  We report on a spectral study at radio frequencies of the giant radio halo in
A2142 (z=0.0909), which we performed to explore its nature and origin. A2142 is
not a major merger and the presence of a giant radio halo is somewhat
surprising. We performed deep radio observations with the GMRT at 608 MHz, 322
MHz, and 234 MHz and with the VLA in the 1-2 GHz band. We obtained high-quality
images at all frequencies in a wide range of resolutions. The radio halo is
well detected at all frequencies and extends out to the most distant cold front
in A2142. We studied the spectral index in two regions: the central part of the
halo and a second region in the direction of the most distant south-eastern
cold front, selected to follow the bright part of the halo and X-ray emission.
We complemented our observations with a preliminary LOFAR image at 118 MHz and
with the re-analysis of archival VLA data at 1.4 GHz. The two components of the
radio halo show different observational properties. The central brightest part
has higher surface brightess and a spectrum whose steepness is similar to those
of the known radio halos, i.e. $\alpha^{\rm 1.78~GHz}_{\rm 118~MHz}=1.33\pm
0.08$. The ridge, which fades into the larger scale emission, is broader in
size and has considerably lower surface brightess and a moderately steeper
spectrum, i.e. $\alpha^{\rm 1.78~GHz}_{\rm 118~MHz}\sim 1.5$. We propose that
the brightest part of the radio halo is powered by the central sloshing in
A2142, similar to what has been suggested for mini-halos, or by secondary
electrons generated by hadronic collisions in the ICM. On the other hand, the
steeper ridge may probe particle re-acceleration by turbulence generated either
by stirring the gas and magnetic fields on a larger scale or by less energetic
mechanisms, such as continuous infall of galaxy groups or an off-axis merger.
