## 1 Introduction  
In medical sciences, magnetic nanoparticles can be applied in diagnostics and medical therapy [1]. As contrast agents in medical imaging, they can improve the quality of imaging and the sensitivity of diagnostic methods, such as magnetic resonance imaging (MRI) [2, 3, 4, 5, 6]. In magnetic hyperthermia, magnetic nanoparticles are used to support the destruction of cancer cells caused by heating [5, 7, 8]. However, their application as drug carriers seems to be the most promising [9, 10, 2]. The magnetic properties of such nanocarites facilitate their targeting to the desired site and limit damage to healthy cells [10]. It also provides an opportunity to increase the effectiveness of treatment while reducing the therapeutic drug dose. All of the applications mentioned above result from the magnetic properties of nanoparticles, their biocompatibility, and sample stability. However, their potential toxicity to the body remains a challenge [10, 11]. Targeted drug delivery, mostly promising in cancer treatment, by magnetic nanoplatforms is related to their interactions at the cellular level, i.e., attachment to the cell, the process of entering it, and its further behavior in the cell [12]. The methods currently used for analyzing interactions at the cell level include flow cytometry, different types of microscopy, and mass spectrometry [13, 14, 15]. However, these methods have significant limitations, and their applicability is related to specific particles and sensitivity, resolution, and availability, related to technical requirements. Alternatively, [PERSON] proposed using electron spin resonance (ESR) spectroscopy to monitor the endocytosis of nanomaterials functionalized with spin labels into cells [16, 17]. Reactive oxygen species (ROS) are constantly produced in cells, and mitochondria are considered their primary endogenous source [18]. Based on the qualitative and quantitative changes in ESR signals from free radicals, the uptake of nanoparticles functionalized with spin labels in cells can be tracked. ESR is a suitable and direct method for studying materials with unpaired electrons, including free radicals [19, 20]. In general, after placing the sample in a magnetic field, the Zeeman effect occurs, which involves splitting the energy levels of the unpaired electron. If the resonance condition is met and an appropriate quantum of radiation with energy corresponding to the energy difference between these levels is supplied to the system, the ESR phenomenon will be registered as the first derivative of the absorption signal [19; 20; 21]. It has been successfully applied in various studies, including those investigating the properties of magnetic nanoparticles [22; 23; 24; 25; 26; 27], iron complexes and free radicals in blood and tissues [28; 29; 30; 31; 32; 33; 34; 35], as well as geological and archaeological materials [36; 37; 38; 39]. ESR studies confirm the penetration of nanoparticles into cells and facilitate monitoring of this whole process. Additionally, magnetic nanoparticles with attached spin labels (TEMPO or TEMPOL), as potential antioxidant agents, have been investigated for their possible use in treating inflammatory diseases, as radioprotectors in radiotherapy, and scavengers of free radicals in cells [17; 32; 40; 41]. As standard, both TEMPO and TEMPOL are used as spin probes in ESR studies [18; 42] due to the presence of stable unpaired electrons. They are applied in biological and medical research with cells and membranes. Because of the possibility of reaction with free radicals, including ROS, they are also studied as potential antioxidants and oxidative stress-reducing agents. For example, [PERSON] et al. [42] studied the influence of TEMPO on yeast cells, considering their physiology, aging, and gene expression changes. Its antioxidant properties were checked by various methods without ESR. On the other hand, [PERSON]'s group [18; 41; 43] used TEMPO and TEMPOL in micelle-type nanoparticles for disease treatment, including chemo- and radiotherapy of cancer.