Altermagnetic (ATM) skyrmions embody a macroscopic realization of microscopic $d$-wave symmetry, as revealed by their unique spin textures in materials. Through lattice rotational symmetry and spin ordering, ATMs show exchange-driven spin splitting with directional dependence, imprinting $d$-wave anisotropy—modulated by the exchange difference $J_1-J_2$—onto skyrmion configurations. Our analysis, combining simulations and theoretical modeling, uncovers a ${90}^{\circ }$ interlayer orientation between elliptical skyrmion pairs, a geometric hallmark validated by $C_4$ symmetry and anisotropic Berry curvature. We propose this angle as a rotational invariant, underscoring ATM skyrmions' potential as topological probes for spintronics and beyond.

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• Skyrmions
• Spintronics
• d-wave
• Altermagnets