Magnonic excitations in the two-dimensional (2D) van der Waals (vdW) ferromagnet CrI3 are studied. We find that bulk magnons exhibit a non-trivial topological band structure without the need for Dzyaloshinskii-Moriya (DM) interaction. This is shown in vdW heterostructures, consisting of single-layer CrI3 on top of different 2D materials as MoTe2, HfS2 and WSe2. We find numerically that the proposed substrates modify substantially the out-of-plane magnetic anisotropy on each sublattice of the CrI3 subsystem. The induced staggered anisotropy, combined with a proper band inversion, leads to the opening of a topological gap of the magnon spectrum. Since the gap is opened non-symmetrically at the K+ and K- points of the Brillouin zone, an imbalance in the magnon population between these two valleys can be created under a driving force. This phenomenon is in close analogy to the so-called valley Hall effect (VHE), and thus termed as magnon valley Hall effect (MVHE). In linear response to a temperature gradient we quantify this effect by the evaluation of the temperature-dependence of the magnon thermal Hall effect. These findings open a different avenue by adding the valley degrees of freedom besides the spin, in the study of magnons.
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