Alteraxial Phonons in Collinear Magnets

Abstract

Axial phonons possessing nonzero angular momentum and resulting magnetic moment can couple to magnetic order. The rich magnetic structures enable phonon angular momentum (PAM) to acquire momentum-space textures analogous to electronic spin structures. However, a systematic framework for classifying these textures, especially their potential higher-order multipolar patterns, has remained elusive. Here, by employing magnetic point group analysis, we develop a complete classification of phonons in collinear magnets, spanning ferro-, antiferro-, and alter-magnets. Our theory distinguishes four fundamental types of magnetic phonons based on symmetry and PAM wave-pattern parity. Strikingly, we reveal a full sequence of axial phonons exhibiting higher-order-wave (from $p$- to $j$-wave) PAM patterns covering both odd and even parities, which we term alteraxial phonons. Our high-throughput calculations predict hundreds of magnetic candidates hosting such alteraxial phonons. Our work establishes a symmetry-guided design principle for axial phonons and related phenomena in magnetic materials.

Figures (3)

• Figure 1: Schematics of three distinct types of circularly polarized phonons in collinear magnets. Circular lattice vibrations in real space (top row), $\Gamma$-centered phonon spectra (middle row) and angular momentum patterns in momentum space (bottom row) for (a) ferro-axial, (b) antiferro-nonaxial and (c) alter-axial phonons in collinear magnets, respectively. The magnetization direction is set as the quantization axis for the phonon angular momentum. Blue and red colors represent the left- and right-handed circular polarization, respectively.
• Figure 2: High-throughput phonon calculations in collinear magnets. The workflow (a) consists of three parts: The gray-shaded part filters out collinear magnets from material databases and provides their crystal and magnetic structures along with the corresponding magnetic point groups (MPG); The cyan-shaded part classifies the phonon type according to the MPG, where the MPG integer denotes the number of symmetry-enforced nodal surfaces of vanishing phonon angular momentum crossing the $\Gamma$ point; The pink-shaded part performs ab initio calculations of magnetic phonon spectra. (b, c) High-throughput screening for all 1029 collinear magnets from the MAGNDATA database, with (b) distribution of materials across the four distinct phonon types and (c) number of materials hosting different wave patterns within the three axial phonon families.
• Figure 3: Phonon spectra and phonon angular momentum (PAM) patterns from ab initio calcualtions on representative materials hosting three different types of alteraxial phonons. CrSb (centro-even-wave), Cr$_2$SbAs (noncentro-odd-wave), and MnSe (noncentro-even-wave) are selected as illustrative cases. For each material, the top row shows the crystal and magnetic structures, the middle (bottom) row presents the $\mathcal{T}$-symmetric ($\mathcal{T}$-broken) phonon spectra and $\Gamma$-centered PAM patterns in the absence (presence) of $\mathcal{T}$-breaking perturbations.