## 1 Introduction  
Since nanotechnology have been rapidly developed in recent decades, nanomaterials with high performances attract a lot of attentions in various applications. Recently, hollow nanoparticles (NPs) are synthesized successfully for practical application, such as catalysis, lithium ion battery and biomedicine because the large surface area and hollow/porous structures are facilitated to loading more drugs or increasing more active reaction sites. Especially, the hollow magnetic (Fe\({}_{3}\)O\({}_{4}\)) NPs show more potentiality in multi-functional application, including fundamental size-dependent magnetism/optoelectronics and targeted drug delivery application due to their low toxicity [1; 2; 3; 4; 5]. Various methods, including hard template method [6; 7; 8], soft template method [9], free template method [10; 11] and sacrificial template method [12; 13; 14; 15] are employed for synthesis of hollow iron oxide NPs. In particular, as for the hard template method, the greatest merit of it is that the grain size of the hollow structure is controllable. However, these steps are cumbersome and the hollow NPs are easy to collapse after removing the template. Comparatively, the soft template method is a low-cost technique for synthesis of hollow Fe\({}_{3}\)O\({}_{4}\). However, the large particle size could restrict its practical application. Moreover, hollow Fe\({}_{3}\)O\({}_{4}\) with small size could be precisely synthesized by sacrificial template method. Nanoscale Kirkendall effect is a typical mechanism for explaining the formation of hollow Fe\({}_{3}\)O\({}_{4}\), which could be exploited and extended for synthesis with metal-containing starting materials. Additionally, the free template method is a common method for preparing the hollow nanostructure, it is easy to operate and to prepare the NPs with uniform size distribution [16; 17; 18]. This method could also be used for synthesis of hollow/mesoporous Fe\({}_{3}\)O\({}_{4}\) NPs. But the disadvantage of this method is that the hollow diameter cannot be precisely controlled by artificial regulation. Hydrothermal route is a typical free template method, and during hydrothermal process, the iron oxide nanoparticle with different morphology and particle sizes could be synthesized by changing the structure direct agents [19; 20; 21; 22]. For example, [PERSON] and co-workers [23] prepared a variety of hollow magnetic NPs by a simple hydrothermal method. Ethylene glycol was used as solvent and reducing agent, and a variety of ammonium salts were added as structure-directing agent for synthesis of the hollow Fe\({}_{3}\)O\({}_{4}\) NPs with various morphologies. Moreover, in our previous work [24; 25], the monodisperse Fe\({}_{3}\)O\({}_{4}\) hollow/mesoporous spheres were synthesized by using ammonium acetate (NH\({}_{4}\)Ac) and ammonium bicarbonate (NH\({}_{4}\)HCO\({}_{3}\)) as a structural guide agent. The produced NH\({}_{3}\) and CO\({}_{2}\) bubbles could be responsible for hollow and mesoporous formation, respectively. After regulating the ratio of NH\({}_{4}\)Ac and NH\({}_{4}\)HCO\({}_{3}\), the Fe\({}_{3}\)O\({}_{4}\) NPs with different morphologies were obtained correspondingly. However, as most literatures reported, the particle-sizes of hollow Fe\({}_{3}\)O\({}_{4}\) NPs are always larger than 200 nm via hydrothermal method, and the intensity of saturation magnetization (\(M_{s}\)) is not satisfied for targeting applications. As a result, an alternative method to fabricate size-controllable magnetite NPs with hollow/mesoporous structure remains as a currently lasting challenge. Herein, hollow/mesoporous Fe\({}_{3}\)O\({}_{4}\) NPs with different particle-sizes are synthesized by facile hydrothermal method.