## 1 Introduction  
The reduction in the size of functional devices of modern electronics has led to a number of problems associated not only with technological limitations, but also with the fact that new physical phenomena that are characteristic of nanoscale objects begin to operate. When working with small electronic devices, quantum size effects become decisive. This also has its advantages, as opportunities arise in the development of subminiature transistors, memory cells, and magnetic and electric field sensors.  
One of the studied effects of nanosized objects is the effect of tunneling magnetoresistance in metal-dielectric composite films, which has been studied for several decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. It should be noted that systems based on cobalt have high values of the TMR effect [5, 6, 7, 8, 9, 10, 11].  
Various scientific groups have carried out studies evaluating the effect of self-organization on the magnetic properties of nanomaterials. The manifestation of properties in nanocomposites depends on the composition and concentration [12, 13, 14, 15, 16]. In this regard, the study of their structural, electrophysical, magnetic, and magneto-optical properties is of interest.  
In this case, the concept of the percolation threshold is introduced. The percolation threshold denotes the amount of the metal component at which a sharp change occurs in the resistance of the nanocomposite, changing its conductivity. It is the region of the percolation threshold that represents the most interesting range of studies. In nanocomposites with compositions near the percolation threshold, special physical properties such as tunneling magnetoresistance can be observed. The most effective and simplest method for obtainingsuch granular nanocomposites is the ion-plasma sputtering method. Iron, cobalt, nickel, and alloys of these elements are often used as the metal components of granular nanocomposites. Oxides of aluminum, silicon, magnesium, and titanium are often used as dielectric components. Unique alloys and compounds are used, but do not always give good results [17; 18; 19].  
Articles [20; 21; 22; 23; 24] present the results of studies on the influence of the formation of the structure of granular nanocomposites on the effect of tunneling magnetoresistance. Oxide and oxide-free matrices were used to obtain nanocomposites. The data obtained led us to conclude that the best characteristics in terms of the maximum value of magnetoresistance were demonstrated using oxide-free matrices.  
It is important to note that high TMR Co multilayer-based device technology requires high-vacuum deposition equipment. This is due to the need to obtain a high-quality interface between the metal-dielectric layers. In the case of manufacturing nanogranular composites, less expensive equipment is required [17].  
The purpose of this work was to perform a comprehensive study of the influence of the atomic composition and structural-phase state of Co\({}_{\mathrm{x}}\)(MgF\({}_{2}\))\({}_{100\times\mathrm{x}}\) nanocomposites on their nonlinear transport and magneto/magneto-optical properties. In this article, we link our previous studies of the phase composition and structure of granular Co\({}_{\mathrm{x}}\)(MgF\({}_{2}\))\({}_{100\times\mathrm{x}}\) nanocomposites [25] with their electrical and magnetic properties.