Controlling Magnetization Reversal and Hyperthermia Efficiency in Core–Shell Iron–Iron Oxide Magnetic Nanoparticles by Tuning the Interphase Coupling

Magnetic particle hyperthermia, in which colloidal nanostructures are exposed to an alternating magnetic field, is a promising approach to cancer therapy. Unfortunately, the clinical efficacy of hyperthermia has not yet been optimized. Consequently, routes to improve magnetic particle hyperthermia, such as designing hybrid structures comprised of different phase materials, are actively pursued. Here, we demonstrate enhanced hyperthermia efficiency in relatively large spherical Fe/Fe-oxide core–shell nanoparticles through the manipulation of interactions between the core and shell phases. Experimental results on representative samples with diameters in the range 30–80 nm indicate a direct correlation of hysteresis losses to the observed heating with a maximum efficiency of around 0.9 kW/g. The absolute particle size, the core–shell ratio, and the interposition of a thin wüstite interlayer are shown to have powerful effects on the specific absorption rate. By comparing our measurements to micromagnetic calculations, we have unveiled the occurrence of topologically nontrivial magnetization reversal modes under which interparticle interactions become negligible, aggregates formation is minimized and the energy that is converted into heat is increased. This information has been overlooked until date and is in stark contrast to the existing knowledge on homogeneous particles.

presents the SEM images of the prepared nanoparticles that were used to verify their spherical shape and estimate the mean average diameter. Particularly, evaporation of pure Fe powder pressurized in a pellet form, under Ar flow (70 torr) resulted in 50 nm nanoparticles (Sample F01: Figure  S1). Under the same pressure, co-evaporation of Fe and Fe 3 O 4 mixtures produces a similar particle diameter but the thickness of oxide on the surface is anticipated to increase as compared to the shell stabilized after natural oxidation (Samples F02-F03: Figures S1). The decrease in particles diameter (down to about 33 nm: Sample F03: Figure S1) was achieved by using lower pressure (50 torr) whereas evaporation of a pure Fe 3 O 4 target at 80 torr enables the production of larger nanoparticles (78 nm: Sample F05: Figure S1) with a very low zero-valent Fe content. We recall the thermal conductivity of a gas is proportional to the mean free path and the gas density. Thus, in the vapor-condensation method, particle size generally increases with increasing the gas-pressure as a result of decreasing mean free path. Additionally, it was observed that the lighter the carrier gas (for instance, by partially replacing Ar with oxygen) the smaller the mean size of the particles (the case of F06 vs. F05: Figure S1). 1 The experimental results of the morphological investigation and X-ray powder diffractometry suggest that crystals possess high quality. The patterns were fitted following the Rietveld methodology on the basis of bcc Fe, spinel oxides (Fe 3 O 4 , γ-Fe 2 O 3 ) and FeO in order to get an indicative quantification of the observed structures. Figure S2. Comparative XRD patterns for samples under study. Inset presents a magnification of (110) diffraction peak suggesting the presence of epitaxial strain in the Fe core. We assume that a shift to higher angle in reciprocal space indicates compression, i.e. reduction in average lattice parameter. Right: Magnification of XRD diagrams in the range of (311), (400) diffraction peaks for Fe 3   Room temperature Mössbauer spectroscopy was used to differentiate the contribution from magnetically distinct phases. Table S1 summarizes the parameters estimated from the curves fitting. Relaxation models provided the best numerical fit, 2 with the very broad spectra lines as a consequence of distributions of the hyperfine parameters due to surface and interface disorder. 3 Figure S4. Mössbauer spectra of samples with varying Fe content: F01-F06 from top to bottom. The spectrum of the parental iron powder, indicated as Fe00, is used as a reference sample.

S3. MICROMAGNETIC SIMULATIONS
In the main text ( Figure 6), we discussed the influence of the main characteristics of the experimental samples: total particle size, core/shell ratio, interlayer spacer and shell crystallites' sizes on the hysteresis loop area. From the experimental results shown in main text Figure 4 there does not seem to exist any simple correlation (based on one parameter) between the characteristics of a given core/shell particle geometry and the released heat. Such apparent heterogeneity in the behaviour is attenuated by different field conditions: note that depending on the field amplitude and frequency, different samples from produce the largest heating, as seen in the main text.
Seeking to shed light on this, we present below our attempts to relate the computed dynamic heating capabilities corresponding to the hysteresis losses (i.e. quasi-static hysteresis loops areas times the frequency) to the measurements in the experimental samples. We show that the choice of the particles structural parameters used in the model highly affect the magnetic switching characteristics.
The modelled hysteresis cycles with applied field up to 30mT for individual nanoparticles with experimental geometries (based on the assumption of no dipole-dipole interparticle interactions) are shown in Figure S8.

It can be noted that:
 For all samples the system exhibits major hysteretic loop, except for sample F03, which seems to be under minor-loop conditions.  Samples F01, F02, F04 and F05 undergo a non-coherent reversal pointed out by the |m| variation, whereas it remains essentially unchanged for samples F03 and F06.  Samples F01 and F05 exhibit parallel coupling between core and shell, whereas F02, F03 and F04 exhibit antiparallel arrangement (note that the sample is a single-phase).  While for samples F01, F02 and F06 the magnetisation follows a symmetric path, in samples F04 and F05 the positive-to-negative and negative-to-positive field branches are clearly asymmetric.
These main aspects are certainly important for understanding magnetic-hyperthermia measurements (for example, having parallel magnetisation coupling would be in principle more desirable because it facilitates larger loop areas). The comparison with the experimental results (see the main text and Fig.S11 show that there is only one sample (F03) with a clear divergence between the theoretical predictions and the measured values.
Thus, we further analysed the magnetic response of sample F03 under higher field amplitudes. The results are shown in Figure S9. Noteworthy, the typical Stoner-Wohlfarth behaviour is recovered, with the particularity of the coherent response of two strongly-coupled lattices in which the core is leading (in contrast to sample F04, for example, where the shell dominates the magnetic switching). In conclusion, by increasing the field amplitude this particular sample F03 may present an extraordinary heating which far exceeds the other samples. The larger heating of F03 sample for larger field amplitude is in qualitatively agreement with the experimental results depicted in main text Figure 4 but the quantitative difference is large. Figure S9. Magnetization versus field loops for sample F03, same as in Figure S8 but now increasing the applied field up to 60 mT.
Our first assumption for the discrepancy between theory and experiment in this sample is to assume non-parallel orientation between the easy axis and the field directions and to investigate the angular dependence of hysteresis loops. The results presented in Fig. S10 show that the hysteresis loops are almost squared for all orientations and the heating is larger than the experimentally observed even for fields applied at 45 degrees to the anisotropy axis. Quantitative comparison of the heating efficiencies is made possible after considering a linear response of the hysteresis loops with the applied frequency. This is shown in Figure S11 that reproduces main text Figure 7 except for sample F03. The simulation clearly overestimates the experimental measurements in this sample.

S4. TRIAL MODEL MODIFICATIONS
To check whether some key ingredient might be missing in the assumed model, some alternative possibilities were tested, mainly related to including surface anisotropies (at the outer layer of the shell, and/or at the interfaces), changing the character of the separating interlayer (to nonmagnetic), or including dynamical effects (results not shown). The results are summarized in the following figures. Figure S12. Same results as shown in Figure S11, but considering a perpendicular surface anisotropy on the outer layer of the shell, of magnitude 100 times larger than that of the shell.  None of the above offers a better agreement between theory and experiment. Including other modifications as e.g. different perpendicular surface anisotropies either at the outer surface of the shell, and/or at the interfaces, always resulted in a worse comparison with the experiment. The same occurs in general with other modifications as e.g. change in the average shell crystallites sizes, or including a crystalline structure in the core. Finally, it is also worth to mention that preliminary results (not shown) indicated that neither thermal fluctuations (at room temperature) or dynamical effects lower the SAR estimation for sample F03 sufficiently to render it comparable with the experimental value.

S5. ROLE OF PARTICLE-PARTICLE DIPOLAR COUPLING ON HEATING PERFORMANCE OF SAMPLE F03
More complicated issues arise in the presence of dipolar interactions in assemblies of nanoparticles, 4 existing a coupling between the dipolar interaction field direction and the alignment of the nanocrystal easy axes . 5 We refer the reader to our former papers, 6,7 for an insight into the effects of nanoparticle aggregation on the heating properties.
Here we have tentatively explored the influence of interparticle dipolar interactions on the heating performance of sample F03. In Figure S15 we consider the effect of a non-switchable particle (i.e. with easy axis closely aligned with the external AC field) that creates a fixed bias field for another switchable nanoparticle situated in a close vicinity. An ensemble of nanoparticles arranged in dimers was considered. Obviously, the strength of the bias field is proportional to the interparticle distance and their relative magnetisation orientations. The results indicate a strong decrease of the heating performance with increasing interparticle coupling, thus supporting the interpretation in terms of magnetic interactions in this sample. The effect is enhanced for interparticle distances smaller than twice the particle diameter, which closely matches the experimental data in the main text Figure 4, measured by calorimetry. Figure S15. SAR values of a F03 particle under the effect of another similar non-switching particle that creates a local bias field, of the strength which depends on the interparticle distances (x-axis, in units of the total diameter of a F03 particle) and arrangements: parallel-aligned particles (0 degrees), at 30 or 60 degrees, as illustrated by the sketches. The green line stands for the weighted average; horizontal blue thick line indicates the experimentally measured SAR, and the dashed red square reproduces the value from the main text Figure 4.