Electrical Readout of Neutral Magnon Hall Transport by Altermagnetic Edges

We develop a boundary theory for electrical readout of neutral magnon Hall transport at a magnetic-insulator-metal interface. For the number-conserving collinear regime considered here, a thermal gradient drives distinct Berry-curvature magnon number, spin, and energy Hall currents. Spin-active exchange absorbs incident magnons and injects angular momentum into a metallic detector. Its spin-odd tangential velocity converts the resulting electron-hole packet into an edge current. For a d-wave altermagnet, \(J_y^{\mathrm{edge}}=-2e\lambda_{\mathrm{AM}}\sin2\theta\,\dot S_N\), whereas a spin-degenerate \(PT\)-symmetric collinear antiferromagnet has vanishing response in this nonrelativistic channel. The mode-resolved law weights each incident Hall component by its magnon spin projection and absorption probability. For a scalar-chirality kagome source, \(\kappa_{xy}^{m,\mathrm{tr}}\propto\phi T^3\) in the quasi-two-dimensional infrared regime. A strong-absorption crossover yields \(J_y^{\mathrm{edge}}\propto T^2\). Chirality and Néel-vector reversals, principal-axis nodes, and a \(90^\circ\) rotation provide direct symmetry tests.