Cation substitution is a promising strategy for modulating the structural properties and optimizing the electrochemical performance of spinel cobalt oxide (Co₃O₄); however, the underlying mechanism of this action induced by different cation substitutions has not yet been clearly addressed.

We studied the magnetic properties of ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Br}}_2\left[{\mathrm{Br}}_{1-x}{\left(\mathrm{OH}\right)}_x\right]$ ($x$ = 0.33), where ${\mathrm{Cu}}^{2+}$ ions form two-dimensional kagome layers. There is no magnetic order down to 50 mK, while the Curie-Weiss temperature is on the order of $-100$ K. At zero magnetic field, the low-temperature specific heat shows a $T^2$ dependence. Above 2 T, a linear temperature dependence term in specific heat emerges, and the value of $\gamma =C/T$ increases linearly with the field. Furthermore, the magnetic susceptibility tends to a constant value at $T=0$. Our results suggest that the magnetic ground state of ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Br}}_2\left[{\mathrm{Br}}_{1-x}{\left(\mathrm{OH}\right)}_x\right]$ is consistent with a Dirac quantum-spin-liquid state with a linearly dispersing spinon strongly coupled to an emergent gauge field, which has long been theoretically proposed as a candidate ground state in the two-dimensional kagome Heisenberg antiferromagnetic system.