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

Abstract

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 $t_{2g}$ tight-binding model, demonstrating that the $g$-wave altermagnetism is primarily a product of second and third nearest neighbor interorbital hybridizations between the $\gamma z$ ($\gamma =x,y$) orbitals, but only a much longer range intraorbital hybridization in the $xy$ orbitals, establishing a strong orbital-selectiveness for the altermagnetism. Notably, by replacing the $xy$ 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 $d_{xy}$-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.

22 pages, 17 figures

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Cited by in corpus (7)

• Hybrid d/p-wave altermagnetism in Ca${}_3$Ru${}_2$O${}_7$ and strain-controlled spin splitting
• Tunneling conductance in superconducting junctions with $p$-wave unconventional magnets breaking time-reversal symmetry
• Relativistic Spin-momentum locking in altermagnets
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Staggered Dzyaloshinskii-Moriya and canting angle in centrosymmetric altermagnetic and ferromagnetic phases: influence on the anomalous Hall effect and Weyl points
• Relativistic spin-momentum locking in ferromagnets
• Altermagnetism from the viewpoint of chemistry