Pairing-induced Momentum-space Magnetism and Its Implication In Optical Anomalous Hall Effect In Chiral Superconductors

TL;DR

This paper explores how momentum-space magnetism, arising from different pairing potentials and spin-orbit coupling, influences the optical anomalous Hall effect in chiral superconductors, highlighting the role of spin degrees of freedom.

Contribution

It generalizes Onsager's relation for the optical Hall effect, identifying two types of momentum-space magnetism linked to pairing potentials and spin-orbit coupling.

Findings

Unitary pairing induces ferromagnetism and complex spin textures in momentum space.

Momentum-space magnetism can cause in-plane optical anomalous Hall effects.

Spin-orbit coupling plays a crucial role in the optical Hall response.

Abstract

The intrinsic mechanisms of the magneto-optical Kerr signal in chiral superconductors often involve multi-orbital degree of freedom. Here by considering a generic single-orbital and spinful Hamiltonian, we generalize the Onsager's relation to obtain the necessary conditions for the optical anomalous Hall effect. Using the down-folding method, we identify two types of effective momentum-space magnetism responsible for the optical anomalous Hall conductivity from non-unitary and unitary pairing potentials respectively. The former is due to the angular momentum of Cooper pair, while the latter requires the participation of the spin-orbit coupling in the normal state and has been largely overlooked previously. Using concrete examples, we show that the unitary pairing can lead to both ferromagnetism and complicated antiferromagnetic spin texture in the momentum space, resulting in an in-plane optical anomalous Hall effect with the magnetism parallel to the Hall-deflection plane. Our work reveals the essential role of spin degree of freedom in the optical anomalous Hall effect.