Interplay between Relativistic Spin-Momentum Locking and Breaking of Inversion Symmetry: conditions for p-wave magnetism

TL;DR

This paper explores how relativistic effects and inversion symmetry breaking influence spin-momentum locking and p-wave magnetism in altermagnetic Ca2RuO4, revealing conditions for various SOC types and magnetic phases.

Contribution

It provides a detailed analysis of the interplay between relativistic spin-momentum locking and inversion symmetry breaking, including modeling of SOC effects and magnetic phase transitions.

Findings

Reproduction of the experimentally observed magnetic ground state of Ca2RuO4.

Identification of conditions under which Rashba or Weyl-type SOC emerge.

Discovery of a magnetic phase transition to an exotic altermagnetic state with weak ferromagnetism.

Abstract

We investigate the interplay between relativistic spin-momentum locking arising from altermagnetism and various forms of inversion symmetry breaking. Depending on the symmetry breaking, this can give rise to Rashba-type spin-orbit coupling (SOC), Weyl-type SOC, or the coexistence of two distinct spin-momentum lockings. We focus on the altermagnetic Ca2RuO4 as a testbed material. Our results reproduce the experimentally observed ground state, which is an A-centered magnetic order with the Neel vector along the b-axis, hosting spin cantings along the a- and c-axes but without weak ferromagnetism. Ca2RuO4 exhibits relativistic spin-momentum locking, with different even-parity wave orders for the three spin components. We interpret the experimental results on doped samples as evidence for a transition from a pure altermagnetic phase to a weak ferromagnetic phase. Under ferroelectric- and antiferroelectric-like distortions, there are no qualitative changes in the non-relativistic spin-momentum locking and in the weak ferromagnetism. However, we observe the rise of the Rashba or Weyl-type SOC. Using numerical and analytical models, we investigate which nodal planes persist when inversion symmetry is broken in the relativistic case. The spin-momentum locking of the other components adopt a p-wave character in the case of Rashba; in contrast, Weyl-type SOC disrupts all nodal planes, leaving only nodal lines. Finally, to simulate a stripe phase with structural distortions along the z-axis, we studied a modulated electric field inducing atomic displacements within one Ca2RuO4 layer. This produces a magnetic phase transition to an exotic altermagnetic state with two non-relativistic spin-momentum lockings hosting weak ferromagnetism. Our research presents a comprehensive analysis of various possible scenarios in altermagnets with breaking of inversion symmetries under relativistic effects