Altermagnets (AMs) are an exotic class of antiferromagnet that exhibit spin splitting even in the absence of net global magnetization and spin-orbit coupling (SOC) effects. In this work, we investigated theoretically the supercurrent nonreciprocity in an Ising-superconductor (ISC)/altermagnet/Ising-superconductor Josephson junction which revealed asymmetric Josephson critical currents, $0\text{−}\pi$ transitions, and an anomalous current-phase relation. A strong Josephson diode efficiency (JDE) is observed due to the combined effects of AM strength and orientations in a conventional superconductor even in absence of SOC. However, it significantly enhances in presence of intrinsic SOC (ISOC), resulting in pronounced diode effect in both the single- and double-band ISC/AM based Josephson junction. Additionally, it is observed that JDE is more prominent at higher AM strengths with intermediate orientations in all scenarios. Notably, it is significantly suppressed for orientations $0^{\circ }$ and ${45}^{\circ }$. Our results also indicate that barrier transparency and AM lengths play a crucial role in optimizing the JDE. In a single-band ISC/AM system JDE persists for any AM length, while it reduces at longer AM junctions in case of a double-band ISC/AM system. Moreover, our results suggest that a diode efficiency of $\approx 52\%$ can be achieved in the proposed Josephson junction in both the single- and double-band ISC/AM Josephson junction by considering strong AM strength. Furthermore, the single-band ISC offers a wide AM orientation range in contrast to the double-band ISC for better tunability and optimization of JDE. Our findings highlight the impact of AM strength, orientation, and ISOC on the JDE efficiency, offering insights for superconducting diode design.

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• Josephson effect
• Spin-orbit coupling
• Spintronics
• Altermagnets
• Josephson junctions
• Tunnel junctions
• Unconventional superconductors
• Bogoliubov-de Gennes equations