Clustering effects of spin radicals on superparamagnetism: calculation for diamond with radiation-induced defects

Abstract

The influence of the clustering degree of electron spin magnetic moments from crystalline defects on the low-temperature magnetic susceptibility of materials is theoretically studied. The susceptibility of two diamond samples containing only identical spin radicals (uncompensated electron spins of radiation defects) with a concentration of 10^19 cm^−3 is calculated. The first sample contains only isolated spin radicals. The second sample contains the same spin radicals grouped into identical spherical clusters—ferrons (clusters). With an average sample concentration of 10^19 cm^−3, the local concentration of spin radicals inside each ferron is assumed to be at the limiting value of 10^20 cm^−3. As the number of spin radicals in each ferron increased from 10 to 350, the diameters of the ferrons increased from 6 to 19 nm, respectively. The low-temperature magnetic susceptibility of both samples is calculated based on the Brillouin function. It is shown that as the number of spin radicals in each ferron increases, the superparamagnetic behavior of the second sample is enhanced. At helium temperatures, in the limit of zero external magnetic field induction, the magnetic susceptibility of the second sample, in which the spin radicals are grouped into ferrons, is much greater than the susceptibility of the first sample, which contains only isolated spin radicals. This finding is supported by experimental measurements of low-temperature magnetic susceptibility in natural type IIa diamond samples irradiated with reactor neutrons.