Diffuse galaxy cluster emission at 168 MHz within the Murchison Widefield Array Epoch of Reionization 0-h field

We detect and characterise extended, diffuse radio emission from galaxy clusters at 168 MHz within the Epoch of Reionization 0-h field: a$45^{\circ} \times 45^{\circ}$region of the southern sky centred on R. A.${}= 0^{\circ}$, decl.${}=-27^{\circ}$. We detect 29 sources of interest; a newly detected halo in Abell 0141; a newly detected relic in Abell 2751; 4 new halo candidates and a further 4 new relic candidates; and a new phoenix candidate in Abell 2556. Additionally, we find nine clusters with unclassifiable, diffuse steep-spectrum emission as well as a candidate double relic system associated with RXC J2351.0-1934. We present measured source properties such as their integrated flux densities, spectral indices ($\alpha$, where$S_\nu \propto \nu^\alpha$), and sizes where possible. We find several of the diffuse sources to have ultra-steep spectra including the halo in Abell 0141, if confirmed, showing$\alpha \leq -2.1 \pm 0.1$with the present data making it one of the steepest-spectrum haloes known. Finally, we compare our sample of haloes with previously detected haloes and revisit established scaling relations of the radio halo power ($P_{1.4}$) with the cluster X-ray luminosity ($L_{\textrm{X}}$) and mass ($M_{500}$). We find that the newly detected haloes and candidate haloes are consistent with the$P_{1.4}$–$L_{\textrm{X}}$and$P_{1.4}$–$M_{500}$relations and see an increase in scatter in the previously found relations with increasing sample size likely caused by inhomogeneous determination of$P_{1.4}$across the full halo sample. We show that the MWA is capable of detecting haloes and relics within most of the galaxy clusters within thePlanckcatalogue of Sunyaev–Zel'dovich sources depending on exact halo or relic properties.