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Linear magneto-birefringence as a probe of altermagnetism

V. Sunko, J. Orenstein

Abstract

Altermagnets are a class of collinear magnets that exhibit non-relativistic spin splitting (NRSS) of electronic bands in the absence of net magnetization. Their potential to generate large spin polarization without spin-orbit coupling has created strong interest in probes that access the underlying order parameter directly. In this Perspective, we show that linear magneto-birefringence (LMB) provides a natural and broadly applicable route to detecting altermagnetic order. Building on the correspondence between the momentum-space structure of NRSS and the ferroic ordering of magnetic multipoles in real space, we demonstrate how $d$-wave and $g$-wave NRSS textures yield distinct LMB responses. We present a symmetry-based framework that identifies the optical geometries and field configurations required to isolate specific multipole components, enabling domain imaging and providing benchmarks for theoretical models of LMB.

Linear magneto-birefringence as a probe of altermagnetism

Abstract

Altermagnets are a class of collinear magnets that exhibit non-relativistic spin splitting (NRSS) of electronic bands in the absence of net magnetization. Their potential to generate large spin polarization without spin-orbit coupling has created strong interest in probes that access the underlying order parameter directly. In this Perspective, we show that linear magneto-birefringence (LMB) provides a natural and broadly applicable route to detecting altermagnetic order. Building on the correspondence between the momentum-space structure of NRSS and the ferroic ordering of magnetic multipoles in real space, we demonstrate how -wave and -wave NRSS textures yield distinct LMB responses. We present a symmetry-based framework that identifies the optical geometries and field configurations required to isolate specific multipole components, enabling domain imaging and providing benchmarks for theoretical models of LMB.

Paper Structure

This paper contains 8 sections, 19 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Magnetic multipoles and altermagnetism
  3. Optical probes of multipolar order
  4. Octupoles: Linear Magneto-Birefringence
  5. Triakontadipoles: Strain Linear Magneto-Birefringence
  6. Measurement of linear magneto-birefringence
  7. Outlook
  8. Acknowledgements

Figures (2)

  • Figure 1: Momentum-space spin textures and corresponding real-space magnetic multipoles. Examples of non-relativistic spin-splitting (NRSS) patterns classified as (a, c) d-wave and (b, d) g-wave, in both planar and bulk forms. Panels (a, b) show "planar" structures, where spin-splitting does not change sign with $k_z$, and panels (c, d) show "bulk" structures, where spin-splitting changes sign with $k_z$. For each structure we show: (i) spatial components of the real-space magnetic multipole; (ii) spin-resolved Fermi surfaces in the $k_x$-$k_y$ plane; and (iii) spin-resolved Fermi surfaces in the $k_x$-$k_z$ plane. For each multipole, we list its real space representation and energy dispersion in $k$-space.
  • Figure 2: (a) Reflection geometry for measuring birefringence and linear magneto-birefringence (LMB) at normal incidence: linearly polarized light, with polarization angle $\varphi$, is focused onto the material; upon reflection, the polarization is rotated by an angle $\theta$. (b) Birefringence signal: polar plot of $\theta$ vs. $\varphi$, where nodal directions indicate the principal optical axes ($\phi_0=0$). (c) Field-linear modification of birefringence: (i) diagonal LMB with unchanged axis orientation ($\phi_H=\phi_0$); (ii) off-diagonal LMB with axis rotation by $\pi/4$ ($\phi_H=\phi_0+\pi/4$).