Spin-triplet superconductors are promising platforms for dissipationless spin transport, which typically originates from the interplay of ferromagnetism and superconductivity. However, ferromagnetism, in turn, suppresses superconductivity. As a class of unconventional magnetic materials, $p$-wave magnets possess the advantage of odd-parity spin splitting without net magnetism. Here we demonstrate through site-resolved spin-polarized band analysis that $p$-wave magnets exhibit nonzero in-plane spin polarization, which is crucial for spin-triplet correlations. We then investigate the $p$-wave magnetic superconductor composed of a $p$-wave $\mathrm{magnet}/s$-wave superconductor hybrid system and calculate the site-resolved equal-spin component of anomalous Green's function, revealing the existence of equal-spin (spin-triplet) Cooper pairs. Next, we construct a normal $\mathrm{metal}/p$-wave magnetic superconductor junction and calculate the equal-spin Andreev reflection coefficient using the nonequilibrium Green's function method. The results show that the equal-spin Andreev reflection coefficient is indeed nonzero, owing to the spin-triplet superconductivity. Finally, we construct a Josephson junction based on $p$-wave magnetic superconductors, study the spin Josephson effect, and identify the emergence of a spin superconducting diode effect.

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• Andreev reflection
• Diodes
• Josephson effect
• Spin-triplet pairing
• Superconducting order parameter
• 1-dimensional systems
• Altermagnets
• Nonequilibrium Green's function