The substellar population in Corona Australis

The substellar initial mass function (IMF) and the formation mechanisms of brown dwarfs (BDs) remain key open questions in star formation theory. IMF characterization in a large number of star-forming regions (SFRs) is essential for constraining these processes. We aim to identify and spectroscopically confirm very low-mass members of the Corona Australis (CrA) SFR to refine its substellar census, determine its low-mass IMF, and compare it to other clusters. Using deep I-band photometry from SuprimeCam/Subaru and data from the VISTA Hemisphere Survey, we identified low-mass BD candidates in CrA. We subsequently obtained NIR spectra of 173 of these candidates with KMOS/VLT, as well as optical spectra for 8 kinematic candidate members using FLOYDS/LCO. The kinematic candidates are confirmed as low-mass stellar members with spectral types M1 to M5. In contrast, all 173 BD candidates observed with KMOS are identified as contaminants. Although the follow-up yielded no new substellar members, it places strong constraints on the number of undetected substellar objects in the region. Combined with literature data, this enables us to derive the substellar IMF, which is consistent with a single power-law slope of alpha = 0.95+-0.06 in the range 0.01-1 MSun or alpha = 0.33+-0.19 in the range 0.01-0.1 MSun. The star-to-BD ratio in CrA is about 2. We also provide updated IMFs and star-to-BD ratios for Lupus3 and ChaI from the SONYC survey, reflecting revised distances from Gaia. Finally, we estimate surface densities and median FUV fluxes for 6 SFRs and clusters and compare their substellar populations as a function of environmental properties. The IMF and star-to-BD ratio show no clear dependence on stellar density or ionizing flux from the massive stars. A combined effect - where one factor enhances and the other suppresses BD formation - also appears unlikely. (Abridged)