  We study the coherence of the near-infrared and X-ray background fluctuations
and the X-ray spectral properties of the sources producing it. We use data from
multiple Spitzer and Chandra surveys, including the UDS/SXDF surveys, the
Hubble Deep Field North, the EGS/AEGIS field, the Chandra Deep Field South and
the COSMOS surveys, comprising $\sim$2275 Spitzer/IRAC hours and $\sim$~16 Ms
of Chandra data collected over a total area of $\sim$~1~deg$^2$. We report an
overall $\sim$5$\sigma$ detection of a cross-power signal on large angular
scales $>$ 20$''$ between the 3.6 and 4.5\mum\ and the X-ray bands, with the IR
vs [1-2] keV signal detected at 5.2$\sigma$. The [0.5-1] and [2-4] keV bands
are correlated with the infrared wavelengths at a $\sim$1$-$3$\sigma$
significance level. The hardest X-ray band ([4-7] keV) alone is not
significantly correlated with any infrared wavelengths due to poor photon and
sampling statistics. We study the X-ray SED of the cross-power signal. We find
that its shape is consistent with a variety of source populations of accreting
compact objects, such as local unabsorbed AGNs or high-z absorbed sources. We
cannot exclude that the excess fluctuations are produced by more than one
population. Because of poor statistics, the current relatively broad
photometric bands employed here do not allow distinguishing the exact nature of
these compact objects or if a fraction of the fluctuations have instead a local
origin.
