## 1 Introduction  
Magnetic nanoparticles have drawn large interest due to their applications in the field of magnetic recording and other areas [1, 2]. The unique magnetic behaviour exposed these materials to a very wide range of medical applications such as drug delivery systems [3], magnetic resonance imaging (MRI) [4, 5, 6, 7], and for cancer therapy [8]. Due to several factors [5, 6], the superparamagnetic iron oxide nanoparticles (SPIONs) such as magnetite (Fe\({}_{3}\)O\({}_{4}\)) and maghemite (\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)) are being studied extensively for medical field applications. The magnetic nanoparticles exhibit interesting magnetic behavior due to finite size effects such as high surface-to-volume ratio, and different crystal structures. When the size of the particle decreases, the surface to volume ratio increases causing a large portion of the atoms to be at the surface compared to those in the core of the particle. This large surface to volume ratio changes the physical, chemical, and mechanical properties compared to those of the bulk materials. The magnetic nanoparticles are assumed to be a single domain particle with uniaxial anisotropy where the orientation of its magnetic moment points \"up\" or \"down\" in a zero field along the easy axis. Below a critical size, the magnetic nanoparticles become a single magnetic domain and retain a superparamagnetic behavior as long as the temperature is above the blocking temperature. In the superparamagnetic state, the magnetization vectors of the nanoparticles fluctuate along the easy axis of magnetization, inducing a large magnetic moment in each nanoparticle. These magnetic moments continuously change their orientations. When a magnetic field is applied externally, superparamagnetic particles exhibit a fast response to changes of magnetic field with zero remnant magnetization and zero coercivity. Thus, in the superparamagnetic region, a magnetic nanoparticle behaves as a large paramagnetic atom. In case of a temperature below the blocking temperature (\(T_{\text{B}}\)), the thermal agitation will not be large enough to cause fluctuations in the magnetic moments of the nanoparticles where they freeze in random orientations very similar to the ferromagnetic state. However, the surface atoms experience a different environment than those on the core of the particle. The surface magnetization is controlled by several parameters such as atomic vacancies, change in atomic coordination, dangling bonds, and lattice disorder [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. These parameters result in disordered surface spins. The magnetic nanoparticles assembly exhibit hysteresis for \(T<T_{\text{B}}\) and a non-hysteric behavior for \(T>T_{\text{B}}\). The magnetic behavior for the monodispersed and non-interacting single domain magnetic particles can be explained on the basis of Neel relaxation and the Bean-Livingston approaches. Saturation magnetization (\(M_{\text{S}}\)), decreases with the cube root of temperature, which is called Bloch's law. One important application of magnetic nanoparticles is magnetic hyperthermia, where the living organ can be heated to a temperature large enough to destroy tumor cells while not affecting healthy ones [6]. This heating process can be achieved by inserting magnetic nanoparticles in the cells and exposing them to an alternating magnetic field. The amount of heat generated by heating the nanoparticles depends on several factors [6]. Most models that are used to understand the heating process are based on [PERSON]'s theory [22] where, as an approximation, the saturation magnetization is considered to be constant with temperature. However, it is well-established that the saturation magnetization of nanoparticles changes significantly with temperature [23; 24; 25; 26; 27; 28]. Core/shell nanoparticles can provide a mechanism of tuning the magnetization of nanoparticles by controlling the core and shell sizes and phases.