## 1 Introduction
As for the magnetic properties of Q-carbon and amorphous carbon, a model was proposed in [15] that makes it possible to explain the magnetic properties of these materials by the presence of unpaired electrons in three-coordinated sp\({}^{2}\)-carbon atoms. In a later publication [47], the assumption was substantiated that in amorphous carbon and Q-carbon having a low specific density, carbon chains, i.e., sp\({}^{1}\) and sp\({}^{2}\) carbon, are responsible for magnetism. Thus, despite significant efforts, there is currently no generally accepted point of view and understanding of the nature of magnetism in pure carbon materials. Moreover, it is not clear whether the mechanism of formation of the magnetic state is common for all carbon systems or whether it differs for different allotropes. The formation of a magnetic state in sp\({}^{2}\)-carbon materials can be considered an established experimental fact, but these materials, unlike diamonds, do not have outstanding physical and chemical properties. Diamond is considered a promising material for high-temperature electronics and spintronics. Weak spin-orbit and hyperfine interactions in diamond contribute to a large diffusion length and coherence time of the electron spin and thus create the necessary conditions for spin manipulation. Irradiation of diamonds with fast reactor neutrons, which modify uniformly their bulk properties in a wide range of damage [48; 49], is one of the ways to form a magnetic state in diamonds. In [50], metastable spin states (of a spin glass type) were found at room temperature in the absence of illumination by CW-ESR measurements in CVD diamond films irradiated with fast reactor neutrons. It should be noted that in a number of studies, false positive results may have been obtained, since metal mills were used to prepare samples of carbon materials, which, in combination with the exceptional hardness of diamond, led to contamination of the samples with metals. False positive results can also be obtained from measurements of diamond crystals. The ambiguity of the results of magnetic measurements for diamonds is often due to studies of synthetic crystals that may contain processing impurities of d- and f-elements. A paramagnetic or ferromagnetic contribution in nominally non-magnetic materials also may originate from magnetic impurities present in the carbon materials. These are diamond grown in HPHT synthesis, in which catalyst metals (Fe, Ni, and Co) are used to dissolve graphite. Besides, additional special measures should be taken in the experimental study of magnetic properties [51]. Polycrystalline CVD diamond films deposited in an activatedplasma (usually a mixture of methane and hydrogen) can contain high concentrations of chemically bound hydrogen, localized mainly at intercrystallite boundaries, as well as paramagnetic nitrogen in substitution positions, which makes it difficult to establish the nature of magnetism in diamond between \"amorphous\" and \"hydrogen\" models. The purpose of this work is to study the effect of fast neutron irradiation with high but subcritical fluences (which does not lead to irreversible graphitization) on the magnetic state of single-crystal hydrogen- and metal-free natural diamond grains.