Elettra | APE-LE Three-dimensional mapping of the altermagnetic spin splitting in CrSb For decades, ferromagnetism and antiferromagnetism have been regarded as the two most fundamental types of magnetic orders. A novel type of collinear magnetism, dubbed altermagnetism, has recently attracted considerable interest in the field of condensed matter physics. In the absence of Spin-Orbit Coupling (SOC), altermagnets exhibit antiparallel collinear spin configuration with zero net magnetization. Unlike conventional antiferromagnets, the spin-opposite sublattices in altermagnets cannot be mapped onto each other by either realspace translation or inversion, lifting the Kramers spin degeneracy and resulting in momentum-dependent spin splitting in the band structure. The altermagnetic spin splitting originates from the interplay between crystal field and magnetic exchange interactions, which can have energy scales on the order of electron-volts (eV), enabling a wide range of exotic phenomena such as the anomalous Hall effect, spin current generation, spin caloritronics and etc.. Moreover, the absence of net magnetization makes altermagnets attractive for ultrafast spin manipulation and high-density, strayfield-free spintronic devices. The key physical manifestations of altermagnets originate from their anisotropic spin-polarized band structure. In this study, using synchrotron-based and spin-resolved Angle-Resolved Photoemission Spectroscopy (ARPES), we uncover a large altermagnetic splitting in CrSb with bulk-type g-wave character. CrSb crystallizes in the hexagonal NiAstype structure, as shown in Fig. 1 (a). The magnetic Cr (aligned along the [001] axis) are parallel within the hexagonal Cr layer and antiparallel between neighboring layers. As illustrated in Fig. 1 (b), the two Cr sublattices with opposite spins in CrSb are related by a spin group symmetry [C2 || Mz] or [C2 || C6z ]. Here C2 is the spin-flip operation, and Mz and C6z are the mirror operation and six-fold rotation along z axis combined with a translation t = (0,0, )c, both only acting in real space. Both the spin group symmetries [C2 || t] and [T || P] (space-time reversal) are broken in CrSb, resulting in momentumdependent altermagnetic spin splitting, unlike conventional antiferromagnets. The special spin group symmetry results in four spin-degenerate nodal planes labeled in Fig. 1 (c), referring to the bulk-type g-wave altermagnetism. The kz-dependent band splitting indicates the ”bulk-type” nature in CrSb, related to its [C2 || Mz] symmetry. We observed the largest altermagnetic spin splitting in CrSb near Fermi level, shown Fig. 1 (d). Its secondary derivative is shown in Fig. 1 (e): two sets of hole bands centered at Γ can be verified with an energy splitting up to 1.0 eV near EF, consistent with Density Functional Theory (DFT) calculations in Fig. 1 (f). The kx-kz map at E = -0.5 eV is shown in Fig. 1 (g): Along the P − Q path, the altermagnetic splitting, i.e., the separation between these two strings, is close to zero at kz = 0 and gradually increases to its maximal value at kz ~ 0.25c*, eventually decreasing to zero at kz = 0.5c*. The in-plane momentum dependence of the band splitting provides direct evidence for the g-wave altermagnetism in CrSb. Fig. 1 (h) shows the kx-ky map at E = -0.65 eV taken at kz ~ 0.28c* plane, where the flower-like pockets centered at Γ can be observed. The constant-energy contours from ab initio calculations are overlaid on top, consistent with the experimental data. To verify the spin polarization of the altermagnetically split bands, spinresolved ARPES measurements were conducted in BL9.2 APE-LE, Elettra. The spin-up/down distribution curves are shown in Fig. 1 (i), taken along the white dashed cut in Fig. 1 (e). Both curves exhibit a double-peak structure with large broadening. The obvious shifting of the peak center between these two curves reflects the spin splittings expected in CrSb. The corresponding spin polarization is extracted and shown in Fig. 1 (j). Our direct observation of appreciable spin polarization provides strong support for the altermagnetic spin splittings in CrSb. Moreover, our Tight-Binding (TB) model analysis indicates that the large altermagnetic splitting arises from strong Third-Nearest-Neighbor (3NN) hopping mediated by Sb ions. Both the Nearest Neighbor (NN) and the Next Nearest Neighbor (NNN) hopping terms preserve the translational spin-flip operation [C2 || t], thus incapable of lifting the Kramers spin degeneracy. By contrast, the second-order hopping process assisted by Sb 5p orbitals provides relatively large 3NN hopping parameters (q1,2,3,4), giving the large altermagnetic splitting. The spin polarized bands obtained from TB model and its dependence on 3NN parameters is shown in Figs. 1 (k-m). In summary, we present direct spectroscopic evidence of bulk-type g-wave altermagnetism in CrSb from high-resolution synchrotron-based and spin-resolved ARPES measurements. Our systematic kz and in-plane momentum dependent study confirms a large altermagnetic splitting up to 1.0 eV near EF, which is in good agreements with DFT. The spin polarization of split bands is further verified by spin-resolved ARPES measurements. Our TB model analysis reveals that the altermagnetic splitting arises mainly from the 3NN hopping of Cr 3d electrons mediated by Sb 5p orbitals, highlighting the important role of electronic coupling between magnetic and nonmagnetic ions. The insight can be important for finding/ tuning altermagnetic materials with enhanced properties. The large altermagnetic splitting near EF, together with the high ordering temperature up to 710 K in CrSb, paves the way for exploring emergent phenomena and practical applications based on altermagnets. Elettra Highlights 2024–2025 12
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