## 2 Structures, Synthesis, and Magnetic Properties of Fe\({}_{3}\)O\({}_{4}\) Nanoparticles
### Fe\({}_{3}\)O\({}_{4}\) Cubic Nanoparticles (CNPs)  
Fe\({}_{3}\)O\({}_{4}\) cubic nanoparticles (CNPs) exhibit either superparamagnetic or ferromagnetic behaviors at room temperature, depending on the size of the NPs and the synthetic methods. However, the preparation of cubic magnetite nanocrystals seems to be more challenging than the preparation of spherical NPs. With the nature of a cubic crystal structure, Fe\({}_{3}\)O\({}_{4}\) tends to undergo isotropic growth that easily results in spherical particles. Several studies demonstrated that CNPs possess better crystallinity and stronger magnetic properties than their spherical counterparts with equivalent sizes [41; 42; 71]. Due to the challenge of maintaining dominant growth along \(<\)11\(>\) surfaces, only a limited number of synthetic methods are available for the preparation of CNPs with sizes ranging from approximately 10 to 180 nm [49; 50; 72]. The available synthetic methods, size control factors, and magnetic properties of the corresponding Fe\({}_{3}\)O\({}_{4}\) CNPs are summarized in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Diameter** & **Precursor and** & **Solvent** & **Size Control** & **Grain Size** & **M\({}_{\mathbf{S}}\) (emu/g)** & **H\({}_{\mathbf{C}}\) (Oe)** & **[Ref.]** \\
**(nm)** & **Reagents** & **Solvent** & **Factor** & **(nm)** & **M\({}_{\mathbf{S}}\) (emu/g)** & **H\({}_{\mathbf{C}}\) (Oe)** & **[Ref.]** \\ \hline
100, 135, 150, 175, 275 & FeCl3\({}_{3}\)\(\cdot\)6H\({}_{2}\)O, NaAc, PVP & EG & Rxn time & 17, 17, 15, 12, 11 & 69, 72, 65, 32, 11 & 106, 42, 66, 21, 28 & [42] \\ \hline
120, 440, 700 & FeCl3\({}_{3}\)\(\cdot\)6H\({}_{2}\)O, NaAc, PEG & EG, DEG & Solvent composition, FeCl3\({}_{3}\) & 18, 17, 17 & 78, 84, 87 & 62, 73, 72 & [43] \\ \hline \hline \multicolumn{8}{c}{UN denotes unknown, as the information was not provided in the literature. SPM denotes superparamagnetic, H\({}_{\mathbf{C}}\) = M\({}_{\mathbf{R}}\) = 0 (at RT). Values in italics indicate that the data were estimated from figures provided in the referenced articles.} \\ \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Edge (nm)** & **Precursor and Reagents** & **Solvent(s)** & **Size Control** & **M\({}_{\mathbf{S}}\) (emu/g)** & **H\({}_{\mathbf{C}}\) (Oe)** & **Ref.** \\ \hline
9.3, 13.4, 15.5, 22.1 & Fe(oleate)\({}_{3}\) Sodium oleate & Octadecene, diphenyl ether, n-tetracosane & Surfactant, Temperature & UN & SPM & [73] \\ \hline
6.5 & Fe(acac)\({}_{3}\) & & & 39.5 & SPM & \\
15 & 1,2-hexadecandiol 30 & Benzyl ether & Heat rate, Reaction time & 80.5 & SPM & [49] \\  & Oleic acid, Oleylamine & & & 83.0 & 100 Oe & \\ \hline
22 & Fe(acac)\({}_{3}\) & & & 152 & 17 & \\
79 & Oleic acid & Benzyl ether & Reaction time, Ligand & 144 & _88_ & [50] \\  & & & & emu/g(Fe) & _115_ & \\ \hline
13 & & & & 54.7 & SPM & \\
45 & & & & 89.9 & \(\approx\)_50_ & \\
67 & Fe(acac)\({}_{3}\) & & & 89.0 & UN & [72] \\
100 & Decanoic acid & Benzyl ether & Ramping rate & 92.8 & UN & \\
124 & & & & 86.0 & UN & \\
180 & & & & 81.9 & \(\approx\)_50_ & \\ \hline
12 & & & & & UN & \\
19 & Fe(acac)\({}_{3}\) & Benzyl ether & Degas temperature, Ramping rate & 80 & UN & [52] \\
25 & Decanoic acid & Benzyl ether & Ramping rate & UN & UN & \\
38 & & & & & UN & \\ \hline
14, 19, 24, 35 & Fe(acac)\({}_{3}\) & Benzyl ether & Ramping rate, Solvent composition & 64, 73, 75, 88 & 26, 28, 7, 23 & [44] \\ \hline
22, 36, 57 & Fe(acac)\({}_{3}\) & & & & & \\ Mg(acetate)\({}_{2}\) Sodium oleate & Benzyl ether & Sodium oleate & UN & UN & [58] \\  & Oleic acid & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Syntheses of Fe\({}_{3}\)O\({}_{4}\) nanocubes and their magnetic properties. [PERSON] and coworkers performed the thermal decomposition of iron(III) oleate in the presence of a sodium oleate surfactant to prepare superparamagnetic cubic Fe\({}_{3}\)O\({}_{4}\) with edge dimensions of 9.3, 13.4, 15.5, and 22.1 nm [73]. Similarly, [PERSON] et al.