The mechanism of indirect exchange interaction leading to ferromagnetism in magnetically doped III-V semiconductors is considered theoretically. The mechanism is based on the interplay of two interactions: ͑i͒ hybridization of band states with shallow impurity ones, and ͑ii͒ direct exchange coupling between localized spins and the band states. The indirect exchange interaction between two Mn impurities occurs when the wave functions of shallow states associated with the Mn atoms overlap. The mechanism does not rely on degenerate carriers, and therefore can describe the ferromagnetic transition in both degenerate and nondegenerate semiconductors. Ferromagnetic critical temperature has been calculated within the percolation approach, and is in good agreement with available experimental data.

This work presents the first proof of concept for the use of molecular fluorescence signatures in medieval colours based on lac dye and brazilwood lake pigments. These two important medieval dyes were tested as markers using their UV–Visible emission and excitation spectra. These medieval paints had been previously fully characterized through a multi-analytical approach. In this work, molecular fluorescence spectra were acquired in manuscripts dating from 12th to 15th c., which were produced in monastic scriptoria or workshops. First, the spectral distribution and relative intensity of the emission and excitation spectra were discussed in detail by comparison with reference compounds, including reproductions of paints based on medieval technical texts. It was possible to group the spectra according to recipe specificities. Then, statistical methods (principal component analysis and hierarchical cluster analysis) were applied to the same fluorescence spectra and the generated clusters were compared with the previous ones. Principal component analysis was initially employed to eliminate redundancy in fluorescence data, so minimizing bias on the hierarchical cluster analysis results. Except for some misplaced spectra, the placement of samples per group was confirmed. The outliers resulted from either a poor signal to noise ratio or occurred because certain paints were unique, such as the colour produced by mixing lac dye and brazilwood, which was found in manuscripts from the Alcobaça monastic scriptorium. Previously, by using infrared or Raman spectroscopies, only lac dye could be detected. Notably, these paints compare well with a recipe that was reproduced from the text by Jean Le Begue, in which both dyes were required.

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