A recently discovered phase of collinear magnets, called an altermagnet, breaks time-reversal symmetry (TRS) and exhibits momentum-dependent spin splitting of the band structure with zero net magnetization. In this work, we theoretically investigate the Josephson junction (JJ) of a spin singlet superconductor (SC)/altermagnet/spin triplet SC and demonstrate that it manifests the field-free Josephson diode effect (JDE). It has also been shown that by applying a gate potential in the altermagnetic regime, one can reverse the sign of efficiency and modulate its magnitude. For comparison we have also studied similar JJs with a ferromagnet as a barrier. Our analysis reveals that to realize the JDE with a TRS-broken barrier region one requires the presence of Rashba spin-orbit interaction, nonidentical superconductors, and either the barrier or one of the SCs should be unconventional with $d$-wave symmetry. Our system can be used as a superconducting rectifier that can be tuned efficiently using gate voltage and system parameters without having external magnetic field.

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• Josephson effect
• Superconductivity
• Altermagnets
• Green's function methods