Chiral Spin-Split Magnons in the Metallic Altermagnet CrSb

Abstract

We report the collective magnetism of the metallic altermagnet CrSb. Magnetic susceptibility and polarized neutron diffraction measurements show that CrSb is a perfectly compensated Ising altermagnet below a Néel temperature of $T_N = 733(4)$ K. Inelastic neutron scattering experiments reveal anisotropic and highly-dispersive antiferromagnetic spin waves with velocities of 61(2) km s$^{-1}$ and 58(2) km s$^{-1}$ along the in-plane and out-of-plane directions, respectively. The observed magnon dispersions along high-symmetry directions of the Brillouin zone are well described by a minimal Heisenberg model up to third nearest neighbors of alternating antiferromagnetic and ferromagnetic character, $J_1 = 23(4)$ meV, $J_2 = -5.4(8)$ meV, $J_3 = 5.2(8)$ meV, and an Ising single-ion anisotropy term $D = 0.15(4)$ meV. We observe clear signatures of chiral spin splitting along the low-symmetry $Γ$-$L$ direction, characteristic of higher-order altermagnetic exchange interactions, the first such observation in a metallic altermagnet.

Figures (3)

• Figure 1: Nuclear and magnetic structure of CrSb.(a) Crystal structure and altermagnetic ordered state of CrSb where the chromium spins are parallel to the c-axis. The nearest neighbor exchange pathways $J_1$ (AFM), $J_2$ (FM), and $J_3$ (AFM) are shown as solid black lines, while the dashed yellow line represents the weaker $J_{11}$ and $J_{12}$ exchange paths responsible for the altermagnetic splitting in the magnon spectrum. (b) The two opposite-spin sublattices, Cr$_{\mathrm{a}}$ and Cr$_{\mathrm{b}}$, are connected by a $C_2$ spin-space and $M_z$ real-space mirror symmetry. (c) Room temperature precession image from single crystal x-ray diffraction along (00$L$) direction parallel to the beam. (d) Longitudinal resistivity measured with $i\parallel c$ showing metallic behavior with RRR = 6 (inset: optical image of a needle-shaped crystal of length close to 1 cm). (e) High-temperature magnetic susceptibility measured with $H\parallel c$ = 0.10 T, showing the onset of AFM order at $T_N$ = 733(4) K. (f) Temperature-dependent integrated intensity of the (111) magnetic Bragg peak obtained with polarized neutron diffraction. Polarization dependence of the (g) (001), (h) (002), and (i) (201) Bragg peaks collected at T = 25 K, confirming the fully compensated altermagnetic ordered state shown in panel (a).
• Figure 2: Determination of the spin Hamiltonian of CrSb from inelastic neutron scattering.(a) Brillouin zone of CrSb with indicated high-symmetry directions. (b) INS spectrum of CrSb measured at 5 K around the (101) Bragg position with an incident neutron energy $E_i$ = 50 meV, revealing a magnon gap of 13(2) meV. The conical dashed lines represents the low-energy spin excitations simulated using the CrSb spin Hamiltonian described in the text. (c) The left panels are INS spectra of CrSb collected with $E_i$ = 750 meV along three high-symmetry directions. The right panels show the corresponding simulated spectra based on the fitted spin Hamiltonian. (d) The left panels show constant-energy slices within the ($H,0,L$) plane at 130, 185, and 230 meV. The right panels are calculated slices using the fitted CrSb spin Hamiltonian for comparison.
• Figure 3: Observation of spin-split magnons.(a) Simulated constant-energy slices within the ($H$$+$$K,\text{-}2K$,2.85) plane at 180 meV, illustrating the evolution of the spin excitation upon increasing the $J_{11}$ exchange parameter. (b) Experimental constant-energy slice acquired within the ($H$$+$$K$,$\text{-}2K$,2.85) plane at 180 meV. The white line denotes the Brillouin zone boundary, guide the eye to the 6-fold intensity distribution, highlighting the presence of splitting along the $(H,0,2.85)$ and its absence along the ($K$,$\text{-}2K$,2.85) direction. (c,d) The 180 meV 1-D intensity profile obtained along the $(H,0,2.85)$ and ($K$,-2$K$,2.85) directions, respectively. A clear splitting of 0.15 r.l.u along the $(H,0,2.85)$ direction and the absence of splitting along the ($K$,-2$K$,2.85) direction is a signature of altermagnetism. This observed splitting in $Q$-space can be produced by $J_{11}$ = 1.8 meV. (e) Simulated INS spectra for the $\Gamma$-L direction, where white dashed ellipsoid shows the location of the magnon splitting, assuming $J_{11}$ = 1.8 meV. (f) Experimental INS data acquired along the $\Gamma$-L direction matches well with simulated data but lacks the energy resolution to clearly resolve the splitting seen in the constant energy slice.