The superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions (JJs) with an anomalous ground state phase shift ${\phi }_0\ne 0,\pi$ $({\phi }_0\text{−}\mathrm{S}/\mathrm{F}/\mathrm{S} \mathrm{JJs})$ enable the implementation of the zero-field Josephson diode effect with the possibility to control the diode efficiency and polarity. It is just as important that in this case ${\phi }_0$ provides a coupling between the superconducting phase and the magnetization of the interlayer. Such ${\phi }_0\text{−}\mathrm{S}/\mathrm{F}/\mathrm{S} \mathrm{JJs}$ can be used for superconducting memory and logic circuit applications. Here we present the results of theoretical calculation of the current-phase relationship (CPR), exhibiting the Josephson diode effect and ${\phi }_0\ne 0,\pi$, for a JJ through a specific magnetic material. As the interlayer of the JJ we consider an ultrathin film of intermetallic lanthanide $\left(Ln\right)$-based compound ${\mathrm{GdIr}}_2{\mathrm{Si}}_2$. Using the density functional theory (DFT) methods, we study the electronic structure and magnetic properties of the film. Then the effective tight-binding Hamiltonian (TBH), demonstrating high quantitative consistency with the electronic properties obtained from DFT calculations, is constructed. The TBH is used to calculate CPR in the framework of the Bogoliubov–de Gennes approach. The CPRs demonstrate a pronounced ${\phi }_0$ of the order of unity and a pronounced Josephson diode effect with the diode efficiency $\lesssim 0.3$. Moreover, the efficiency can be controlled via rotation of in-plane magnetization in the interlayer. The prospects for utilizing alternative magnetic $Ln$-based materials of the $Ln{T}_2{X}_2$ family ($T$ is a transition metal and $X$ is a $p$ element from groups III–V) for the implementation in ${\phi }_0\text{−}\mathrm{S}/\mathrm{F}/\mathrm{S} \mathrm{JJs}$ are also discussed.

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• Josephson effect
• Spin-orbit coupling
• Antiferromagnets
• Ferromagnets
• Josephson junctions
• Magnetic thin films
• Superconductors
• Bogoliubov-de Gennes equations
• Density functional theory
• First-principles calculations
• Tight-binding model