## 2 Materials and Methods  
Co\({}_{\mathrm{x}}\)(MgF\({}_{2}\))\({}_{100\times\mathrm{x}}\) nanocomposite films with different contents of metallic cobalt (Co) in the MgF\({}_{2}\) dielectric matrix were obtained on glass substrates via ion-beam sputtering [17]. Film deposition was conducted in a vacuum chamber (10\({}^{-6}\) Torr) filled with Ar (purity 99.992%) up to a total gas pressure of 8 \(\times\) 10\({}^{-4}\) Torr. A magnetic system consisting of permanent magnets, a magnetic circuit, and an anode was used as a source of ion-beam sputtering. Argon ionization was carried out in the magnet gap in the immediate vicinity of the anode. A high magnetic field strength (80 kA/m) was created in this magnet gap. In turn, a positive bias (4 kV) was applied to the anode. The perpendicular configuration of the magnetic and electric fields in the area of the magnetic gap led to the emergence of an independent glow discharge. Under the action of an electric field, Ar+ was ejected from the plasma, creating a high-energy ion beam, which was directed at the target. The optimal plasma current was \(\sim\)170 uA. This mode ensured a deposition rate of nanocomposite films of \(\sim\)1.5 um/h.  
The crystal structures of the Co\({}_{\mathrm{x}}\)(MgF\({}_{2}\))\({}_{100\times\mathrm{x}}\) nanocomposites were determined on a diffractometer using CoK\(\alpha\) radiation (DRON 4-07). Samples were collected at an accelerating voltage of 29 kV in the X-ray tube with an anode current of 26 mA. The intensity of the scattered X-rays was recorded in continuous scanning mode with a detector rotation speed of 1 deg./min. in the angle range 2\(\Theta\) (10-100\({}^{\circ}\)) according to the Bragg-Brentano geometry. The phase composition was determined using the International Center for Diffraction Data's PDF Release 2012 (ICDD).  
The Co concentration in atomic % and the thicknesses of film composites were determined using electron probe X-ray spectral microanalysis on an attachment to a JEOL JSM-6380 LV scanning electron microscope (Japan) with an error not exceeding 1.5% of the content of the measured element at beam energies of 5 keV.  
The tunneling magnetoresistance effect was studied using the four-probe method on an ECOPIA HMS-3000 instrument. The maximum value of the voltage was 10 volts. The device package included a certified magnetic attachment with a magnetic induction of B = 5.5 kG.  
The impedance of the investigated samples was measured by applying alternative signals using an Elins Z-1500] impedance meter. These studies were carried out at room temperature in the frequency range from 1 mHz to 3 MHz. The amplitude of the alternating measuring signal did not exceed 100 mV. The measurement error did not exceed 5%. The analysis of the impedance spectra was carried out within the framework of a model of serially connected parallel equivalent circuits using the procedure for processing experimental data with modern software.  
To study the magnetic properties of nanocomposites, we used an automated Lake Shore 7404 VSM vibrating magnetometer with a sensitivity of 10\({}^{-5}\)-10\({}^{-7}\) C\({}^{\circ}\)cm\({}^{3}\). Studies of the magneto-optical response were carried out on an automated magneto-optical spectrometer in the incident light energy range E from 0.5 to 4 eV at room temperature. The amplitude of the applied alternating magnetic field reached 3 kOe. An important feature of this method is the study of the equatorial Kerr effect when the object is in a variable magnetic field. This method has very high accuracy relative to the intensity of light (up to 10\({}^{-5}\)).