## 1 Introduction  
Inducing intrinsic magnetism in the nominally nonmagnetic carbon materials containing only s- and p-electrons is an intriguing yet challenging task [1]. The experimental discovery of magnetism in polymerized fullerenes [2] and in graphite irradiated with protons [3, 4] has stimulated numerous experimental and theoretical studies of the magnetic properties of pure carbon structures. Lightweight non-metallic magnetic carbon materials with a Curie point above room temperature are very promising for applications in medicine and biology as a unique biocompatible magnet [5] as well as in nanotechnology, telecommunications, and carbon electronics. The variety of chemical compounds of carbon is explained by the ability of its s- and p-electrons to form hybrid electronic orbitals in different proportions. The electronic subsystem of a cooperative system of carbon atoms is very labile and is characterized by many metastable states, while transitions from one state to another are possible (switching effects) even with the same fixed configuration of nuclei. The allotropy of carbon leads to the formation of pure carbon structures with a wide variety of and often opposite properties [6]. Therefore, it is not surprising that the main experimental successes towards obtaining pure carbon ferromagnets are associated with films or 2D objects with close proportions of sp\({}^{3}\) and sp\({}^{2}\) carbon, and high concentration of defects, including hydrogenated ones, in which hydrogen seems to play a stabilizing role, preventing the transition of sp\({}^{3}\) carbon to sp\({}^{2}\) carbon. Various synthesis methods have been tried to obtain magnetic carbon. The defect-induced magnetism in carbon materials (mainly ion-implanted diamonds) was studied experimentally and theoretically in [7; 8; 9; 10; 11; 12; 13; 14] etc. Two mutually consistent basic models dominated for a long time, explaining the manifestations of the magnetism of pure carbon materials--the \"amorphous\" one with variable sp\({}^{3}\)/sp\({}^{2}\)-carbon hybridization [15] and the \"hydrogen\" one, according to which the decisive role of reactive hydrogen was assumed [16]. The measurements [17] confirmed the ferromagnetism of proton-irradiated carbon films without metal impurities. The superparamagnetism found [18] during measurements on a SQUID magnetometer in proton-irradiated diamonds grown in high-pressure autoclaves (HPHT synthesis) was explained by the interaction of amorphous carbon (formed upon irradiation) and ferromagnetic impurities contained in the HPHT sample. Unusual behavior of the magnetic moment in HPHT synthetic nitrogen-doped diamond crystals was also observed due to the existence of superparamagnetic and superconducting regions [19]. Measurements on a SQUID magnetometer in [20] irradiated with 1-2 MeV proton beams ultra-pure CVD (chemically vapor deposited) diamonds confirmed the presence of high-temperature paramagnetic properties. Based on photoluminescence data, it was suggested that vacancies have a decisive influence on magnetism in diamonds. However, the Raman spectra presented in the same article [20] do not support this hypothesis. CVD diamond crystals implanted with deuterium ions [21] also demonstrate magnetism. A hysteresis was observed in the CW-ESR (continuous wave electron spin resonance) spectra of CVD diamonds implanted with hydrogen isotopes and annealed in vacuum at temperatures in the range from 1000 to 1300 \({}^{\circ}\)C, which indicates the ordering of electron spins. This effect was enhanced in natural diamonds implanted with hydrogen in the channeling mode. The absence of ferromagnetic impurities in the untreated crystals of natural and CVD diamond and the coincidence of C-H bond breaking temperatures and disappearance of hysteresis in EPR spectra made it possible to consider deuterium (hydrogen)-vacancy complexes as the most probable cause of spin ordering. Ferromagnetism was revealed [22] in nanocrystalline diamond films implanted with 35 keV nitrogen.