Conditions for orbital selective altermagnetism in Sr$_2$RuO$_4$: tight binding model, similarities with cuprates and implications on superconductivity

The vibrational modes in Sr $_{2}$ RuO $_{4}$ easily induce octahedral rotations without tilting. Being on the verge of a magnetic instability, such propensity of octahedral rotation may also produce magnetic fluctuations. In this work, we analyze the long-range magnetic phase diagram incorporating such octahedral rotations and demonstrate the possibility of an altermagnetic phase in Sr $_{2}$ RuO $_{4}$ . Using ab-initio calculations, we first study single layer Sr $_{2}$ RuO $_{4}$ with octahedral rotations, obtaining an orbital-selective $g$ -wave altermagnetic phase. We further provide an effective $t_{2 g}$ tight-binding model, demonstrating that the $g$ -wave altermagnetism is primarily a product of second and third nearest neighbor interorbital hybridizations between the $γ z$ ( $γ = x, y$ ) orbitals, but only a much longer range intraorbital hybridization in the $x y$ orbitals, establishing a strong orbital-selectiveness for the altermagnetism. Notably, by replacing the $x y$ orbital with the $x^{2} - y^{2}$ orbital, a similar tight-biding model may be used to investigate the hole-doped cuprate superconductors. We then study bulk Sr $_{2}$ RuO $_{4}$ , where we find the altermagnetic phase as the magnetic ground state for a range of finite octahedral rotations. In the bulk, interlayer hopping breaks some of the symmetries of the $g$ -wave altermagnet, resulting in a $d_{x y}$ -wave altermagnet, still with orbital selectiveness. We also include relativistic effects through spin-orbit coupling and obtain that an effective staggered Dzyaloshinskii-Moriya interaction generates weak ferromagnetism. Finally, we discuss the implications of the altermagnetic order on the intrinsic superconductivity of Sr $_{2}$ RuO $_{4}$ . Assuming in-plane and intraorbital pairing, the altermagnetism favors spin-singlet $d_{x^{2} - y^{2}}$ -wave or $g$ -wave pairing, or (nematic or chiral) combinations thereof.

Conditions for orbital selective altermagnetism in Sr $_{2}$ RuO $_{4}$ : tight binding model, similarities with cuprates and implications on superconductivity

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Conditions for orbital selective altermagnetism in Sr $_{2}$ RuO $_{4}$ : tight binding model, similarities with cuprates and implications on superconductivity

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Conditions for orbital selective altermagnetism in Sr22​RuO44​: tight binding model, similarities with cuprates and implications on superconductivity

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Conditions for orbital selective altermagnetism in Sr22​RuO44​: tight binding model, similarities with cuprates and implications on superconductivity

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Conditions for orbital selective altermagnetism in Sr $_{2}$ RuO $_{4}$ : tight binding model, similarities with cuprates and implications on superconductivity

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Conditions for orbital selective altermagnetism in Sr $_{2}$ RuO $_{4}$ : tight binding model, similarities with cuprates and implications on superconductivity

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