Achieving intrinsic Chern insulators (CIs) with zero net magnetization remains a long-standing and formidable challenge. Here, motivated by the unique opportunities that topological magnons offer for low-dissipation transport, we propose a general theoretical framework for realizing magnon CIs in filling-enforced fully compensated ferrimagnets with vanishing net magnetization. Moreover, we demonstrate that strong asymmetric intralayer Heisenberg interactions induce a type-III (broken-gap) magnonic band alignment, characterized by nonoverlapping magnon frequency gaps of the two layers, thereby enabling the emergence of magnon CIs. Remarkably, the asymmetric Bose-Einstein occupations of oppositely chiral magnon branches offer a distinct advantage in generating a giant magnon thermal Hall conductivity, which is forbidden in conventional antiferromagnets. Based on the Heisenberg-Dzyaloshinskii-Moriya model and first-principles calculations, we identify the experimentally accessible ${\mathrm{CrI}}_3/{\text{CrGeTe}}_3$ and ${\mathrm{CrI}}_3/{\text{CrSiTe}}_3$ heterostructures as ideal material platforms for realizing the proposed magnon CIs with fully compensated ferrimagnetism. These heterostructures host the nonzero magnon Chern numbers and chiral edge states, and remarkably display the strongly enhanced magnon thermal Hall effect comparable to that of ferromagnets, establishing fully compensated ferrimagnets as a promising platform for topological magnon transport without net magnetization.

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• Anomalous Hall effect
• Magnons
• Thermal Hall effect
• 2-dimensional systems
• Magnetic systems
• Topological materials
• Density functional theory
• Heisenberg model
• Spin wave theory