Magnetic-field distributions at interstitial sites in nondilute alloys

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Abstract
Monte Carlo simulations are presented of the instantaneous, dipole magnetic-field probability distribution at an interstitial site in the paramagnetic state of a polycrystalline material involving random alloying of magnetic and nonmagnetic ions on a site, for magnetic concentrations from 1.0 down to 0.03, with particular reference to zero-field (ZF) muon spin relaxation (μSR) in such alloys. In the polycrystalline case, the distribution of local-field magnitudes is more directly related to the ZF μSR than the distribution of field-component values usually discussed. For magnetic-ion concentrations less than about 0.3, the field-magnitude distribution develops a two-site form, and the two types of site are shown to be those with at least one magnetic ion in the nearest-neighbor shell (‘‘high field’’), and those with zero magnetic ions in the nearest-neighbor shell (‘‘low field’’). Correspondingly, directly simulated static ZF μSR asymmetry spectra develop a two-minimum (two-site) form for the same concentrations. While an approximately Lorentzian component distribution is known to occur in the extreme dilute limit, the approach to that limit from finite concentrations will not be in a simple manner. The high-field distribution must approach that due to a single isolated magnetic moment as concentration decreases, and the low-field distribution evolves from a Gaussian (Maxwellian) shape at its high-concentration (near 0.3) limit toward a more Lorentzian shape. Probability distributions part way between Gaussian and Lorentzian limits are discussed in terms of the Pearson type-VII line shape.