D-Wave Phonon Angular Momentum Texture in Altermagnets by Magnon-Phonon-Hybridization

TL;DR

We address how altermagnets can host chiral phonons by coupling magnons and phonons through a chirality-selective interfacial DMI, producing magnon polarons with phonon angular momentum textures that reflect the underlying $d$-wave spin texture. The approach combines a minimal 2D altermagnetic model with a linear spin-wave and magnetoelastic coupling analysis, revealing avoided crossings and sublattice-resolved $L_{ph}^z$ up to $\hbar/2$. This work establishes a mechanism for even-parity phonon angular momentum textures and proposes a phonon angular momentum splitter effect, highlighting potential applications in phononic analogues of electronic responses and tunability via magnetic fields.

Abstract

In altermagnets, the magnon bands are anisotropically spin-split in reciprocal space without relativistic or dipolar spin-spin interactions. In this work, we theoretically study magnons and phonons coupled by spin-lattice interaction in a two-dimensional square-lattice $d$-wave altermagnet. We show that phonon-chirality-selective magnon-phonon hybridization can be caused by interfacial Dzyaloshinskii-Moriya interaction leading to the emergence of hybrid quasiparticles that possess finite phonon angular momentum. These hybrid quasiparticles are called magnon polarons and consist of spin-polarized magnons and chiral phonons. Their phonon angular momentum texture follows the $d$-wave character of the magnon spin texture opening up the possibility of phononic counterparts to the electronic response effects in altermagnets, such as a \emph{phonon angular momentum splitter effect}, i.e., the generation of a transverse phonon angular momentum current induced by a temperature gradient -- the bosonic analogue of the spin-splitter effect.

Figures (5)

• Figure 1: Visualization of the generation of phonon angular momentum in altermagnets through the coupling with the underlying spin-split magnon band structure. Their hybridization selectively depends on the circular polarization of the phonons and, thus, it separates left- and right-handed phonons imprinting an alternating phonon angular momentum texture in reciprocal space.
• Figure 2: (a) Illustration of the minimal altermagnetic model. It comprises antiferromagnetic nearest-neighbor interactions and directional, ferromagnetic next-nearest neighbor interactions as indicated by the gray checkerboard pattern. (b) Magnon and phonon modes in the absence of spin-lattice coupling. The color indicates the magnon spin. Thus, the phonon modes are depicted in gray while the red and blue colors confirm the spin-dependent splitting of the magnon modes. Along the nodal lines $\overline{\Gamma \mathrm{M}}$ the two magnon bands are degenerate. Inset: Brillouin zone of the magnetic (structural) unit cell shown in black (gray). (The coordinate systems of the real and reciprocal spaces are rotated by 45° to each other.) The parameters used for the calculations are $J_{\mathrm{AFM}} = -1$, $J_{\mathrm{FM}_1} = 0.383$, $J_{\mathrm{FM}_2} = 0.5$, and $S = 1$.
• Figure 3: Coupling strength between the (a) upper, (b) lower magnon branch and the circularly and sublattice-polarized phonon modes. The background color and the line color indicate the signs of the magnon spin and the phonon angular momentum, respectively. The matching of colors indicates the chiral selectivity of the magnon-phonon coupling $\hat{H}_{\text{mpc}}$ [\ref{['eq:mpc']}]. Note that the magnon modes are degenerate along $\overline{\Gamma \mathrm{M}}$.
• Figure 4: Coupled magnon-phonon hybrid system. (a) Band structure of the magnon polarons along a high-symmetry path in the magnetic Brillouin zone. The color indicates the magnon/phonon character of the quasiparticles. The region highlighted by the green box and arrow is displayed in greater detail in (b)-(e). (b) Zoom of the avoided crossing pattern and quasiparticle character indicated by color. (c) Illustration of the same region but depicting the phonon angular momentum. (d), (e) Sublattice-resolved phonon angular momentum for sublattice $\uparrow$ and sublattice $\downarrow$, respectively. The insets demonstrate the real-space vibrational motion (amplitude and phase) of the respective sublattices. The parameters used for the calculations are $J_{\mathrm{AFM}} = -1$, $J_{\mathrm{FM}_1} = 0.383$, $J_{\mathrm{FM}_2} = 0.5$, $S = 1$, $M = 10$, $K_{\mathrm{L}}^{(1)} = 160$, $K_{\mathrm{T}} = K_{\mathrm{L}}^{(2)} = 40$, $D = 0.25$, and $a = 1$.
• Figure 5: Phonon angular momentum for all bands across the entire Brillouin zone. Non-zero angular momentum occurs around regions of avoided crossings and clearly reflects the $d$-wave character of the altermagnet. Bands are labeled in descending order starting with the highest energy. Parameters same as in \ref{['fig:hybridized_system']}.