  Context. The Australia Telescope Large Area Survey (ATLAS) aims to image a 7
deg2 region centred on the European Large Area ISO Survey - South 1 (ELAIS-S1)
field and the Chandra Deep Field South (CDF-S) at 1.4 GHz with high sensitivity
(up to ~10 \muJy) to study the evolution of star-forming galaxies (SFGs) and
Active Galactic Nuclei (AGN) over a wide range of cosmic time. Aims. We present
here ancillary radio observations at a frequency of 2.3 GHz obtained with the
Australia Telescope Compact Array (ATCA). The main goal of this is to study the
radio spectra of an unprecedented large sample of sources (~2000 observed, ~600
detected in both frequencies). Methods. With this paper, we provide 2.3 GHz
source catalogues for both ATLAS fields, with a detection limit of 300 \muJy.
We compute spectral indices between 1.4 GHz and 2.3 GHz using matched
resolution images and investigate various properties of our source sample in
dependence of their spectral indices. Results. We find the entire source sample
to have a median spectral index of 0.74, in good agreement with both the
canonical value of 0.7 for optically thin synchrotron radiation and other
spectral index studies conducted by various groups. Regarding the radio
spectral index as indicator for source type, we find only marginal correlations
so that flat or inverted spectrum sources are usually powered by AGN and hence
conclude that at least for the faint population the spectral index is not a
strong discriminator. We investigate relation between spectral index and
redshift for our source sample and find no such correlation at all. We do find
a significant correlation between redshift and radio to near-infrared flux
ratio, making this a much stronger tracer of high-z radio sources. We also find
no evidence for a dependence of the radio-IR correlation on spectral index.
