shell thickness, and chemical composition) and therefore it is not possible to conclude about the specific role of the dipolar interactions in the heat release. The studies present in the literature about the dipolar interactions and their role in the heating dissipation are mainly devoted to single-phase nanoparticles, but their role is still debated with contradictory results showing improvement 30,[34][35][36]41 or deterioration [30][31][32][33]45 of the heating abilities that consequently are hardly predictable. Indeed, the shape and the size of the aggregate influence the role of the dipolar interaction, being commonly beneficial when ordered clusters (e.g. chains) are formed, but detrimental if NPs are randomly oriented. Some authors define the dipolar coupling constant λ as:

Eq. 20S
Where μ is the magnetic moment and d the mean diameter. For λ>2, the system is considered strongly interacting and aggregate may happen. When λ<2, the interparticle interactions are negligible. 37 For our samples (in the form of powder), λ is always <2, therefore dipolar interaction should be negligible. Nevertheless, as we report in Figure 14S, it is evident from the FC curve that dipolar interactions are present both in the powder and in the dispersions. However, in the selected concentration range (0.7-3.4 mg/mL) no significant effect can be detected, as can be seen after rescaling the curves to relative values. We can see that both the ZFC and FC curves are almost overlapped underlying that no changes occur in the strength of dipolar interactions increasing the concentration. To clarify the behavior of dipolar interaction with concentration, a cobalt ferrite sample has been measured (DXRD = 7.7 nm, a repeatability of the sample CoC) where both the effects of the concentration (3.4 mg/mL and 7.8 mg/mL) and the coating (cetyl trimethylammonium bromide (CTAB) and polyethylene glycol trialkoxysilane (PEG-TMS)), on SAR were studied ( Figure 15S).