Table 1. Observational and measured properties

Infrared reflectance spectroscopy:

The IR reflectance spectra were acquired from the table of the two stones, the material being isotropic, the spectrum is not lattice directions dependent. The spectrum of the 0.84 ct spinel is shown in figure 2, that of the 0.93 ct spinel is not displayed since there is no difference compared to the 0.84 ct stone's one. The spectra are characteristic of natural spinel (synthetic verneuil spinel's spectrum significantly differ with an extra band at 940 cm^-1 and the flux-grown synthetic spinel has a spectrum fully comparable with the natural spinel, therefore indistinguable with this method).

UV-VIS-NIR spectroscopy:

The spinel being an isotropic material does not require particular care for acquiring the spectrum. The UV-Vis-NIR spectra of the two stones were acquired with the light path perpendicular to the stone's table and entering the stone through the culet. The spectra are very similar, thus only one is shown in figure 3, this is that of the 0.84 ct spinel.

The spectrum shows two characteristic broad bands at 388 and 538 nm that are due to the presence of Cr³⁺ in the lattice structure. These features are well-known and result from the spin-allowed ⁴A₂ → ⁴T₁ and ⁴A₂ → ⁴T₂ transitions. The hump at 419 nm is  related to the Cr³⁺ spin-forbidden transitions. The very small feature at 478 nm is possibly attributed to Fe³⁺ (⁶A_1g → ⁴A_1g). The features at 687, 699 and 708 nm are the commonly called 'organ-pipe' emission bands that can also be observed with a hand-held spectroscope. These photoluminescence emissions are visible in the absorption spectra because of the spectrophotometer technology that uses a CCD and a full range UV-Vis-NIR light source. This will not occur with a spectrophotometer using a monochromator on light source end-side.
The spin-allowed ⁴A₂ → ⁴T₂ transition band is located at 538 nm, such position tends to indicate the spinel stone was not heated above 800° C. This band shifts to 542, 545 nm or even more if the spinel was submitted to heat. 

Photoluminescence spectroscopy:

As seen in the UV-Vis-NIR spectrum (figure 3), Cr³⁺ photoluminescence emissions are just visible with a simple halogen light source. Using SWUV or a 405 nm laser should be quite easy to excite the Cr³⁺ luminescence. The spectrum of the 0.84 ct spinel (figure 4) acquired with a 405 nm laser shows the Cr³⁺ strong red luminescence with its so characteristic 'organ-pipe' structure. The same zoomed-in spectrum is presented in figure 5 to focus on Cr³⁺ emission's spectral range.

The main emission at 686, 688 nm is related to the R-lines (R1 and R2, splitting may not be observed), the ZPL (Zero Phonon Line) and the LPM (Lattice Phonon Modes). Others emissions are also known as the R and N side bands. Separating the R lines from each other, the R lines from the ZPL and LPM requires a very high resolution and properly calibrated spectrophotometer as the ones used in Raman spectrophotometer and to operate at low temperature such as LNT (Liquid Nitrogen Temperature). The R-lines are separated by just a bit less than 2 cm^-1 that is only 0.09 nm, the ZPL from R1 is about 5 cm^-1 thus 0.23 nm. All emissions in spectrum of figure 5 are in fact composed of 3 to 5 emission lines that cannot be resolved with a spectrophotometer with a resolution of 0.7 to 1 nm.

The interesting feature is the ZPL / R-lines, according to their position, usually between 684.2 and 685.2 nm, here nearly 686 nm, indicates the spinel is not heated nor a synthetic one (verneuil and flux-grown). Even if the lines cannot be resolved, each emission group (675-677, 686-688, 698-701, 708-710 and 718 nm) is well defined and quite distinct from others. In synthetic spinels and heated ones, they are all present but much less distinct than in this case. The scale of the figure 5 spectrum  makes them looking packed down.

Conclusion:

All data (classical gemology and spectroscopy) are consistent with unheated natural spinel. The pink color is caused by Cr³⁺ as the main chromophore.