## 1 Introduction  
In recent years, spinel ferrites have attracted much attention from researchers due to their versatile magnetic properties and wide range of applications. Nanosized ferrites have shown enhanced optical and magnetic properties compared to their bulk counterpart because of better magnetic coupling between the sub-lattices (tetrahedral (Td) or octahedral (Oh)) [1]. Due to improved properties,the nanosized ferrites have been used for a broad range of applications, including: Fundamental research into industrial (sensors, refrigeration, transformers, electrical devices, disk recording, etc.) and medical applications (drug delivery, MRI (magnetic resonance imaging) technology separation, cancer therapy, biosensing, etc.) [2; 3; 4; 5; 6; 7; 8; 9; 10]. Ferrites are also most frequently used as magnetic absorbing materials owing to their cost effectiveness, excellent magnetic loss, and good stability [8]. Another advantage of nanosized spinel ferrites is that one can tune the magnetic properties by optimizing the size of the nanoparticles. A general structure of spinel ferrites is MFe\({}_{2}\)O\({}_{4}\) (M = manganese, cobalt, zinc, magnesium, etc., Co, Zn, Mg, etc.). In this crystalline structure, anions (oxygen) form face-centered cubic arrangements and metal cations (M\({}^{2+}\) and Fe\({}^{3+}\)) occupy either Td or Oh interstitial sites [11]. From the available ferrites, manganese-based ferrites (MnFe\({}_{2}\)O\({}_{4}\)) are considered as more significant because of their high Ms (saturation magnetization) and low loss of power at high frequencies [12]. Manganese ferrites are widely studied owing to their wide range of applications, such as in microwave industries, protecting the barrier against the harm of microwave, satellite communication, microwave dark room, etc. [13]. Furthermore, nanosized ferrites can provide better communication at high frequencies (10 kHz to a few MHz) with great stability because of their high electrical resistivity [13; 14]. Recently, Co-Zn-substituted spinel-type ferrites have been studied and found attractive for bio-medical applications because of their suitable room temperature magnetic properties [15; 16]. Spinel ferrites have also multiferroic applications. Multiferroic nanostructures have attracted lots of attention by researchers due to their unique benefits compared with bulk multiferroics. The interface between the piezoelectric phase and the ferromagnetic phase is well established and leads to a high magnetoelectric coupling effect by reducing the coupling loss [17; 18]. Nanoparticles (NPs) possessed tremendous biological applications [19; 20; 21; 22; 23] as they have a dimension of less than 100 nm. There are various types of NPs, like metallic NPs, ceramic NPs, and polymeric NPs, and this classification is based on their size, shape, and property [19; 23; 24]. Over the past few years, metallic nanoparticles (MNPs) have been used in the field of medicine and pharmaceutical sciences [22; 24]. There are many approaches, which have been developed to synthesize diverse and customized MNPs that can be used in experimental medicine, drug design, drug delivery, electrical and electronic engineering, electrochemical sensors, and biochemical sensors [23; 24]. There has been an enormous increase in the rate of cancer occurrence around the world, and due to the non-availability of robust treatment, the rate of cancer morality has also been increasing. In this background, there is the need for an alternative approach to tackle this issue. MNPs possess better capabilities to treat the cancer as MNPs have an enhanced reactive surface area, which improves the therapeutic efficacy of the treatment. To the best of our knowledge, Mn\({}_{0.5}\)Zn\({}_{0.5}\)Eu\({}_{x}\)Sm\({}_{x}\)Fe\({}_{1.5-2x}\)O\({}_{4}\) (0.01 \(\leq\) x \(\leq\) 0.05) NPs have been synthesized (hydrothermally) and characterized, and its cytotoxicity and antibacterial activity was studied for the first time in this study.