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We propose the existence of a symmetry-protected topological Dirac nodal line(DNL) magnonic phase in layered honeycomb collinear antiferromagnets even inthe presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that themagnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D)honeycomb collinear antiferromagnets cancels out in the layered honeycombcollinear antiferromagnets. In other words, the magnon spin Nernst effect ineach 2D antiferromagnetic layer cancels out the succeeding layer. Hence, theBerry curvature vanish in the entire Brillouin zone due to the combination oftime-reversal and space-inversion ($\mathcal{PT}$) symmetry. However, uponsymmetry breaking by an external magnetic field, we show that a non-vanishingBerry curvature and Chern number protected topological magnon bands are inducedin the non-collinear spin structure. This leads to an experimentally accessiblemagnon thermal Hall effect in the $\mathcal{PT}$ symmetry-broken topologicalDNL magnonic phase of layered honeycomb antiferromagnets. We propose that thecurrent predicted results can be experimentally investigated in the layeredhoneycomb antiferromagnets CaMn$_2$Sb$_2$, BaNi$_2$V$_2$O$_8$, andBi$_3$Mn$_4$O$_{12}$(NO$_3$).

Topological magnon nodal-lines and absence of magnon spin Nernst effect in layered collinear antiferromagnets