Flat band driven competing charge and spin instabilities in the altermagnet CrSb

Abstract

The confinement of electronic wavefunctions in momentum space can give rise to flat electronic bands, where the quenching of kinetic energy enhances the density of states and amplifies interaction effects. Such conditions are fertile ground for emergent quantum phases, as spin, charge and lattice degrees of freedom become strongly entangled. In these regimes, subtle competitions between intertwined order parameters often dictate the macroscopic ground state, producing complex and sometimes unexpected collective behavior. Here we show that the altermagnet CrSb provides a realization of this scenario, and uncover short-range charge-order fluctuations at the M point of the Brillouin zone, q*=(1/2 0), persisting above the Neel temperature (TN). Remarkably, these fluctuations collapse upon entering the magnetically ordered phase, revealing a direct and robust competition between charge and spin order. At TN, the phonon dispersion at q* develops a pronounced Kohn-like anomaly, signaling strong electron-phonon coupling in the vicinity of the magnetic transition. Below TN, exchange striction dramatically renormalizes the associated soft phonon mode by approximately ~6 meV, the largest spin-phonon coupling ever reported. First-principles calculations attribute this behavior to a strong coupling between nearly dispersionless electronic states and a phonon branch that appears unstable at the harmonic level only when no magnetic order is considered, revealing the large sensitivity of the lattice to magnetic symmetry breaking. The competition between charge and spin order parameters, amplified by flat-band physics, drives the observed phonon anomaly and its abrupt reconstruction at TN. With its chemically simple structure and symmetry-protected altermagnetic state, CrSb emerges as a model platform to explore how flat electronic bands mediate giant spin-phonon coupling and competing broken symmetries.

Figures (4)

• Figure 1: Crystal and magnetic structure of CrSb and DFT calculations. (A) Antiferromagnetic unit cell of CrSb, with alternating collinear magnetic moments on the Cr sites oriented along the c-axis. (B) Brillouin zone of CrSb in the space group P6$_3$/mmc, showing the high symmetry directions. (C-D) Temperature dependence of the lattice parameters. The temperature dependence of the volume is mostly determined by the c-axis expansion with increasing temperature. (E) Harmonic DFPT phonon dispersion of CrSb in the paramagnetic state (blue), overlaid with the magnetic calculations (red). (F-G) Electronic band structure of CrSb obtained from DFT in the non-magnetic (F) and antiferromagnetic phases (G) with the DOS in the side panels. The total DOS phonon DOS (black line) is projected into Cr $3d$ and Sb $5p$ states. The color code in the band structure indicates the strength of the real part of the static band resolved nesting function $\chi_{n}(\mathbf{k})=\sum_m\sum_\mathbf{q}(f_n(\mathbf{k})-f_m(\mathbf{k}+\mathbf{q}))/(\epsilon_n(\mathbf{k})-\epsilon_m(\mathbf{k}+\mathbf{q})+i\delta)$, being $f_n(\mathbf{k})$ the occupation of the state $n$ at wavevector $\mathbf{k}$, $\epsilon_n(\mathbf{k})$ its energy, and $\delta$ a finite infinitesimal real number. The scale bar is common for both plots.
• Figure 2: Diffuse Scattering results. (A-F) Comparison of the DS maps measured at 300 K (bottom part) and above $T_\mathrm{N}$ (upper part). Appropriate Laue symmetry was applied to the reconstructed layers to remove detector gaps and improve signal-to-noise ratio. (G-H) Temperature dependence of DS integral intensity and correlation length, respectively, obtained after peak fitting in the regions of interest (ROIs) shown in (A) and (E). The color scheme corresponds to the respective ROIs. The error bars represent the fit uncertainty.
• Figure 3: Inelastic x-ray scattering and Kohn-like anomaly. (A-B) Top panels, energy-momentum IXS maps along the H03 direction at 293 K and 750 K, respectively, showing the soft phonon dispersion and enhancement of phonon intensity near the AFM transition temperature. Bottom panels, first-principles calculated IXS spectral functions including the structure-factor $S_n(\mathbf{q}+\mathbf{G})$. An arbitrary linewidth is chosen for visualization. The magnetic and non-magnetic phonons were obtained via DFPT at the harmonic level and considering non-perturbative anharmonicity within the SSCHA at 750 K, respectively. The SSCHA phonons are calculated from the Hessian of the SSCHA free energy (see Ref. PhysRevB.96.014111 for more details). (C) Representative IXS spectra at the (0.5 0 3) M point measured between 200 K and 950 K. The elastic line (zero energy loss) and two individual phonon modes are shown as area plots, together with their total fit (solid line) for each spectrum. (D) Fitted $\omega_1$ phonon dispersion as a function of temperature, highlighting the Kohn-like anomaly at the M point at high temperature. (E) Temperature dependence of the $\omega_1$ phonon energy at the M point measured along the H03 and HH2 directions, together with the nearly unchanged higher-energy optic mode $\omega_2$. (F-G) Fitted $\omega_1$ phonon intensity and linewidth, respectively, as a function of momentum transfer at selected temperatures. The error bars represent the fit uncertainty.
• Figure 4: Fermiology and linear response electron-phonon coupling in CrSb. (A) Fermi-surface of the non-magnetic phase. (B) Calculated nesting function $\chi_0"(\mathbf{q})=\sum_{nm\mathbf{k}}\delta(\epsilon_n(\mathbf{k})-E_F)\delta(\epsilon_m(\mathbf{k}+\mathbf{q})-E_F)$ for the non-magnetic (black) and magnetic (red) phases. (C) Spin-resolved Fermi surface of the magnetic phase. Red and blue tones denote spin-up and spin-down bands, respectively. (D) Linear-response electron–phonon linewidths for the non-magnetic (black) and magnetic (red) phases. (E) Temperature dependence of the AFM neutron scattering intensity (blue diamonds, adapted from singh2025chiral), the nearest-neighbour in-plane Cr--Cr distance (black filled circles), and the phonon intensity of the $\omega_{1}$ mode (open circles). (F) Candidate lattice distortions of the non-magnetic phase involving in-plane and out-of-plane displacements of Cr and Sb atoms.