## 1 Introduction  
Spinel ferrite nanoparticles such as NiZn, MnZn have gained much attention for several applications [1; 2; 3; 4; 5], including high frequency circuits, the cores of radiofrequency (RF) transformers, inductors, antennas and radar absorbing materials, based on their high resistivity and low loss at high frequency. They also have great potential as an efficient catalysts and/or catalyst supports for decomposing organic or inorganic pollutants [6; 7]. NiZn ferrite nanoparticles are becoming more and more important in the field of bio-medical applications for instance magnetic resonance imaging (MRI), drug delivery systems and hyperthermia treatment of cancer by using their appropriate magnetic properties, antimicrobial activity and biological compatibility [8; 9]. Figure 1 shows the spinel structure (the lattice parameter is about 0.84 nm) is formed by 24 cations (Fe\({}^{2+}\), Zn\({}^{2+}\), Co\({}^{2+}\), Mn\({}^{2+}\), Ni\({}^{2+}\), Mg\({}^{2+}\), Fe\({}^{2+}\), Gd\({}^{2+}\)) and 32 O\({}^{2-}\) anions and generally has a chemical form of AB\({}_{2}\)O\({}_{4}\), which is designated as a cubic closed-packing of O\({}^{2-}\) ions [10; 11; 12; 13]. The round and  
the square brackets represent the tetrahedral interstitial A site and the larger octahedral interstitial B site, respectively. Zinc ferrite is called a normal spinel structure of the form ZnFe\({}_{2}\)O\({}_{4}\), where Zn\({}^{2+}\) ions occupy the tetrahedral sites and Fe\({}^{3+}\) ions occupy the octahedral sites [13]. Nickel ferrite is called an inverse spinel structure of the form FeNiFeO\({}_{4}\), where Ni\({}^{2+}\) ions occupy the octahedral sites, and half the Fe\({}^{3+}\) ions occupy the tetrahedral sites and the other half occupy the octahedral sites [10]. NiZn ferrite is a kind of solid solution composed of Ni ferrite and Zn ferrite, which can be expressed as the form Zn\({}_{x}\)Fe\({}_{(1-x)}\)Ni\({}_{(1-x)}\)Fe\({}_{(1+x)}\)O\({}_{4}\). The magnetic properties of the NiZn ferrite are strongly dependent on the number of 3d unpaired electrons of transition metals. The Zn\({}^{2+}\) ions do not have any unpaired electrons (or Bohr magneton) in the 3d orbital, while Ni\({}^{2+}\) ions have two unpaired electrons and Fe\({}^{3+}\) ions have five unpaired electrons in the 3d orbital. Therefore, the appropriate loading of the Ni\({}^{2+}\) ion, which has unpaired electrons into the crystal structure of ZnFe\({}_{2}\)O\({}_{4}\) provides much better magnetic properties, e.g., higher saturation magnetization (M\({}_{\text{s}}\)) and lower coercivity (H\({}_{\text{c}}\)) [14; 15] because an addition of transition metal ions leads to the movement of some Fe\({}^{3+}\) ions from the octahedral sites to the tetrahedral sites, and the unequal of Fe\({}^{3+}\) ions in both lattice sites effectively produce the remainder of unpaired electrons, which generate and increase the magnetism [16]. In general, with a reduction in particle size, the coercive force gradually increases until it reaches the maximum value, but if the size of the particle is reduced to a critical size, the thermal effect becomes even more intense and produces super paramagnetic characteristics in which each particle becomes a single domain with not only very low magnetic loss but also very high magnetic permeability [17; 18]. Moreover, the superparamagnetic particles have a zero coercive force and high magnetization, so the control of the particle size is very important because the properties of the nanocrystals strongly depend upon that. Properties of NiZn ferrite nanoparticles are greatly sensitive to the synthesis method and its preparation conditions. There are many methods for the synthesis of ferrite nanoparticles, including sol-gel, co-precipitation, high energy ball milling and thermal decomposition [19; 20; 21; 22; 23]. Thermal decomposition method has more advantages than other methods in synthesizing uniform and fine-nanoparticles with a high crystallinity. Also, it is easy to control particle size and particle size distribution with this method [24; 25].