We analyse a sample of 24 damped Lyman-alpha (DLA)/moderate DLA systems at 0.3<z<2.2, all with measurement of the weak MnII absorption lines, to investigate which elemental ratios could possibly be used as tracers of either dust depletion or nucleosynthesis effects. We applied a component-by-component analysis and show that the standard method which uses column densities integrated over the whole absorption profiles could substantially underestimate the abundance of rare elements relative to Fe. The apparent correlation we found between [Mn/Fe] and [Zn/Fe] cannot be accounted for by any dust depletion sequence: it implies either variations of the intrinsic Mn abundance relative to Fe from -0.3 to +0.1 dex and/or a relation between depletion level and metallicity. The correlation between [Mn/Fe] and metallicity strengthens the assumption of intrinsic variations of [Mn/Fe] although some marginal correlation between [Zn or Si/Fe] and [Zn/H] is present as well. The variations of [Ti/Fe] vs. [Zn/Fe] cannot be fitted by a single dust depletion sequence either. At high metallicity, [Fe/H]dc>~-0.5, the intrinsic (dust-corrected) abundance pattern of Si, Ti, Cr and Mn in DLA absorbers closely follows the trends observed in Galactic stars and these absorbers should thus have a chemical evolution similar to that of our Galaxy. At lower metallicity, some absorbers do follow the trends present in Galactic stars but a substantial fraction of them have elemental ratios (in particular [Si/Fe]dc and [Mn/Fe]dc) closer to the solar values than Galactic stars. This could be explained by a larger contribution of type Ia supernovae to the chemical enrichment of these DLA absorbers than in Galactic stars of similar metallicity. This metal-poor DLA absorber population could trace HI-rich dwarf galaxies. (Abridged)
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