# Magnetic Vortex and Hyperthermia Suppression in Multigrain Iron Oxide Nanorings
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reaction** & **Crystallite** & **Outer Diameter** & **Inner to Outer** & **M\({}_{\rm S}\)** & **AR in Water at 800 Oe (W/g)** \\
**Time (h)** & **Size (nm)** & **(nm)** & **(g)** & **(emu/g)** & **(emu/g)** & **AR in Water at 800 Oe (W/g)** \\ \hline
3 & 15 & 100 & 0.5 & 52 & 150 & 155 \\
5 & 15 & 110 & 0.55 & 54 & 130 & 262 \\
8 & 17 & 110 & 0.5 & 55 & 140 & 342 \\
12 & 18 & 105 & 0.5 & 57 & 155 & 186 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Crystallite size, dimensions, magnetic parameters including saturation (\(M_{S}\)) and coercive field (\(H_{\rm C}\)), and specific absorption rate (SAR) at 300 K for Fe\({}_{3}\)O\({}_{4}\) nanorings. Figure 2: Representative bright-field TEM images of multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after hydrothermal reaction time: (**a,b**) 5 h, (**c**) 8 h, (**d**) 12 h. Inset of (**a**) shows a magnified view of the nanorings. the samples could be due to presence of defects, along with large intra- and inter-particles dipolar interaction of multigrain rings. The \(H_{\rm C}\) values of all the samples are almost the same. The shape of the loop and the presence of remanence and coercivity in the magnetic hysteresis (\(M\)-\(H\)) loops of multigrain Fe\({}_{3}\)O\({}_{4}\) nanoring samples indicate a typical soft ferromagnetic character. It has been shown that the single-crystalline Fe\({}_{3}\)O\({}_{4}\) nanoring samples with similar dimensions possess a shape-induced vortex-domain structure [35]. However, in the present case, we did not observe onion-vortex-onion or onion-to-onion structured ground states, despite the theoretical phase diagram suggesting the formation of a vortex-domain structure [37; 38; 39; 40; 41]. This result clearly indicates that the microstructure of rings play an important role in determining their magnetic ground state. Theoretically, it was predicted that even if the dimension of a nanorings falls in the vortex state in the ground state phase, it might get trapped in a metastable state because of defects or inter-particle distance [37; 38; 39; 40; 41]. The absence of a shape-induced vortex-domain structure in multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings could be related to these effects. The values of \(M_{\rm S}\) in the Fe\({}_{3}\)O\({}_{4}\) nanoring samples increased gradually with the increase in reaction time. The \(M_{\rm S}\) values are in the range of 55 emu/g for all the Fe\({}_{3}\)O\({}_{4}\) nanoring samples and are smaller than the theoretical magnetization value of bulk magnetite at room temperature (\(\sim\)92 emu/g). The small variation of the \(M_{\rm S}\) at 300 K with the change in hydrothermal reaction time can be attributed to the variation in size and crystalline quality of the nanorings. The zero-field-cooled (ZFC) magnetization vs. temperature curve for all the samples (not shown here) showed a sharp drop in magnetization below 120 K, which can be attributed to the Verwey transition linked with the metal insulator transition in Fe\({}_{3}\)O\({}_{4}\)[27; 28]. Due to poor crystalline quality, non-stoichiometric effect and defects, this transition--which is related to the crystal structure of Fe\({}_{3}\)O\({}_{4}\)--often gets suppressed in nanoparticles [46; 47]. The occurrence of the Verwey transition in the Fe\({}_{3}\)O\({}_{4}\) nanorings indicates the realization of high crystalline quality and single phase Fe\({}_{3}\)O\({}_{4}\) nanostructures. The occurrence of the Verwey transition confirms the high crystalline quality of the multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings. The high coercivity, the ring shape, and strong inter- and intra-particle interactions of the samples indicate the high effective magnetic anisotropy of the multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings. The estimation of the effective magnetic anisotropy of the Fe\({}_{3}\)O\({}_{4}\) nanorings was done using radio frequency (RF) transverse susceptibility (TS).