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Symmetry classification of magnetic octupole current based on multipole representation theory

Yuuga Takasu, Satoru Hayami

TL;DR

The paper develops a complete multipole framework for the symmetry classification of magnetic-octupole (MO) conductivity tensors in altermagnets, clarifying how MO currents differ from spin currents. By decomposing the MO conductivity into Ohmic and Hall parts and linking them to electric-type and magnetic-type multipoles, the authors show that MO responses extend up to rank-5 and can exist even when spin conductivities are symmetry-forbidden. Time-reversal symmetry governs which MO contributions are dissipative, with TR-odd multipoles enabling dissipative MO currents in TR-broken phases. A tight-binding model demonstrates how symmetry lowering from Oh to $mar{3}$ activates MO conductivities and illustrates the distinct roles of $Q$ (electric-type) and $G$ (ET) multipoles, providing guidance for experimental identification and material design.

Abstract

Magnetic octupole (MO) currents have recently attracted significant attention as a driving force for the Neel vector dynamics in d-wave altermagnets, a new class of antiferromagnets that exhibit nonrelativistic spin-split band structures. From a symmetry perspective, the MO includes an axial-dipole component analogous to that of the spin, making it essential to clarify how MO currents differ from spin currents. We here investigate the correspondence between MO conductivities and electronic multipoles, which provide a unified and powerful framework for symmetry analysis. We derive the multipole representation of the rank-five MO conductivity tensor and classify its symmetry-allowed components for all crystallographic point groups, in direct comparison with spin conductivity. We show that time-reversal-even electric-type multipoles give rise to the dissipationless MO current, whereas time-reversal-odd magnetic-type multipoles generate dissipative MO current under an applied electric field. Complementing this macroscopic analysis, the linear-response calculations for a microscopic tight-binding model demonstrate how MO conductivities are activated by symmetry lowering, exemplified by the symmetry reduction from Oh to Th. Our results elucidate the symmetry distinctions between MO currents and spin currents, and provide insights into their experimental identification.

Symmetry classification of magnetic octupole current based on multipole representation theory

TL;DR

The paper develops a complete multipole framework for the symmetry classification of magnetic-octupole (MO) conductivity tensors in altermagnets, clarifying how MO currents differ from spin currents. By decomposing the MO conductivity into Ohmic and Hall parts and linking them to electric-type and magnetic-type multipoles, the authors show that MO responses extend up to rank-5 and can exist even when spin conductivities are symmetry-forbidden. Time-reversal symmetry governs which MO contributions are dissipative, with TR-odd multipoles enabling dissipative MO currents in TR-broken phases. A tight-binding model demonstrates how symmetry lowering from Oh to activates MO conductivities and illustrates the distinct roles of (electric-type) and (ET) multipoles, providing guidance for experimental identification and material design.

Abstract

Magnetic octupole (MO) currents have recently attracted significant attention as a driving force for the Neel vector dynamics in d-wave altermagnets, a new class of antiferromagnets that exhibit nonrelativistic spin-split band structures. From a symmetry perspective, the MO includes an axial-dipole component analogous to that of the spin, making it essential to clarify how MO currents differ from spin currents. We here investigate the correspondence between MO conductivities and electronic multipoles, which provide a unified and powerful framework for symmetry analysis. We derive the multipole representation of the rank-five MO conductivity tensor and classify its symmetry-allowed components for all crystallographic point groups, in direct comparison with spin conductivity. We show that time-reversal-even electric-type multipoles give rise to the dissipationless MO current, whereas time-reversal-odd magnetic-type multipoles generate dissipative MO current under an applied electric field. Complementing this macroscopic analysis, the linear-response calculations for a microscopic tight-binding model demonstrate how MO conductivities are activated by symmetry lowering, exemplified by the symmetry reduction from Oh to Th. Our results elucidate the symmetry distinctions between MO currents and spin currents, and provide insights into their experimental identification.

Paper Structure

This paper contains 34 sections, 99 equations, 2 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Symmetry of Magnetic Octupole Conductivity
  3. Correspondence to Multipole
  4. Comparison between the magnetic octupole and spin conductivities
  5. Classification under 32 point groups
  6. Time-reversal property
  7. Model Analysis
  8. Tight-binding model
  9. Numerical Results
  10. Summary
  11. Angle dependence of multipole
  12. Multipole expressions of MO conductivities
  13. rank-0 c-multipoles
  14. rank-1 c-multipoles
  15. rank-2 c-multipoles
  16. ...and 19 more sections

Figures (2)

  • Figure 1: The broadening factor $\delta$ dependence of (a) the polar multipole $Q$ components of MO Hall conductivities $\sigma_{xy}^{(\mathrm{H})}(Q)$ and (b) the axial multipole $G$ components of MO Hall conductivities $\sigma_{xy}^{(\mathrm{H})}(G)$.
  • Figure 2: The strength of the ETD octupole $g$ dependence of (a) the polar multipole $Q$ components of MO Hall conductivities $\sigma_{xy}^{(\mathrm{H})}(Q)$ and (b) the axial multipole $G$ components of MO Hall conductivities $\sigma_{xy}^{(\mathrm{H})}(G)$.