We present a comprehensive study of strain-induced topological magnon phase transitions in insulating three-dimensional (3D) topological chiral antiferromagnets on the kagome-lattice. We show that by applying (100) uniaxial strain, 3D insulating antiferromagnetic Weyl magnons (WMs) manifest as an intermediate phase between a strain-induced 3D magnon Chern insulator (MCI) with integer Chern numbers and a 3D trivial magnon insulator with zero Chern number. In addition, we show that strain suppresses the topological thermal Hall conductivity of magnons in these systems. Due to the similarity between 3D insulating and metallic kagome chiral antiferromagnets, we envision that the current results could also manifest in the 3D antiferromagnetic topological Weyl semimetals Mn$_3$Snslash Ge.
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