Characterizing the diffuse continuum excitations in the classical spin liquid $h$-YMnO$_3$

We extend previous inelastic neutron scattering results on the geometrically frustrated antiferromagnet hexagonal-YMnO$_3$, which has been suggested to belong to the class of classical spin liquids. We extend the energy transfer coverage of the diffuse signal up to 6.9 meV within a wide temperature range around the ordering temperature, $T_\mathrm{N}$. The two distinct diffuse signals in the a-b plane, the signal localized at $\Gamma$' and the scattering intensity connecting $\Gamma$' points over the M', are shown to be only weakly energy dependent. In addition, an external magnetic field of up to 10.5 T applied along c is shown to have no effect on the diffuse signal. In the orthogonal scattering plane, the signals are shown to be dependent on l only through the magnetic form factor, showing that the correlations are purely two-dimensional, and supporting its origin to be the frustrated Mn$^{3+}$ triangles. This result is corroborated by atomistic spin dynamics simulations showing similar scattering vector and temperature behaviours. Lastly, data for the spin wave scattering in the (h, 0, l) plane allow for a discussion of the magnetic ground state where better agreement is found between the data and an ordered structure of the $\Gamma_1$ or $\Gamma_3$ symmetry, albeit crystal electric field arguments dismisses the $\Gamma_1$ as possibility.