Due to spin-orbit coupling (SOC), a quantized spin Hall conductivity has not yet been reported in realistic materials. Here, we tackle this challenge by predicting robust quantized spin Hall conductivity in monolayer ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$. The underlying physics originates from the unrecognized mirror-spin coupling (MSC), which couples spin-up and spin-down states into two orthogonal mirror eigenstates. We show that the perfect MSC can naturally emerge in the two-dimensional altermagnets with out-of-plane Néel vector and horizontal mirror but without SOC. Remarkably, the MSC can dramatically weaken the spin hybridization of the systems when SOC is included. When SOC is neglected, ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$ is an altermagnetic Weyl semimetal with MSC. With SOC, it evolves into the first material candidate for two-dimensional magnetic mirror Chern insulator. Remarkably, under the protection of MSC, the spin hybridization of both bulk and topological edge states in ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$ with SOC at low energy is negligible. As a consequence, a quantized spin Hall conductivity emerges within the bulk band gap of the system. By unveiling this effect, our findings represent a significant advancement in spin Hall transport, and broaden the material candidates hosting intriguing altermagnetic phenomena.

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• Edge states
• Electronic structure
• First-principles calculations
• Magnetism
• Symmetry protected topological states
• Topological materials
• Topological phases of matter