Altermagnetism, ARPES, symmetry, non-relativistic band splitting

TL;DR

Altermagnetism describes a spin-polarized electronic structure that preserves zero net magnetization due to spin-group symmetries, yielding momentum-dependent nonrelativistic spin splitting. The paper surveys ARPES-based methods (ARPES, SARPES, CD-ARPES) within the spin-group framework and reviews key materials (e.g., RuO$_2$, KV$_2$Se$_2$O, Rb$_{1-\delta}$V$_2$Te$_2$O, MnTe, CrSb, MnTe$_2$), detailing direct band- and spin-resolved fingerprints and domain-dependent phenomena. It discusses emerging candidates and platforms, including 2D layered systems, density-wave coexisting altermagnetism, and Weyl-topology coupling, highlighting domain and strain engineering as routes to control spin textures. The outlook points to micro-beam ARPES, in-situ STM integration, and heterostructures as essential for resolving remaining debates and unlocking spintronic and correlated quantum technologies based on altermagnetic order.

Abstract

Altermagnetism arises from composite real-space and spin-space symmetries, combining zero net magnetization with pronounced momentum-dependent spin splitting. This review highlights the pivotal role of angle-resolved photoemission spectroscopy (ARPES), along with its spin-resolved (SARPES) and circular-dichroism (CD-ARPES) variants, in directly visualizing nonrelativistic band splitting and spin textures in altermagnets. Within the spin-group framework, we distinguish ferromagnetic, antiferromagnetic, and altermagnetic orders and elucidate the symmetry origin of spin polarization. We then systematically review representative systems: the debated d-wave prototype RuO2, layered d-wave altermagnets KV2Se2O and Rb1-delta V2Te2O, and a series of g-wave compounds including MnTe (domain-tunable) and CrSb (topological), together with the noncoplanar antiferromagnet MnTe2 and other emerging candidate platforms. Overall, ARPES has become a key probe for resolving symmetry-driven spin splitting. Future advances in micro/nano-beam and in-situ spectroscopies, combined with strain and domain engineering, heterostructure design, and exploration of broader unconventional magnetic states, are expected to drive the joint evolution of altermagnetism and photoemission spectroscopy, paving the way for spintronic and correlated quantum research.

Figures (10)

• Figure 1: Fundamental magnetic phases: classification and microscopic origins. a. Comparison of the three fundamental magnetic phases—FM, AFM, and AM—in terms of their crystal structure, time-reversal symmetry, band dispersion, and nontrivial spin group. Red (blue) arrows indicate spin-up (spin-down) statesvsmejkal2022beyondvsmejkal2022emergingmazin2022altermagnetismcheong2024altermagnetismgao2025ai. b. Representative spin-polarization symmetries of $d$-, $j$-, or $i$-wave altermagnetic statesvsmejkal2022beyondvsmejkal2022emergingtamang2025altermagnetismbai2024altermagnetism. c. Example of altermagnetic RuO$_2$, where the two Ru sublattices (Ru$_1$, Ru$_2$) are connected by a composite symmetry operation $[C_{2}||C_{4z}t]$.
• Figure 2: Experimental principles and spectral characteristics of advanced ARPES techniques. a. Schematic diagram of ARPES working principle lv2019angle-resolved. b. Representative ARPES energy-momentum dispersion spectrum zhang2022angle-resolved. c. Schematic illustration of SARPES apparatus with spin detection okuda2011efficient. d. Typical spin-resolved energy distribution curves measured by SARPES zhang2022angle-resolved. e. Operational principle of CD-ARPES using circularly polarized light yen2024controllable.
• Figure 3: Summary of the major advances in the magnetic studies of RuO$_2$berlijn2017itinerantzhu2019anomalousfeng2022anomalousfedchenko2024observationzhang2025probingkessler2024absencewenzel2025fermihiraishi2024nonmagneticplouff2025revisitingwu2025fermiwang2025robustuchida2020superconductivityruf2021strainliu2024absence. a. Neutron diffraction revealing scattering intensity at structurally forbidden reflections. b. Resonant X-ray scattering showing polarization-dependent intensity indicative of a magnetic contribution. c. Transport measurements on epitaxial thin films revealing an anomalous Hall effect. d. ARPES combined with magnetic circular dichroism, providing momentum-resolved evidence for time-reversal symmetry breaking at the band-structure level. e. X-ray magnetic linear dichroism measurements showing pronounced, orientation-dependent dichroic signals. f. ARPES results of single crystals and thin films, in good agreement with nonmagnetic DFT calculations. g. $\mu$SR measurements (left) setting stringent upper bounds on the Ru magnetic moment, and neutron diffraction measurements (right) showing no clear magnetic peak at (100). h. ARPES and SARPES results showing the absence of the momentum-dependent band splitting expected for altermagnetism. i. Complementary probes of the electronic ground state, including optical conductivity (left) and quantum oscillations (right), whose data are better reproduced by nonmagnetic calculations.
• Figure 4: Electronic and magnetic properties of the layered altermagnet KV$_2$Se$_2$Ojiang2025metallic. a. Crystal structure of KV$_2$Se$_2$O showing the V$_2$O planes with alternating spin orientations connected by the spin-group symmetry [$C_2||C_{4z}$]. b. Comparison between experimental ARPES dispersions and theoretical band calculations along high-symmetry directions. c,d. Fermi surface mappings and corresponding calculations. e. Temperature-dependent $^{51}$V NMR spectra under $\mu_0H=0.8$ T. f. Band dispersions and SARPES momentum distribution curves (MDCs) and spin polarizations along cuts 1 and 2. g. Band dispersions along cuts 3 and 4, where $\alpha$, $\beta$, $\gamma$, and $\delta$ denote the original bands, while $\alpha'$, $\gamma'$, and $\delta'$ represent their folded counterparts. h. Temperature-dependent energy distribution curves (EDCs) showing that the SDW gap persists above the transition temperature. i. Schematic magnetic structure of the SDW phase. The antiparallel spin sublattices are linked by the [$C_2||M_{1\bar{1}0}$] symmetry, maintaining compensated magnetization while preserving the underlying $d$-wave altermagnetic order.
• Figure 5: C-paired SVL and its experimental verification in layered altermagnet Rb$_{1-\delta}$V$_2$Te$_2$Ozhang2025crystal. a. Schematic illustration of three types of SVL. In T-paired SVL, spin splitting at opposite valleys arises from SOC. Type-I C-paired SVL features isotropic conductance for both spin channels, leading to non-polarized spin currents, while Type-II C-paired SVL exhibits anisotropic conductance and enables pure spin currents under an in-plane electric field. b. Crystal and magnetic structure of Rb$_{1-\delta}$V$_2$Te$_2$O. c,d. Calculated and ARPES-measured Fermi surfaces in the $k_x$–$k_y$ plane. e. ARPES intensity plot along $\Gamma$–$X$–$M$–$Y$–$\Gamma$ showing the main $\alpha$, $\beta$, and $\gamma$ bands, where the $\alpha$ and $\gamma$ branches carry spin polarization of one sign, and $\beta$ exhibits the opposite sign. The dashed red and blue curves represent calculated bands with opposite spin polarization. f. Temperature-dependent ARPES spectra measured along the $M$–$X$–$M$ direction from 30 K to 300 K. g. SARPES measurements taken along Cut 1 (top) and Cut 2 (bottom). Panels (1) show the spin-resolved band dispersions, and panels (2) display the extracted spin polarizations. h. QPI patterns from STS and corresponding JDOS and spin-dependent scattering probability (SSP) simulations.