## 2 Materials and Methods  
We have synthesized iron oxide Fe\({}_{3}\)O\({}_{4}\)/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) core/shell nanoparticles through the usual co-precipitation method. The FeCl\({}_{3}\cdot\)6H\({}_{2}\)O (0.1 M) and FeCl\({}_{2}\cdot\)4H\({}_{2}\)O (0.05 M) were used as precursor materials. The precursor materials were dissolved in deionized water separately and mixed at room temperature after which ammonium hydroxide solution (25%) was slowly added until PH reached 10. The mixed solution was kept at 80 \({}^{\circ}\)C and the reaction was made to occur in atmospheric pressure. The reaction time was varied between 1 and 3 h to get different size nanoparticles (reaction times of 1, 2 and 3 h resulted in shell thicknesses of 1, 3 and 5 nm, respectively). The final precipitation was collected and dried at 120 \({}^{\circ}\)C in vacuum. There are two main parameters in our synthesis method, (1) the reaction time and (2) the diffusion time. The reaction time was varied to obtain different initial particle diameters. The atomic oxygen plays a major role inducing \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) phase. This is due to the direct logarithmic kinetic diffusion with a logarithmic relation between \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) thicknesses versus oxygen exposure time [36]. The diffusion was allowed to occur in an ambient atmosphere (in the presence of oxygen). In this way, the reaction mechanism which involves inward anionic diffusion is responsible for the occurrence of \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) phase at the core surface. The diffusion time was varied to obtain different \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) shell thicknesses. By trial and error, we have optimized these two parameters to obtain fixed core and different shell thicknesses. The larger the reaction time, the larger is the initial particle size. The larger the oxidation (diffusion) time, the larger is the oxidized layer (shell thickness). Thus, to obtain larger/smaller shell thickness, we started with larger/smaller particles (longer/shorter reaction times) and allowed for longer/shorter diffusion times. By optimizing these two parameters we were able to determine the suitable initial particle size for each diffusion time such that we obtained a fixed core for each case [37]. We found that when the reaction time is 1 h and the diffusion time is 1 h the core diameter is 8 nm and the shell thickness is 1 nm. When the reaction time is 2 h and the diffusion time is 2 h, the core diameter is 8 nm and the shell thickness is 3 nm. When the reaction time is 3 h and the diffusion time is 3 h, the core diameter is 8 nm and the shell thickness is 5 nm.  
The X-ray diffraction (XRD) analysis was conducted using a PANalytical X'Pert Pro (Almelo, The Netherlands) X-ray diffractometer. The morphology of the nanoparticles were confirmed by high resolution transmission electron microscopy (HRTEM), and selected area electron diffraction (SAED). The transmission electron microscopy (TEM) measurements were performed using an FEL, TECNAI G\({}^{2}\) F30, S-TWIN (GG Eindhoven, The Netherlands) microscope operating at 300 kV equipped with a GATAN Orius SC1000B CCD camera (GG Eindhoven, The Netherlands). A SQUID (San Diego, CA, USA) from Quantum Design, was used to conduct the magnetic measurements. Magnetic moment versus applied magnetic field up to \(\pm\)3 T was measured for all the samples at several temperatures (2, 10, 30, 50, 70 and 100 K) after cooling the samples in the zero-field cooled (ZFC) and field-cooled (FC) states. The samples with shell thicknesses of 1, 3 and 5 nm are named as S1, S2 and S3, respectively.