Optical and transport anisotropies in spin-textured altermagnets

Abstract

Spin textures are ubiquitous in antiferromagnets, yet their consequences for altermagnets remain largely unexplored. We show that spatial variations of the Néel order act on the low-energy electrons as effective gauge fields, leading to strong anisotropies in both dc transport and optical absorption, even without intrinsic spin-orbit coupling. As a concrete example, we analyze a coplanar spin helix and predict that the principal axes of the conductivity and linear dichroism are set by the helix wave vector and can be tuned by the texture geometry. Our results point to polarization-resolved optics and anisotropic transport as direct probes of textured altermagnetic states, and suggest a simple route to direction-selectivity.

Figures (5)

• Figure 1: (a) Real-space spin texture for a planar spin helix with propagation vector $\bm{q}=q\cos(\phi_q)\,\hat{\bm{x}}+q\sin(\phi_q)\,\hat{\bm{y}}$, shown for three helix orientations $\phi_q$. Momentum-resolved sublattice-polarized spectral function for a $d$-wave (b) and $g$-wave (c) altermagnet. Parameters used: $m=1.0$, $K^x=1.0$, $q=0.2$, $\mu=3$, $\eta=0.08$, $K^z_d=0.3$, $K^z_g=0.9$.
• Figure 2: Helix--orientation dependence of the dc conductivity, shown in the basis defined by the helix direction $\hat{\bm q}$ and its in-plane perpendicular $\hat{\bm q}_\perp$. Top row: longitudinal components $\sigma_{\parallel}=\hat{\bm q}\cdot\boldsymbol{\sigma}\cdot\hat{\bm q}$ and $\sigma_{\perp}=\hat{\bm q}_{\perp}\cdot\boldsymbol{\sigma}\cdot\hat{\bm q}_{\perp}$, normalized to the Drude value $\sigma_0=\mu\tau/\pi$. Bottom row: off-diagonal component $\sigma_{\times}=\hat{\bm q}\cdot\boldsymbol{\sigma}\cdot\hat{\bm q}_{\perp}$, which diagnoses any residual misalignment between $\hat{\bm q}$ and the principal axes of the conductivity tensor. Left column: representative $d$-wave altermagnet, showing a pronounced splitting between $\sigma_{\parallel}$ and $\sigma_{\perp}$ with a characteristic fourfold ($\pi/2$-periodic) $\phi_q$ modulation. Right column: representative $g$-wave altermagnet, where the $\phi_q$ dependence is strongly reduced in amplitude (with a weak $\pi/4$-periodic modulation). Here and in the following $\eta=0.03$ while the other parameters are the same as in Fig. \ref{['fig:helix_FS']}.
• Figure 3: (a) Total optical absorption $\mathfrak A(\omega)$ for different orientations $\phi_q$ from $0$ (red line) to $\pi/2$ (blue line). (b) Corresponding linear dichroism $\mathfrak D(\omega)$. (c) Frequency-dependent orientation $\theta_{+}(\omega)$ of the principal absorption axis (defined modulo $\pi$). The vertical dashed line marks the representative frequencies $\omega_0$ used in panel Fig.\ref{['fig:absorption_axis']}(a).
• Figure 4: (a) Principal absorption axis versus spiral direction for different frequencies. In the pinning regime, $\omega<\omega_p$, the principal absorption axis is pinned to be along the crystal axes, while for the tracking regime, $\omega>\omega_p$, the principal absorption axis tracks the helix direction. (b) Momentum-space origin of the dichroic response. The color map shows the anisotropic interband oscillator strength for two helix orientations (rows) and two probe frequencies $\omega$ (columns), as indicated in each panel. The black dashed contour marks the resonant condition $E_{+}(\bm{k})-E_{-}(\bm{k})=\omega$, while the thick gray circle indicates the Fermi surface of the underlying bands. The areas where the two meet is where $W_\omega(\bm{k})$ is nonzero.
• Figure 5: Perturbative channels in the comoving-frame doublet. (a) First order: $V_{0,p}$ and $V_{z,p}$ act within a given spin sector, while $V_{x,f}$ flips the physical spin and couples the two doublets. (b) Second order: only channels with an even number of transverse flips survive upon projection, so the leading correction comes from the $\sigma_\perp$--$\sigma_\perp$ processes built from $V_{0,f}$ and $V_{z,f}$, whereas diagonal $V_{x,p}$ terms are already contained in $P H P$.