  Low-frequency radio observations are revealing an increasing number of
diffuse synchrotron sources from galaxy clusters, dominantly in the form of
radio halos or radio relics. The existence of this diffuse synchrotron emission
indicates the presence of relativistic particles and magnetic fields. It is
still an open question what mechanisms exactly are responsible for the
population of relativistic electrons driving this synchrotron emission. The
LOFAR Two-metre Sky Survey Deep Fields offer a unique view of this problem.
Reaching noise levels below 30 $\mu$Jy/beam, these are the deepest images made
at the low frequency of 144 MHz. This paper presents a search for diffuse
emission in galaxy clusters in the first data release of the LOFAR Deep Fields.
We detect a new high-redshift radio halo with a flux density of $8.9 \pm 1.0$
mJy and corresponding luminosity of $P_{144\mathrm{MHz}}=(3.6 \pm
0.6)\times10^{25}$ W Hz$^{-1}$ in an X-ray detected cluster at $z=0.77$ with a
mass estimate of $M_{500} = 3.3_{-1.7}^{+1.1} \times 10^{14} M_\odot.$ Deep
upper limits are placed on clusters with non-detections. We compare the results
to the correlation between halo luminosity and cluster mass derived for radio
halos found in the literature. This study is one of few to find diffuse
emission in low mass ($M_{500} < 5\times10^{14} M_\odot$) systems and shows
that deep low-frequency observations of galaxy clusters are fundamental for
opening up a new part of parameter space in the study of non-thermal phenomena
in galaxy clusters.
