## 3 Results and Discussion
### Magnetic Properties of Diamonds Irradiated with Fast Neutrons
The presence of high concentrations of hydrogen-containing defects explained the manifestations of magnetism in various carbon materials [4; 16; 18; 21; 22]. The coincidence of the values of the magnetic susceptibility measured in this work for natural hydrogen-free diamonds and in the [48] for CVD diamond films irradiated with fast neutrons with the same fluence (\(5\times 10^{20}\) cm\({}^{-2}\)) indicates that hydrogen-containing radiation defects do not significantly affect the magnetic properties of radiation-disordered diamonds. In Figure 6, a nonmonotonic dependence of \(\chi_{\rm diff}\) on \(B\) is seen in the range from \(-0.5\) to \(0.5\) T for \(T=2\) K, which may be due to the heating and cooling of diamond grains during their magnetization reversal. This finds support in measurements [92; 93], where the thermal nature of the nonmonotonicity of hopping magnetoresistance in semiconductor materials (Ge of \(p\)-type and 3C-SiC of \(n\)-type) at temperatures below 1.5 K is shown. Note that irradiation of IIa diamond grains with neutron fluence of 3 \(\times\) 10\({}^{20}\) cm\({}^{-2}\) led to a noticeable increase in dielectric losses with maximum at frequency of 50 kHz [94]. Recently, many new artificial ferromagnetic materials have been discovered and investigated, which were made by introducing defects into nonmagnetic host crystals [95; 96]. Diamond as a pure carbon material with its high material purity is a good candidate for the investigation of defect-induced ferromagnetism after graphitic materials [3; 7; 29; 43; 44; 45], silicon carbide [96], and oxides [97]. Figure 6: Differential magnetic susceptibility \(\chi_{\rm diff}(B)=(\mu_{0}/V){\rm d}M/{\rm d}B\) (in SI units) of natural diamond grains (113 pcs, \(V\approx 7.4\) mm\({}^{3}\)) irradiated with fast neutrons (\(F=5\times 10^{20}\) cm\({}^{-2}\)). The measurement absolute temperatures (\(T=2\) and 4 K) are shown in the figure. The nature of the defects responsible for magnetism in radiation-modified diamonds remains questionable. The data presented above testify in favor of the fact that the magnetism in the samples under study is due to intrinsic defects of radiation origin. In diamonds with a moderated level of damage, we previously detected [98] the so-called amber centers [99; 100], which are large spherical aggregates consisting of 40 to 60 vacancies [101]. However, at high levels of damage, the conditions for diffusion of vacancies change significantly, and the absorption bands characteristic of amber centers with maxima near 4100 cm\({}^{-1}\) are not observed in the IR spectra. We believe that the most probable defects providing ferromagnetism in diamond are centers with variable sp\({}^{2}\)/sp\({}^{3}\) hybridization. As is known, the maximum phonon frequency in a pure sp\({}^{3}\) carbon material does not exceed 1350 cm\({}^{-1}\). The centers that appear in the Raman spectra in the composition of the \"1640\" band contain single or chain C=C groups. This feature cannot be assigned to any pure form of sp\({}^{3}\)-carbon [102]. Judging by the Raman spectra, the concentration of centers that appear in the 1400-1800 cm\({}^{-1}\) range is quite high. The behavior of a system of dilute defects in a host lattice that interact magnetically on a finite lengthscale can be described using percolation theory [103]. Such studies are in progress.