Altermagnetic boosting of chiral phonons

Abstract

Chirality characterizes the asymmetry between a structure and its mirror image and underlies a wide range of chiral functionalities. In crystallographically chiral materials, phonons with non-zero linear momentum $\textbf{k}$ can acquire a $k$-induced longitudinal magnetization, giving rise to chiral phonons. Helical spin order, with its proper screw-type configuration, breaks all mirror symmetries and therefore carries magnetic chirality. Such helical spins also generate non-relativistic spin splitting for any quasiparticle excitations propagating along the screw axis. To explore the possible connection between chiral phonons and magnetic chirality, we investigated the crystallographically polar and chiral compound (Mn,Ni)$_3$TeO$_6$, which hosts three distinct states: a paramagnetic state, a helical spin state with magnetic chirality, and a collinear spin state without magnetic chirality. We find an approximately tenfold enhancement of chiral-phonon coupling in the helical spin state along the screw axis, compared with both the paramagnetic and collinear spin states. These results identify a new route to amplify chiral phonons through an altermagnetic effect arising from the broken parity-time symmetry in helical spins. %from non-relativistic spin splitting.

Figures (5)

• Figure 1: Cartoon illustration of chiral phonons induced by helical spins. (a) crystal structure of Mn-doped Ni$_3$TeO$_6$ and illustration of its chiral phonons (the collective rotation of O ions is predominantly but not totally in the $ab$-plane and is shown for the second mode from the top of the spectrum given in Fig. \ref{['DFT']}). Ni$_3$TeO$_6$ crystallizes in a noncentrosymmetric corundum structure with three nonequivalent Ni sites. The crystal contains two kinds of honeycomb layers formed by edge-sharing NiO$_6$ and TeO$_6$ octahedra. Ni$_{\rm I}$O$_6$ and Ni$_{\rm II}$O$_6$ are ferromagnetically coupled and form one honeycomb layer, while Ni$_{\rm III}$O$_6$ and TeO$_6$ form the other. These honeycomb layers stack along the $c$-axis, generating a polar crystal structure Zivkovic2010OhNatComm2014WangAPLM2015. Additionally, the relative positions of these octahedra in the $ab$-plane revolve along the $c$-axis, demonstrating the handedness of crystal chirality. When Mn is doped into Ni$_3$TeO$_6$, the Mn ion predominantly occupies the Ni$_{\rm I}$ and Ni$_{\rm II}$ sites KimPRM2021. (b) Illustration of helical spins. Mn-doped Ni$_3$TeO$_6$ shows an incommensurate helical spin order between 60 K and 74 K. The arrows, with lengths indicating their relative magnitudes, represent the Ni or Mn spins, which are ferromagnetically aligned in each honeycomb layer, as depicted by colored disks. The modulation vector of helical spins was determined as $\vb{k} = (0, 0, 1.5{\pm}\delta)$ with $\delta = 0.146$ in r.l.u. KimPRM2021.
• Figure 2: Schematic diagram of O $K$-edge RIXS with circular polarization. This diagram illustrates the transitions involved in the O $K$-edge RIXS. Circularly polarized X-rays with energy $\omega_i$, polarization $\bm{\epsilon}_c$, and wavevector $\bm{k}_i$ excite an electron from the $1s$ core shell into an unoccupied state in the O $2p$ band through the dipole operator $\hat{D}_{\epsilon} ={\bm{\epsilon}_c}{\cdot}\bm{p}^{\dagger}s$, where $\bm{p}^{\dagger}$ and $s$ are creation and annihilation operators of the $2p$ and $1s$ electrons, respectively. The intermediate state is governed by a propagator $G$ determined by the ground-state Hamiltonian $H_0$ and the intermediate-state Hamiltonian $H_{\rm I}$, and the inverse core-hole lifetime $\Gamma$. The system then relaxes to the RIXS final state through $\hat{D}_{\epsilon}^{\dagger}$, emitting X-rays with energy $\omega_f$, polarization $\bm{\epsilon}'_c$, and wavevector $\bm{k}_f$. The energy loss is given by $\omega = \omega_{i} - \omega_f$. The electron-phonon coupling in RIXS leads to a measurement of phonon excitations AmentEPL2011geondzhianPRB2020DashwoodPRX2021okamotonpjQM2025. For chiral phonons, the RIXS circular dichroism, i.e., the contrast between RCP and LCP, results from the circular polarization of phonons.
• Figure 3: O $K$-edge XAS and photon-energy dependent RIXS of Mn-doped Ni$_3$TeO$_6$. (a) X-ray absorption spectrum measured using fluorescence-yield, RCP, and normal incidence relative to the $ab$ plane at 50 K. $\omega_{0}$ is XAS peak at 531.3 eV. (b) RIXS spectra measured using LCP at 50 K for the incident photon energies indicated by the vertical colored bars shown in (a). Spectra are vertically shifted for clarity. The inset illustrates the experimental geometry. The sample surface was the (001) plane. The scattering plane was in the $ac$ plane of the crystal, while the incident and the scattering angles were 50$^{\circ}$ and 90$^{\circ}$, respectively.
• Figure 4: Circular dichroism in chiral phonons of Mn-doped Ni$_3$TeO$_6$. (a) & (b) O $K$-edge RIXS of Mn-NTO sample measured with incident photon energy of $\omega_{0}-0.5$ eV and $q = (-0.027, 0.0135, 0.83)$ with RCP (red) and LCP (blue) at various temperatures at domain A(a) and B(b). RIXS spectra are normalized to the elastic peak intensity. Yellow and blue background indicate the antiferromagnetic (AFM) phases with helical spins (yellow) and collinear spins (blue). Clear difference between RCP and LCP, i.e. circular dichroism (CD) in phonon structures are observed at helical AFM phase though not or negligibily small at paramagnetic and collinear AFM phase. Sign of CDs are reversed between opposite chirality domains; negative (positive) in the domain A(B). (c) Transmission polarized optical microscope image of the sample. Bright and dark regions correspond to the domains of opposite chiralities: A (blue) and B (red) marks are the measured position of each domain and diameters of the marks show the incident beam size of 50 $\mu$m. (d) Temperature dependence of the CD ratio $2\times\frac{\rm RCP-LCP}{\rm RCP+LCP}$ of the first phonon structure at $\sim$90 meV. Strong CD as $\sim$30 % were observed in the helical AFM phase though those in the paramagnetic and collinear AFM phases were negligibly small as less than 5 %.
• Figure 5: DFT results of the lattice dynamics and phonon chirality simulations. (a) The phonon dispersion for the high-energy modes. The spectra are given for the primitive cell and the collinear antiferromagnetic. The color scale bar indicates the calculated value of the $z$-component of the circular phonon polarization for each mode. (b) The Brillouin Zone of the primitive cell of Ni$_3$TeO$_6$. The momentum transfer ${\bf Q}$ in RIXS measurements is (0.263 0.290 0.277) in units of the reciprocal lattice for the primitive cell.