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Liu Yang, 1, 2 Yuan-Yuan Jiang, 3 Xiao-Yan Guo, 1,* Yi-Dong Liu, 1, 2 Xian-Zhe Chen, 4 Wen-Jian Lu, 1 Yu-Ping Sun, 5,1,6
Ming Li, 7,† and Ding-Fu Shao 1,§
1 Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
2 University of Science and Technology of China, Hefei 230026, China 3 Anhui Provincial Key Laboratory of Magnetic Functional Materials and Devices, School of Materials Science and Engineering, Anhui
University, Hefei 230601, China 4 Frontier Institute of Chip and System, State Key Laboratory of Integrated Chips and Systems, Zhangjiang, Fudan International Innovation
Center, Fudan University, Shanghai 200433, China 5 Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of
Sciences, Hefei 230031, China 6 Collaborative Innovation Center of Microstructures, Nanjing University, Nanjing 210093, China
7 University of Electronic Science and Technology of China, Chengdu 611731, China
† [email protected]; ‡ [email protected]; § [email protected] Altermagnets provide a promising platform for spin-polarized transport without net magnetization, but their transport properties are usually discussed in terms of momentum-space spin splitting. Here, using first-principles calculations and quantum transport simulations, we show that the charge-ordered altermagnet α-Fe 2 PO 5 exhibits a distinct form of realspace spin selectivity despite weak altermagnetic spin splitting near the Fermi level. The charge order creates inequivalent Fe 2+ and Fe 3+ sites within each sublattice, while the puckered C-type antiferromagnetic stacking suppresses intersublattice transport. As a result, electron and hole doping activate spin-polarized transport predominantly through Fe 3+ - and Fe 2+ -based channels, respectively. These atom-selective channels carry opposite spin polarizations on the two antiferromagnetic sublattices, giving rise to a globally compensated charge current with hidden Néel spin character. We further propose an all-in-one α-Fe 2 PO 5 tunnel junction, where matching or mismatching atom-selective conduction channels yields orders-of-magnitude conductance modulation. Our findings establish a real-space design principle for atomically controlled spin functionality and spintronic devices.
The study of charge and spin transport in magnetic materials has long been dominated by a momentum-space perspective, where electronic band structures provide a powerful framework for understanding macroscopic conduction properties. In particular, spin-polarized transport in ferromagnets is well explained by spin-split bands, leading to phenomena such as magnetoresistance [1-8] and spin-transfer torques. [9-11] This approach has been successfully extended to antiferromagnetic (AFM) systems in recent years, where symmetry analysis has revealed unconventional AFM phases—such as non-collinear antiferromagnets [12-19] and altermagnets [20-31]—that exhibit momentum-dependent spin splitting even in the absence of net magnetization. These discoveries have established that antiferromagnets can also support spin-dependent transport properties, enabling high-performance spintronic devices such as AFM tunnel junctions. [14-18,32-35]
While such a momentum-space description effectively captures macroscopic transport signatures, it often over-looks the local and atomically-resolved character of elec-tron flow. In real materials, spin-polarized currents may propagate along specific atomic paths, guided by the local magnetic order, the stacking sequence of magnetic layers, and the valence states and orbital occupations of constituent atoms. These microscopic details are averaged out in con-ventional band-theory approaches, yet they are crucial for understanding spatially heterogeneous transport, especially in doped or chemically complex systems where electronic states become highly localized.
Importantly, this real-space perspective has already yielded significant insights into the nature of local spin transport. [36-40] For instance, in collinear antiferromagnets with specific magnetic stackings—such as the C-type, A-type, and X-type orders—the arrangement of magnetic sublattices directly governs the emergence and pathway of sublattice-confined spinpolarized currents, i.e., the Néel spin currents. [36] These phenomena underscore that the real-space magnetic architecture is a fundamental determinant of spin current propagation, providing a critical complement to the momentum-space picture.
To further explore emergent local transport phenomena in complex magnetic structures, we investigate α-Fe 2 PO 5 —a collinear altermagnetic insulator with a puckered C-type stacking and a charge-ordered state of Fe 2+ and Fe 3+ cations that distorts the FeO 6 octahedral chains. [41,42] Based on firstprinciples calculations, we demonstrate that this system hosts doping-dependent, atom-selective Néel spin currents. Although the structural distortion induces strong in-plane anisotropy and associated d-wave altermagnetism, the spin splitting near the Fermi level remains weak due to suppressed intra-sublattice coupling. Remarkably, calculations of local conductance reveal that the spin current flows exclusively along distinct atomic channels depending on doping type: predominantly through Fe 3+ 1 The Fe X2 sites host Fe 3+ ions with FeO 6 octahedra sharing faces with the Fe 2+ chains on one side and alternate with PO 4 tetrahedra on the other, collectively constructing a three-dimensional framework. Correspondingly, the calculated magnitudes of magnetic moments for Fex 1 and Fe X2 are 3.89 μB and 4.23 μB, respectively, in good agreement with experimental data. [41,42]
α-Fe 2 PO 5 adopts a puckered C-type AFM configuration. Magnetic moments are ferromagnetically aligned along each puckered chain running along [010], while neighboring chains belonging to different magnetic sublattices are coupled antiferromagnetically. The Néel vector lies along the chain direction. Within a given sublattice, Fe 2+ O 6 and Fe 3+ O 6 octahedra are connected via face-sharing, producing strong intra-sublattice magnetic coupling, whereas octahedra belonging to different magnetic sublattices are linked only through corner-sharing oxygen atoms, resulting in much weaker inter-sublattice coupling.
The spin space group of α-Fe 2 PO 5 is , in which the two magnetic sublattices break the combined spacetime inversion symmetry but are related by a rotation-translation symmetry operation, placing α-Fe 2 PO 5 in the class of altermagnets and allowing spin-split band structure. This symmetry allows momentum-dependent spin splitting while simultaneously imposing strong constraints on its magnitude and distribution in reciprocal space, as illustrated in Figs. 2 and 3.
Fig. 2 shows the calculated band structure and density of states (DOS) near the Fermi level (E F ) for α-Fe 2 PO 5 . The system exhibits an overall semiconducting state, with bands remaining nearly spin-degenerate along most high-symmetry directions over the Brillouin zone (Fig. 1c). Notably, along the Γ-U direction, finite but small spin splitting appears in both the conduction and valence bands, as highlighted in Fig. 2(b). Near the conduction-band minimum (CBM) and valence-band maximum (VBM), the spin splitting reaches approximately 6.9 and 9.8 meV.
To further characterize the weak altermagnetic splitting in momentum space, we examine the spin-resolved constantenergy surfaces and the corresponding conducting channels at four representative energies, and in the conduction band and and in the valence band, as marked by the blue dashed lines in Fig. 2(c). As shown in the top two rows of Fig. 3, the spin-up and spin-down constant-energy surfaces have nearly identical shapes at all selected energies, consistent with the small spin splitting observed in the band structure in Fig. 2(b).
We further project these states onto the two-dimensional transverse Brillouin zone perpendicular to [010] transport direction to calculate the transverse-momentum-resolved spin
-based channels under electron doping and Fe 2+ -based channels under hole doping. This behavior cannot be inferred from band dispersions or momentum-space spin splitting alone; it requires resolving how site-selective electronic states are connected into continuous transport pathways in real space. By combining realspace magnetic structure analysis with atom-resolved electronic states, we elucidate how the local stacking environment and atomic valence govern the spin-current pathways. Building on this atom-selective transport mechanism, we further propose a proof-of-principle all-in-one tunnel junction based on α-Fe 2 PO 5 and show that orders-of-magnitude conductance modulation can be achieved by controlling the matching and mismatching of real-space atomic conduction channels. Our findings not only deepen the understanding of microscopically heterogeneous spin transport, but also provide guidelines for designing materials with atomically controlled spin conduction for functional spintronic devices.
First-principles calculations were performed within the framework of density functional theory (DFT) [43] using the QuantumATK. [44] The calculations employed a spin-polarized GGA+U functional [45,46] with an effective Hubbard U = 3 eV applied to the Fe 3d orbitals, non-relativistic Fritz-Haber Institute (FHI) pseudopotentials, [47,48] and a plane-wave cutoff energy of 80 Ry. Quantum transport calculations were performed using the non-equilibrium Green’s function (NEGF) formalism. [49,50] A k-point grid of 11×11×101 was used along the transport direction.
α-Fe 2 PO 5 crystallizes in an orthorhombic structure with space group Pnma and exhibits AFM order below 250 K. Its crystal and magnetic structures are shown in Fig. 1. The projection onto the (010) plane (Fig. 1a) highlights the pronounced in-plane structural anisotropy and reveals two magnetically inequivalent sublattices, denoted as Fe A and Fe B within the unit cell. As illustrated in the side view in Fig. 1(b), each magnetic sublattice contains two crystallographically distinct Fe sites with different valence states. Specifically, the Fex 1 (X = A, B) sites are occupied by Fe 2+ ions, whose FeO 6 octahedra share O-O edges to form one‑dimensional chains extending along the [010] axis.
, where ↑ ∥ and ↓ ∥ are the transverse-momentum-resolved numbers of conducting channels. As shown in the bottom row of Fig. 3, the nonzero spin polarization occupies only a small portion of the transverse 2 where equivalent Fe atoms host a mixed-valence of +2.5, an itinerant d electron shared between the Fe sites must align antiparallel to the five localized d electrons. Then, the structural distortion lifts this equivalence, splitting the bands and producing Fe X1 and Fe X2 sites, yet the spin character of the states at both the CBM and VBM remains antiparallel to the local moments.
Therefore, although the total DOS is spin-degenerate and the spin splitting in the band structure is very weak, the electronic states near the band edges exhibit strong site- and spin-selective features. Consequently, electrons doped into the CBM or holes doped into the VBM predominantly occupy a single spin channel localized on a specific Fe valence site, providing the microscopic prerequisite for sublattice-dependent spin transport and facilitating the emergence of Néel-type spin currents in α-Fe 2 PO 5 .
To explicitly demonstrate how charge or spin currents are distributed among inequivalent atomic sites in real space, we hereby turn to an analysis of the sublattice-resolved transport by computing the bond-resolved charge transmission = ↑ + ↓ (Figs. 4a and b) and the corresponding spin-resolved bond transmission = ↑ − ↓ (Figs. 4c and d) along the [010] direction, following Ref. [37]. We use ( ) as the representative energy to show the case of the n-doped (p-doped) α-Fe 2 PO 5 . For , charge transmission is dominated by hopping within ferromagnetically aligned chains formed by Fe 3+ ions (Fig. 4a). In contrast, for , transport proceeds primarily along Fe 2+ chains. This valence-dependent transport behavior directly reflects the orbital-resolved DOS in Fig. 2(c), where CBM (VBM) states originate predominantly from Fe 3+ (Fe 2+ ) ions. In both doping regimes, charge transmission between neighboring
3
arises from the large inter-chain separation and the cornersharing connectivity between sublattices, which significantly weakens inter-sublattice hopping. Consequently, charge transport in α-Fe 2 PO 5 is effectively confined within individual magnetic sublattices and proceeds predominantly along the chain direction.
The corresponding spin-resolved bond transmission (Figs. 4c and 4d) further reveals pronounced sublattice and valence selectivity. Spin transport is almost entirely confined to intrasublattice bonds, demonstrating that spin-polarized carriers propagate coherently along the ferromagnetically aligned chains. Electron doping activates spin transport predominantly on Fe 3+ sites, whereas hole doping restricts it to Fe 2+ sites, which, again, reflects the site-resolved spin polarization of the electronic states (Fig. 2c). This spin selectivity of the electronic states near E F effectively acts as a spin-dependent filter that blocks spinconserving hopping between sublattices, which strongly suppresses the inter-sublattice spin transport, even though Fe A and Fe B chains are structurally connected through shared oxygen atoms. Consequently, α-Fe 2 PO 5 supports highly spin-polarized and valence-ordered spin transport along the chain direction. An electric field applied along [010] drives parallel charge currents in Fe A and Fe B chains but with opposite spin polarizations, giving rise to robust Néel spin currents within the globally spin neutral charge current.
Visualization of the real-space current distribution within the unit cell (Figs. 4e and 4f) further clarifies the microscopic hopping mechanisms. Under electron doping, electrons hop between neighboring Fe 3+ O 6 octahedra via intervening PO 4 tetrahedra, forming the shortest available hopping path. In contrast, hole-doped transport is dominated by direct hopping between adjacent Fe 2+ O 6 octahedra through shared O-O edges. These distinct hopping geometries underpin the observed atomselective spin-current channels.
This doping-tunable, atom-selective Néel spin current presents intriguing opportunities for novel physics and device applications. As a proof of principle, we consider an all-in-one α-Fe 2 PO 5 tunnel junction along the [010] direction, in which the left and right regions are charge doped and serve as conducting electrodes, while the central pristine region remains insulating and acts as the tunnel barrier, as schematically shown in Fig. 5(a). The doping type on each side may be controlled independently, for example, by electrostatic or ionic-liquid gating, allowing the active atomic conduction channel to be selected separately in the two electrodes. Electron doping activates Fe 3+ -based channels, whereas hole doping activates Fe 2+ -based channels. Therefore, identical doping on the two sides produces matched real-space channels, while opposite doping produces mismatched channels.
We consider two representative doping regimes: and qualitatively represent shallow n- and p- doping, whereas 4 Table 1: The total transmissions ( ) for the all-in-one α-Fe 2 PO 5 tunnel junction.
T1 1 1 1 1 1 2 2 2 2 2 2
and represent a deeper-doping regime. A common feature in both regimes is that the transmission is much larger when the two electrodes have the same doping type, namely , , , and , than when they have opposite doping types, namely
and , as listed in Table 1. Thus, switching the relative doping polarity of the two electrodes provides a direct way to switch the junction between high- and low-transmission states
If one only considers the shallow-doping case, the suppressed transmission in the configuration may appear to originate from a momentum-space channel mismatch. As shown in Fig. 5(b,c), at the n-doped energies , the conducting channels appear away from the zone center, while at the holedoped energies , the available conducting channels are mainly located around the Brillouin-zone center. Consequently, the left and right electrodes in the configuration have the negligible overlap in their available ∥ -resolved conducting channels, naturally leading to weak transmission (Fig. 5d).
However, this momentum-space picture alone cannot explain the deeper-doping case. While the transmission in the configuration is indeed larger than that of due to the deeper doping level, it remains significantly lower compared to the case of or (Table 1). In the configuration, the n- and p-doped electrodes exhibit a partial overlap of their ∥ -resolved conducting channels (Figs. 5e and f). Nevertheless, the transmission remains strongly suppressed even within the overlapping region. This behavior demonstrates that the ON/OFF effect is not governed solely by momentum-space channel overlap. Instead, its more fundamental origin lies in the mismatch of real-space atom-selective transport pathways. Electron doping activates Fe 3+ -based channels, whereas hole doping activates Fe 2+ -based channels. Because these two types of atomic channels are spatially distinct and only weakly connected, a carrier injected from an Fe 3+ -dominated channel on one side cannot efficiently continue into an Fe 2+ -dominated channel on the other side. Therefore, matched doping preserves continuous real-space atomic pathways and yields a hightransmission state, whereas opposite doping breaks this channel continuity and produces a low-transmission state.
These results establish real-space atom-selective channel matching as the central mechanism behind the large ON/OFF modulation in the proposed α-Fe 2 PO 5 junction (Table 1). Although relatively large doping levels are used here to make the contrast between the two channel types explicit, the essential channel selectivity already appears near the band edges, suggesting that sizeable conductance modulation may be achievable at lower carrier densities.
Moreover, since doping renders the DOS of either Fe 2+ or 3+ Fe atoms fully spin-polarized, an injected spin current can flow only into one type of spin-polarized atomic channel. This enables spin torque to be precisely applied to specific atoms within a chosen sublattice. Such a highly asymmetric spin torque is expected to induce unconventional magnetic dynamics.[51] Experimentally, such atom-selective Néel spin currents can be detected in real space using spin-polarized scanning tunneling microscopy (SP-STM). [52]
In summary, we have demonstrated atom-selective spinpolarized transport in the charge-ordered altermagnet α-Fe₂PO₅. Although the altermagnetic spin splitting near the Fermi level is weak, charge-order-induced site-selective band-edge states and suppressed inter-sublattice connectivity enable electron and hole
5 doping to activate distinct Fe 3 ⁺- and Fe 2 ⁺-based transport channels. The opposite spin polarizations on the two antiferromagnetic sublattices give the compensated charge current a hidden Néel spin character. The proposed all-in-one junction further shows that real-space channel matching can be converted into a large conductance modulation. These findings not only highlight the decisive role of real-space magnetic connectivity and valence order in spin transport of altermagnets but also provide a design principle for spintronics.
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Acknowledgments. This work was supported by the National Key R&D Program of China (Grant No. 2024YFB3614100 and 2022YFA1403200), the National Natural Science Foundation of China (Grants Nos. 12241405, 12274411, and 12504098), the Basic Research Program of the Chinese Academy of Sciences Based on Major Scientific Infrastructures (Grant No. JZHKYPT2021-08), and the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-084). The calculations were performed at Hefei Advanced Computing Center.
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