  Diffuse cluster-scale synchrotron radio emission is discovered in an
increasing number of galaxy clusters in the form of radio halos (RHs), probing
the presence of relativistic electrons and magnetic fields in the intra-cluster
medium. The favoured scenario to explain their origin is that they trace
turbulent regions generated during cluster mergers where particles are
re-accelerated. In this framework, RHs are expected to probe cluster dynamics
and are predicted to be more frequent in massive systems. Statistical studies
are important to study the connection of RHs with cluster dynamics and to
constrain theoretical models. Furthermore, low-frequency surveys can shed light
on the existence of RHs with very steep radio-spectra, a key prediction of
turbulent models. We study the properties of RHs from clusters of the second
catalog of Planck Sunyaev Zel'dovich detected sources that lie within the 5634
deg^2 covered by the second Data Release (DR2) of the LOFAR Two-meter Sky
Survey. We find that the number of observed RHs, their radio flux density and
redshift distributions are in line with what is expected in the framework of
the re-acceleration scenario. In addition, the fraction of clusters with RHs
increases with the cluster mass, confirming the leading role of the
gravitational process of cluster formation in the generation of RHs. These
models predict a large fraction of RHs with very steep spectrum in the DR2
Planck sample, this will be tested in future studies, yet a comparison of the
occurrence of halos in GMRT and LOFAR samples indeed shows a larger occurrence
of RHs at lower frequencies suggesting the presence of a number of very steep
spectrum RH that is preferentially detected by LOFAR. Using morphological
information we confirm that RHs are preferentially located in merging systems
and that the fraction of newly LOFAR discovered RHs is larger in less disturbed
systems.
