We experimentally investigate charge transport in In–CrSb and In–CrSb–In proximity devices, which are formed as junctions between superconducting indium leads and thick single crystal flakes of altermagnet CrSb. For double In–CrSb–In junctions, \(dV{\text{/}}dI(B)\) curves are mirrored in respect to zero field for two magnetic field sweep directions, which is characteristic behavior of a Josephson spin valve. Also, we demonstrate Josephson diode effect by direct measurement of the critical current for two opposite directions in external magnetic field. We interpret these observations as a joint effect of the spin-polarized topological surface states and the altermagnetic spin splitting of the bulk bands in CrSb. For a single In–CrSb interface, the superconducting gap oscillates in magnetic field for both field orientations, which strongly resembles the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) behavior. FFLO is based on finite-momentum Cooper pairing, therefore, it is fully compatible with the requirements for the Josephson diode effect.
