  Hard X-ray surveys have proven remarkably efficient in detecting intermediate
polars and asynchronous polars, two of the rarest type of cataclysmic variable
(CV). Here we present a global study of hard X-ray selected intermediate polars
and asynchronous polars, focusing particularly on the link between hard X-ray
properties and spin/orbital periods. To this end, we first construct a new
sample of these objects by cross-correlating candidate sources detected in
INTEGRAL/IBIS observations against catalogues of known CVs. We find 23
cataclysmic variable matches, and also present an additional 9 (of which 3 are
definite) likely magnetic cataclysmic variables (mCVs) identified by others
through optical follow-ups of IBIS detections. We also include in our analysis
hard X-ray observations from Swift/BAT and SUZAKU/HXD in order to make our
study more complete. We find that most hard X-ray detected mCVs have
P_{spin}/P_{orb}<0.1 above the period gap. In this respect we also point out
the very low number of detected systems in any band between
P_{spin}/P_{orb}=0.3 and P_{spin}/P_{orb}=1 and the apparent peak of the
P_{spin}/P_{orb} distribution at about 0.1. The observational features of the
P_{spin} - P_{orb} plane are discussed in the context of mCV evolution
scenarios. We also present for the first time evidence for correlations between
hard X-ray spectral hardness and P_{spin}, P_{orb} and P_{spin}/P_{orb}. An
attempt to explain the observed correlations is made in the context of mCV
evolution and accretion footprint geometries on the white dwarf surface.
