The paper investigates the band topology and optical conductivity in two-dimensional d-wave altern magnetic metals, considering the presence of substrate-induced Rashba spin-orbit coupling. The authors use a 2D band Hamiltonian near the Γ point under an external magnetic field to study the altern magnet band structure. They find that time-reversal symmetry breaking due to altern magnetism, combined with Rashba coupling and an external magnetic field, can lead to non-trivial band topology. The topological phases can be tuned by magnetic field strength and direction, and are classified by their Chern numbers. The authors also investigate the charge response by computing the full optical conductivity tensor with and without magnetic fields, focusing on magneto-optical responses, which are the finite-frequency analog of the Berry curvature-induced anomalous Hall conductivity. Using experimentally realistic parameters for RuO₂, they estimate the Faraday angle in the absence of magnetic fields. The study reveals that broken time-reversal symmetry can result in a non-zero Faraday angle, with an estimated value of $\theta_F \sim 10^{-5}$ rad. Overall, the tunable electric conductivity in altern magnets makes them a promising platform for manufacturing non-reciprocal quantum devices without the need for external magnetic fields.The paper investigates the band topology and optical conductivity in two-dimensional d-wave altern magnetic metals, considering the presence of substrate-induced Rashba spin-orbit coupling. The authors use a 2D band Hamiltonian near the Γ point under an external magnetic field to study the altern magnet band structure. They find that time-reversal symmetry breaking due to altern magnetism, combined with Rashba coupling and an external magnetic field, can lead to non-trivial band topology. The topological phases can be tuned by magnetic field strength and direction, and are classified by their Chern numbers. The authors also investigate the charge response by computing the full optical conductivity tensor with and without magnetic fields, focusing on magneto-optical responses, which are the finite-frequency analog of the Berry curvature-induced anomalous Hall conductivity. Using experimentally realistic parameters for RuO₂, they estimate the Faraday angle in the absence of magnetic fields. The study reveals that broken time-reversal symmetry can result in a non-zero Faraday angle, with an estimated value of $\theta_F \sim 10^{-5}$ rad. Overall, the tunable electric conductivity in altern magnets makes them a promising platform for manufacturing non-reciprocal quantum devices without the need for external magnetic fields.