Chiral magnons in antiferromagnets offer a unique bosonic platform to explore quantum tunneling phenomena, including Klein tunneling, in experimentally accessible regimes. Here, we investigate the tunneling dynamics of magnon wave packets in ${\mathrm{MnF}}_2$ nanowires exhibiting anti-parity-time $\left(\text{anti}\text{−}\mathcal{PT}\right)$ symmetry under magnetic-field-controlled potential steps. By varying the wave vector $k$ and external magnetic fields, we design distinct channels for chiral and Klein tunneling. Our theoretical and numerical analysis shows that helicity and chirality are preserved during tunneling, and the magnonic particle–antiparticle pair creation occurs—a definitive signature of Klein tunneling. We explore how key parameters, such as magnetic field strength, wave vector, and wave packet width, influence tunneling dynamics and identify resonant transmission conditions across barriers and wells. Notably, in the Klein tunneling regime, the combined transmission and reflection exceed unity, as barriers effectively act as potential wells for antiparticles. These findings pave the way for approaches in the manipulation and amplification of chiral magnons, as well as in the engineering of bosonic tunneling effects in magnonic systems.

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• Bosons
• Magnetism
• Tunneling & traversal time
• Nanowires