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Low-frequency radio observations are revealing an increasing number ofdiffuse synchrotron sources from galaxy clusters, dominantly in the form ofradio halos or radio relics. The existence of this diffuse synchrotron emissionindicates the presence of relativistic particles and magnetic fields. It isstill an open question what mechanisms exactly are responsible for thepopulation of relativistic electrons driving this synchrotron emission. TheLOFAR 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 madeat the low frequency of 144 MHz. This paper presents a search for diffuseemission 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 $P_{144\mathrm{MHz}}=(3.6 \pm0.6)\times10^{25}$ W Hz$^{-1}$ in an X-ray detected cluster at $z=0.77$ with amass estimate of $M_{500} = 3.3_{-1.7}^{+1.1} \times 10^{14} M_\odot.$ Deepupper limits are placed on clusters with non-detections. We compare the resultsto the correlation between halo luminosity and cluster mass derived for radiohalos found in the literature. This study is one of few to find diffuseemission in low mass ($M_{500} < 5\times10^{14} M_\odot$) systems and showsthat deep low-frequency observations of galaxy clusters are fundamental foropening up a new part of parameter space in the study of non-thermal phenomenain galaxy clusters.

Diffuse Radio Emission from Galaxy Clusters in the LOFAR Two-metre Sky Survey Deep Fields