## 4 Conclusions  
The magnetic properties of hydrogen-free natural diamond samples with the highest possible degree of radiation disordering (or subcritical radiation damage) were studied. The selection of irradiated with fast neutron diamonds was carried out according to their Raman spectra. It was found that Raman spectra of diamonds with extremely high subcritical radiation damage have an intense band with a maximum near 1575 cm\({}^{-1}\), boson peak, and a structural band at 900-1300 cm\({}^{-1}\) due to the phonon confinement effect. It is shown that in the diamonds with subcritical radiation damage, the Raman band with a maximum near 1575 cm\({}^{-1}\) is a superposition of at least three bands with maxima at 1465, 1530 and 1620 cm\({}^{-1}\), and the overtones of these three bands and a combination band 1530 + 1620 cm\({}^{-1}\) dominate in the second-order Raman spectra of such samples. It is shown that both the position of the maximum of the intense band near 1575 cm\({}^{-1}\) and the ratio of the amplitudes of this band and the boson peak with a maximum near 420 cm\({}^{-1}\) can serve as a criterion for reaching the level of critical radiation damage of diamond. The magnetic moment of natural diamond grains irradiated with fast neutrons was measured at cryogenic temperatures. For the first time, it has been established that for the observed Curie-Weiss temperature \(\Theta\approx 150\) K of the transition from the ferromagnetic to the diamagnetic state, the energy of the exchange magnetic interaction of uncompensated spins is \(J\approx 1.7\) meV. The differential magnetic susceptibility of irradiated diamond grains with subcritical radiation damage (113 pcs, with a total volume \(V\approx 7.4\) mm\({}^{3}\)) at the temperature of 2 K in the limit of zero external magnetic field (\(B\approx 0\)) is \(\chi_{\rm diff}(B\approx 0)\approx 1.8\times 10^{-3}\) SI units. Virgin diamond grains of the same quantity and total volume in the temperature range from 2 to 300 K were diamagnetic with \(\chi_{\rm diff}\approx-1\times 10^{-5}\) SI units. The most probable defects that provide ferromagnetism in diamond are the centers with variable sp\({}^{2}\)/sp\({}^{3}\) hybridization, which are observed in Raman spectra in the spectral range 1400-1800 cm\({}^{-1}\) characteristic for sp\({}^{2}\)/sp\({}^{3}\) hybridization, namely, in the intense Raman band with a maximum near 1575 cm\({}^{-1}\). The coincidence of the magnetic susceptibility values measured in this work for natural hydrogen-free diamonds and the literature data for CVD diamond films irradiated with fast neutrons with almost the same fluence (\(5\times 10^{20}\) cm\({}^{-2}\)) indicates that hydrogen-containing radiation defects do not have a significant effect on the magnetic properties of radiation-disordered diamonds. Conceptualization, N.A.P., A.V.K. and A.A.K. ; methodology N.A.P. and A.V.K. ; validation, S.A.V. and A.V.K. ; investigation, N.A.P., A.V.K., A.A.K., I.A.S., O.N.P., A.I.K., M.V.K. and R.A.K. ; writing--original draft preparation, A.V.K. ; writing--review and editing, N.A.P. and A.A.K. ; visualization, S.A.V. and A.A.K. ; project administration, N.A.P. and A.A.K. ; funding acquisition, N.A.P. and A.A.K. All authors have read and agreed to the published version of the manuscript. **Funding:** The reported study was funded by Russian Science Foundation, grant no. 22-72-10108 \"Fundamental studies of structure transformations, optical and magnetic properties of diamond under the influence of fast neutron irradiation, ion implantation and femtosecond laser radiation\" (Raman study), Belarusian National Research Program \"Materials Science, New Materials and Technologies\" and by Belarusian Republican Foundation for Fundamental Research, grant No. F21 RM-137. **Data Availability Statement:** Additional data is available upon request to the corresponding authors. **Acknowledgments:** A.A.K. and M.V.K. acknowledge the financial support from the Russian Science Foundation; N.A.P. and S.A.V.