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Abstract: The imaginary part of the second harmonic of the reversible parallel susceptibility (RPS) has been recently demonstrated to be a sensitive probe for determining the anisotropy fields in polycrystalline hard magnetic materials, by means of the singular point detection technique (SPD). A modified SPD theory is depicted here considering the presence of domain walls in the multi-domain crystallites, on the basis of Néel''s phase theory. Measurements performed on Ba-ferrite random powder show that the energy losses related to domain wall motion are likely at the origin of the observed effect. [Copyright &y& Elsevier]