## Materials and Methods  
Iron oxide nanoparticles were synthesized by soft chemistry methods, according to the so-called \"Massart\" pathway through the nanoprecipitation of Fe(II) and Fe(III) ions in a basic medium (VWR, Fontenay-sous-Bois, France), followed by an oxidation of the magnetite into maghemite [12]. Nanoparticles had a mean diameter of 7 nm and a polydispersity following a lognormal law of 0.4. An already published size sorting process was applied to the sample to obtain 10.6 \(\pm\) 6.2 nm large nanoparticles with a narrower size polydispersity [13]. The principle is based on the phase separation of the particles by tuning the balance between attractive (magnetic attraction together with Van Der Waals) and repulsive (surface charges) forces that are governed by the size of the particles. Nitric acid (playing the role of a salt) is added in a controlled manner to induce a phase separation between concentrated droplets containing the largest particles and the main phase containing the smallest particles. Typically, 5 mL of HNO\({}_{3}\) at 8.3 mol\(\cdot\)L\({}^{-1}\) (VWR, Fontenay-sous-Bois, France) was added to 1 L of ferrofluid. The beaker was placed on a magnet and the supernatant (S) was removed. The precipitate phase (C) was washed with acetone (three folds) and diethyl ether (three folds) and redispersed in distilled water. HNO\({}_{3}\) was added to the supernatant and the same process was repeated until the final supernatant remained clear from nanoparticles. Cerium oxide nanoparticles were also synthesized by a soft chemistry process using cerium nitrate solution in a basic medium [14]. Cerium oxide nanoparticles were used as-synthesized without further size sorting. Their mean diameter corresponded to 7.8 \(\pm\) 5.2 nm. Both particle types were coated with poly(acrylic acid) polymers with molecular weight of 2100 g/mol (denoted PAA in the rest of the document, Sigma Aldrich, Darmstadt, Germany) to ensure a good colloidal stability as well as to introduce a large amount of negative charges for the following electrostatic interaction with the positive polyelectrolyte [15]. Figure 1 represents the transmission electron microscope (TEM) images of PAA-CeO\({}_{2}\) and PAA-Fe\({}_{2}\)O\({}_{3}\) nanoparticles and their size distribution with a Gaussian fit. Additionally, PAA-CeO\({}_{2}\) and PAA-Fe\({}_{2}\)O\({}_{3}\) particles were dialyzed to remove the residual free PAA chains put in excess during the coating to ensure a complete coating of both iron oxide and cerium oxide nanoparticles. Poly(trimethylammonium)acrylate)-b-poly(acrylamide) block copolymers were synthesized by Madix(r) controlled radical polymerization [16]. The copolymer was abbreviated PTEA\({}_{11\text{K}}\)-b-PAM\({}_{30\text{K}}\), where the indices indicate the molecular weights targeted by the synthesis. The role of the poly(acrylamide) block is preponderant because it will ensure a steric repulsion between aggregates, thus allowing a good colloidal and structural stability against sedimentation that is mandatory to obtain highly concentrated samples for hyperthermia evaluation. Dispersion of PAA-CeO\({}_{2}\), PAA-Fe\({}_{2}\)O\({}_{3}\), and PTEA\({}_{11\text{K}}\)-b-PAM\({}_{30\text{K}}\) copolymer solution were prepared at 0.5 wt % and with 0.5 M NH\({}_{4}\)Cl. We varied the proportion \(r\) of Fe\({}_{2}\)O\({}_{3}\)/CeO\({}_{2}\) from 1.5 to 0.17 and always kept the ratio of nanoparticles/polymer equal to 0.5 to ensure an excess of the complexingPTEA\({}_{11\text{K}}\)-b-PAM\({}_{30\text{K}}\). Results obtained with a mixture of both particles were compared to iron oxide nanoparticles only, aggregated with the same pathway. As demonstrated in our previous work, a dilution from 0.5 M NH\({}_{4}\)Cl to 0.1 M NH\({}_{4}\)Cl allowed for the formation of aggregates [17; 18; 19]. Samples were centrifuged and the supernatant was eliminated to access a higher concentration of iron oxide nanoparticles in the final samples in the range of 0.1-0.5 wt % to ensure a measurable temperature increase during hyperthermia analysis.