The coupling between real-space inhomogeneity coordinates and spin $\left(\mathbf{r}\text{−}\mathbf{s}\right)$ provides an alternative route to achieve efficient spin manipulation in spintronics beyond the conventional momentum-spin $\left(\mathbf{k}\text{−}\mathbf{s}\right)$ coupling paradigm. Here, we demonstrate an unexpected manifestation of one-dimensional (1D) $\mathbf{r}\text{−}\mathbf{s}$ coupling via floating edge states in two-dimensional altermagnets with electric-field and gate-doping tunability. The 1D edge-spin $\mathbf{r}\text{−}\mathbf{s}$ coupling ensures that carrier transport is exclusively carried by the edge states with quantized spin conductance, giving rise to an unconventional edge tunnel magnetoresistance effect that can be switched on or off. As a proof of concept, we computationally design an altermagnetic edge tunnel junction based on a ${\mathrm{Cr}}_2{\mathrm{Se}}_2\mathrm{O}$ monolayer to demonstrate its edge transport and controllability via the Néel order or an electric field. Our findings propose a general prototype altermagnetic device for next-generation low-dimensional spintronics.

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• Quantum transport
• Spintronics
• Altermagnets
• Antiferromagnets
• Magnetic tunnel junctions
• Methods in transport