# Magnetic Vortex and Hyperthermia Suppression in Multigrain Iron Oxide Nanorings
## 3 Results and Discussion
We have established the TS method as a precise tool for investigating the anisotropic magnetic properties of a variety of systems, single crystals, thin films, and nanoparticles [48; 49; 50; 51]. For a Stoner-Wohlfarth particle with its magnetic hard axis aligned parallel to the DC field, TS spectra should display peaks at the anisotropy fields (\(\pm H_{\rm K}\)) and switching fields (\(\pm H_{\rm S}\)) as the DC field is swept from positive to negative saturation [52]. Figure 3: **(a)** Magnetic hysteresis loops of the multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after different hydrothermal reaction times, measured at 300 K. **(b)** Representative bipolar transverse susceptibility (TS) curves taken at 300 K for multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after 8 h of reaction. Inset of **(a)** shows the low-field region of the hysteresis loops. Bipolar TS curves taken at 300 K for multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after 8 h reaction are displayed in Figure 3b. We obtained no variation in the \(H_{\text{K}}\) values for multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after different hydrothermal reaction time of 3, 5, 8, and 12 h, so we have presented the results for multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after 8 h of reaction. We have noted that for the Fe\({}_{3}\)O\({}_{4}\) nanorings, the switching peak was merged with the anisotropic peak, resulting in a difference in the positive and negative \(H_{\text{K}}\) values, along with a slight difference in the peak height (Figure 3b). Here, we have used a positive \(H_{\text{K}}\) value. The presence of distinct \(H_{\text{K}}\) peaks at 300 K in the TS spectra indicates high effective anisotropy in the Fe\({}_{3}\)O\({}_{4}\) nanorings. In nanoparticles, the thermal fluctuations dominate anisotropy energy at room temperature; thus, sustaining magnetic anisotropy at room temperature in nanostructures is challenging [53]. The value of effective \(H_{\text{K}}\) at 300 K for multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings after 8 h reaction was found to be 440 Oe, which is higher than the \(H_{\text{C}}\) value of 140 Oe. The effective magnetic anisotropy, \(H_{\text{K}}\), roughly corresponds to the coercive field in the non-interacting system of nanoparticles. The higher value of \(H_{\text{K}}\) of multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings compared to \(H_{\text{C}}\) could be due to the strong intra- and inter-nanoring interactions. Our recent reported works have revealed that the heating efficiency of magnetic nanostructures can be enhanced by increasing the saturation magnetization (\(M_{\text{S}}\)) or the shape and magnetic anisotropy (\(H_{\text{K}}\)) of the nanostructures [27; 28]. To estimate the heating efficiency (SAR) of the multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings, the SAR values were calculated using both calorimetric and dynamic hysteresis loop measurements. For calorimetric measurements, the heating curves as a function of time were recorded for all the multigrain Fe\({}_{3}\)O\({}_{4}\) nanorings at a concentration of 1 mg/mL, both in water and agar (random and aligned). By dispersing the nanorings in a 2% weight agar solution, we constrained the Brownian motion of the nanorings using the higher viscosity of 2% weight agar solution, and also fixed their orientation. A 2% weight agar solution also imitates the characteristics of the cell cytoplasm and extra cellular matrix, which is critical for in vivo testing of magnetic hyperthermia [54]. The heating efficiency of the nanorings was calculated using the initial slope method. In this method, the SAR of the nanoparticles can be calculated using the following equation:  
\[\text{SAR}=\ \frac{\Delta T}{\Delta t}\ \frac{C_{p}}{|\varphi} \tag{1}\]  
where \(\frac{\Delta T}{\Delta t}\) represents the initial slope of the heating curves, \(C_{p}\) is the specific heat capacity of the liquid medium (4.186 J/g \({}^{\circ}\)C for water), and \(\varphi\) is the mass of magnetic material per unit mass of liquid.