## 4 Discussion  
From the results presented above for the emittance at RT (Figure 9) and at 1300 \({}^{\circ}\)C (calculated as thermal emission divided by the blackbody profile, Figure 3b), we can observe that the band maxima shift to longer wavelengths at high temperature, as illustrated above and ascribed to the crystal thermal expansion. Added to that, the spectral bandwidth of the emittance is larger at high temperatures. For example, for sample Co0.04-50, the full width at half maximum (FWHM) at RT is 2680 cm\({}^{-1}\), while at 1300 \({}^{\circ}\)C one finds values up to 3400 cm\({}^{-1}\). Assuming that we are far enough from saturation for this cobalt content (small absorption) these widths are near to the spectral bandwidths of true absorption bands, thus being 13 to 30% wider at 1300 \({}^{\circ}\)C than at room temperature. Such broadening is usual for 3d ions, as they present large electron-phonon coupling that mediates the shape of the absorption bands [30]. As a first approximation, the oscillator strength of the absorption band is independent of temperature, such that if the FWHM increases, its peak absorption decreases, and we can assume that the absorption coefficient at the band maximum could be from 13 to 30% smaller at 1300 \({}^{\circ}\)C than at RT. We can therefore conclude that the emittance at high temperatures associated to the cobalt dopant might be from 0.9 to 0.7 times that at RT for low dopant concentrations, slowing down slightly the increase as cobalt content increases. Another difference between absolute emittance values of the intense NIR band at RT and 1300 \({}^{\circ}\)C may arise from the known increase of the inversion parameter with temperature. Estimates for the present samples, as shown in Appendix A, would add an extra factor around 0.84, a smaller emittance at 1300 \({}^{\circ}\)C. At high enough cobalt content, emittance saturates at the maximum emittance, which for these samples is around 0.93, due to the reflectance at the external surface. The dependence of the emittance with cobalt content at selected wavelengths is plotted in Figure 10a for both processing rates. The emittance depends very slightly on the microstructure, if any, with slightly higher values for the samples solidified at 750 mm/h. On the contrary, it is determined by the cobalt concentration. This is also true for the emittance estimated from the thermal emission measured at 1300 \({}^{\circ}\)C (Figure 10b). In the measurements at high temperature the data have a larger scatter, as they are sensitive to misalignment or sample diameter. The actual diameter of the sample on which the given data were measured is written on the plot. The figures highlight the same overall trend for the RT and high temperature emittances. The emission at 1500 nm shows a saturation behavior while the emission at 2400 nm increases more or less linearly up to around 0.3 at% Co in the samples. However, a clear difference in the relative values between both spectral ranges and temperatures is observed. If we take as a quantitative reference the saturation value of the 1500 nm band, it is evident that the emittance at 2300-2400 nm is higher at 1300 \({}^{\circ}\)C than at RT. From the above given absorption spectra, the absorption cross-section of cobalt-doped spinel at 2300 nm is \(\approx\)8 \(\times\) 10\({}^{-21}\) cm\({}^{2}\), corresponding to the transition \({}^{4}\)A\({}_{2}\)(\({}^{4}\)F) to \({}^{4}\)T\({}_{2}\)(\({}^{4}\)F). This is a very weak absorption as the transition is electric dipole forbidden. Using level positions as given by [PERSON] [27], the transition of \({}^{4}\)T\({}_{2}\)(\({}^{4}\)F) to \({}^{4}\)T\({}_{1}\)(\({}^{4}\)F) is expected at wavelengths from 2250 nm to 4470 nm at RT (and around 500 cm\({}^{-1}\) red shifted at 1300 \({}^{\circ}\)C, as observed for the 1500 nm transition), that is, it would overlap to the electric dipole forbidden transition.