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Emergent d-wave altermagnetism in chlorine-adsorbed FeSe monolayer

Zi-Hao Ding1 , Ze-Feng Gao1 , Kai Liu1 , Peng-Jie Guo1 ,∗ and Zhong-Yi Lu1 ,2†

arXiv:2607.15197v1 [cond-mat.mtrl-sci] Jul 2026

  1. School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education),

Renmin University of China, Beijing 100872, China and

2. Hefei National Laboratory, Hefei 230088, China

2. Hefei National Laboratory, Hefei 230088, China (Dated: July 17, 2026) The recent emergence of altermagnetism has opened new frontiers in condensed matter physics, yet material platforms capable of hosting both intrinsic altermagnetic order and superconductiv- ity remain exceedingly rare. Here, based on symmetry analysis and first-principles calculations, we propose a realistic route to engineer robust altermagnetism in monolayer FeSe, a prototypical iron-based superconductor. By designing a stoichiometric Fe2 S e2 C l structure through single-side Cl adsorption and introducing gate-tunable hole doping, we achieve a highly stable altermagnetic ground state. Our calculations reveal a synergistic mechanism: hole doping firmly stabilizes the checkerboard magnetic order, while the asymmetric ligand environment intrinsically breaks the out- of-plane spatial inversion symmetry. Consequently, this interplay induces a giant altermagnetic spin splitting of up to 620 meV. Crucially, we demonstrate that this altermagnetic state and its giant spin splitting are highly resilient, persisting even in a 10-layer slab model that accurately simulates the bulk limit. By introducing altermagnetism into the well-established FeSe-based superconduct- ing family, our findings identify Fe2 S e2 C l as a promising platform for spintronic applications and motivate future studies of the possible interplay between altermagnetism and superconductivity.

I. INTRODUCTION Altermagnetism has recently emerged as a fundamen- tally distinct magnetic phase, uniquely combining the fully compensated macroscopic magnetization of antifer- romagnets in real space with the momentum-space spin polarization characteristic of ferromagnets [1, 2]. Driven by either crystal potentials or spontaneous correlations, altermagnets exhibit unconventional anisotropic (e.g., d-, g-, or i-wave) alternating spin polarization without rely- ing on relativistic spin-orbit coupling [3]. This distinctive electronic structure fundamentally breaks macroscopic time-reversal symmetry, giving rise to a host of novel phenomena, including spin currents [4–8], a diverse fam- ily of anomalous Hall effects [9–16], and ferroelectricity [17–20]. Furthermore, altermagnetism can induce novel density wave phases [21–24], further enriching the land- scape of correlated phenomena. In particular, its inter- play with superconductivity and altermagnetic fluctua- tions is being actively investigated—both as an intrinsic phenomenon in bulk systems where pairing and alter- magnetic order coexist, and in heterostructures where it is induced via the proximity effect [25–32]. In a more fundamental sense, these materials can be viewed as the magnetic counterpart to unconventional d-wave super- conductors, deepening the profound physical analogy be- tween magnetism and superconductivity. Indeed, a compelling connection between alter- magnetism and high-temperature superconductivity is rapidly emerging in canonical material families. For ex- ample, La2 C uO4 , the parent compound of cuprate su- perconductors, has been identified as an altermagnet ∗ [email protected] † [email protected] [1]. Recent first-principles studies have revealed that high-pressure vacancy-ordered iron selenides (A2 F e4 S e5 phase) undergo a magnetic phase transition from a block- spin antiferromagnetic phase to an intrinsic N´eel alter- magnetic phase [33]. However, material candidates for altermagnetism-related superconductivity (SC) are cur- rently still lacking and remain elusive. In this context, FeSe, the structurally simplest iron-based superconduc- tor, emerges as an exceptionally promising platform. It hosts remarkably rich physics, where its unique nonmag- netic nature provides a challenging testing ground for conventional spin-fluctuation pairing mechanisms. Fur- thermore, the superconducting transition temperature (Tc ) of FeSe exhibits striking tunability. The Tc of FeSe, while below 8 K at ambient pressure [34], reaches 36.7 K under an applied pressure of 8.9 GPa [35]. Owing to its weak interlayer van der Waals bonding, FeSe is easily processed via mechanical exfoliation or chemical inter- calation. Moreover, carrier density in FeSe flakes can be drastically tuned through ionic liquid gating, which further enhances the superconductivity up to 43 K [36]. Monolayer FeSe grown on SrTiO3 substrates by molecu- lar beam epitaxy (MBE) has achieved high-temperature superconductivity exceeding 65 K [37–39], opening ex- citing new avenues for exploring two-dimensional inter- facial superconductivity enhancement. Theoretical pre- dictions suggest that applying an out-of-plane electric field to monolayer FeSe with a checkerboard magnetic or- der can induce an altermagnetic state accompanied by a quantized spin Hall conductivity [40]. However, in mono- layer FeSe, the checkerboard order is merely one of sev- eral competing magnetic phases, and the primary role of the applied electric field is simply to render the top and bottom ligand layers chemically distinct. Such an ap- proach relies heavily on extrinsic perturbations and spe- cific metastable states. Consequently, a natural question

2 arises: can robust altermagnetism be induced in mono- layer FeSe? In this work, we propose a practical route to re- alize a stable altermagnetic phase in monolayer FeSe through single-side Cl adsorption—forming a stoichio- metric Fe2 S e2 C l structure—combined with hole doping via ionic gating. Our systematic investigations reveal that hole doping effectively stabilizes the checkerboard magnetic order as the robust ground state. Concur- rently, the asymmetric Cl adsorption permanently distin- guishes the top and bottom ligand environments, intrinsi- cally breaking the out-of-plane spatial inversion symme- try. This synergistic interplay naturally induces a robust altermagnetic state, yielding a giant altermagnetic spin splitting of up to 620 meV. Crucially, this altermagnetism and its associated spin splitting remain highly robust even when the model is extended to a 10-layer slab to accurately simulate the realistic bulk limit. More funda- mentally, because FeSe is a prototypical iron-based super- conductor, integrating altermagnetism into this specific material family paves the way for exploring the elusive coexistence of altermagnetic order and superconductiv- ity. This ultimately establishes a highly viable material candidate for future topological quantum computing and spintronic applications. Lattice constant (Å) E - E D i m e r ( m e V / F e ) E D i m e r - E C h e c k e r b o a r d ( m e V / F e ) Doping level (hole/Fe) Dimer Checkerboard a c b c a b (a) Fe Se Cl (b) (c) (d) FIG. 1. (a) Top and (b) side views of the monolayer Fe2 S e2 C l crystal structure. (c) Relative energies of various magnetic configurations as a function of the lattice constant, calculated with respect to the dimer order. (d) Energy difference be- tween the dimer and checkerboard magnetic orders, defined as ∆E = Ed imer − Ec heckerboard, as a function of the hole dop- ing level. II. RESULTS AND ANALYSIS The monolayer Fe2 S e2 C l crystallizes in a tetragonal lattice structure belonging to the space group P 4mm (No. 99) with C4 v point group symmetry. As illustrated in Figs. 1(a) and 1(b), the primitive cell is formed by an FeSe monolayer with single-sided Cl adsorption directly above the top Se atom. Consequently, the inversion sym- metry I is broken, while the C4 z rotational symmetry is preserved. The fully optimized lattice constant is cal- culated to be 3.796 ˚A, which is in good agreement with previous experimental reports for single unit-cell FeSe grown on SrTiO3 (3.82 ˚A) [41] and bulk FeSe (3.765 ˚A) [34]. The overall structure of the FeSe monolayer is well preserved within Fe2 S e2 C l, suggesting the potential for similar superconducting behavior. To investigate the stability of the monolayer Fe2 S e2 C l, we first examine six different adsorption sites, as shown in Fig. S1 of the Supplemental Material [42]. Our calcu- lations identify Site 1, where the Cl atom is positioned directly above the top Se atom with a bond length of 2.4 ˚A, as the most energetically favorable adsorption site. Subsequently, we investigate four different Cl c overages (0.125, 0.25, 0.5, and 1 ML) using a 2 √ 2 × 2 √ 2 × 1 su- percell. Here, a coverage of 1 ML is defined as the atomic density of the top Se layer. As illustrated in Fig. S2, we consider three representative atomic configurations for both the 0.25 and 0.5 ML cases. After structural opti- mization, we calculate the adsorption energies at various coverages. The negative values indicate that the adsorp- tion is an exothermic process. Importantly, the adsorp- tion energy becomes progressively more negative with in- creasing coverage, suggesting that the system reaches its most stable state when all available positions are fully oc- cupied (Table S1). Furthermore, our phonon calculations [Fig. 2(a)] and molecular dynamics simulations (Fig. S3) demonstrate the dynamical and thermal stabilities of the structure. At 300 K, no significant distortion, disorder, clustering, or structural phase transitions are observed. We therefore conclude that a stable, stoichiometric 2D material, Fe2 S e2 C l, is formed via single-sided Cl adsorp- tion on the monolayer FeSe. To investigate the magnetic properties of the mono- layer Fe2 S e2 C l, we consider eight d ifferent magnetic con- figurations based on a 2 √ 2 × 2 √ 2 × 1 supercell, as il- lustrated in Fig. S4. Initially, we perform total-energy calculations as a function of the lattice constant over the range from 3.76 ˚A to 4.00 ˚A. This range encompasses the lattice constants of both bulk FeSe (3.765 ˚A) and the SrTiO3 (STO) substrate (3.905 ˚A) [43]. As depicted in Fig. 1(c), within the lattice constant range of 3.76 ˚A to 4.00 ˚A, the dimer order consistently exhibits the lowest energy, followed by the checkerboard order. At the fully optimized lattice constant of 3.796 ˚A, the total energy of the dimer order is calculated to be 24.186 meV/Fe lower than that of the checkerboard order. However, from the perspective of spin group symmetry, the dimer order in the monolayer Fe2 S e2 C l does not classify as an altermag- net, because the two opposite spin sublattices are related by a lattice translation. Given that the system intrin- sically breaks inversion symmetry, it is only within the checkerboard order that the two spin sublattices can be connected by a crystalline rotation or mirror symmetry, thereby making the material a textbook altermagnet.

3 As an effective approach for tuning magnetic proper- ties, carrier doping has been established as a pivotal route to stabilize metallic altermagnetism in correlated mate- rials with competing magnetic interactions [44, 45]. This is particularly viable given that systematic modulation of carrier density via liquid gating has been successfully employed to drive the evolution of superconductivity in FeSe thin films [36]. We calculate the magnetic ground states across various hole doping levels. The dimer and checkerboard configurations consistently remain the two lowest-energy orders across all considered doping levels. As depicted in Fig. 1(d), we find that with progressive hole doping, the magnetic ground state undergoes a tran- sition from the dimer order to the checkerboard order, which intrinsically hosts altermagnetism. E n e r g y ( e V ) DOS (state/eV) Γ M Y X (a) (b) (c) (d) F r e q u e n c y ( T H z ) FIG. 2. (a) Phonon spectrum of monolayer Fe2 S e2 C l along high-symmetry paths, calculated for the checkerboard alter- magnetic order. (b) Distribution of the spin density, where red and blue isosurfaces represent the spin-up and spin-down densities, respectively. (c) Electronic band structure and the corresponding density of states (DOS) calculated with- out spin-orbit coupling (SOC). The large altermagnetic spin splitting of ∼620 meV is highlighted by the light green arrow. (d) Spin-resolved Fermi surface. In the following, we choose the specific doping level of 0.25 hole/Fe indicated in green in Fig. 1(d) as a represen- tative example to elucidate the altermagnetic properties of Fe2 S e2 C l. At this doping level, the total energy of the checkerboard altermagnetic order is 12.19 meV/Fe lower than that of the dimer order. The anisotropic electric crystal potential introduced by the Cl atoms gives rise to anisotropic exchange interactions, resulting in a highly anisotropic spin density within the system, as shown in Fig. 2(b). In addition, the two Fe sublattices, charac- terized by antiparallel magnetic moments, are related by spin group symmetry operations {C2 | |C4 z }, {C2 | |Md } , and {C2 | |Md ⊥} . Here, the Md and Md ⊥ denote mirror reflections with respect to the diagonal axes ˆd = ˆx + ˆy and ˆd⊥ = ˆx − ˆy, respectively. These symmetry opera- tions satisfy the fundamental requirements for altermag- netism. Consequently, this real-space anisotropy is an- ticipated to induce a large momentum-dependent spin splitting. Our electronic band structure calculations cor- roborate this hypothesis. As depicted in Fig. 2(c), in the absence of spin-orbit coupling (SOC), the electronic structure is metallic, with partially filled Fe d orbitals dominating the states around the Fermi level. The den- sity of states for the spin-up and spin-down channels are perfectly symmetric, indicating a fully compensated macroscopic magnetization. Fe2 S e2 C l indeed exhibits a distinct momentum-dependent spin splitting, confirming its altermagnetic order. Near the Fermi level, a signif- icant splitting of up to nearly 620 meV is observed be- tween the spin-up and spin-down channels along the Γ- X(Y)-M paths. Crucially, the spin polarization exactly reverses when rotating from the Γ-X-M to the Γ-Y-M paths. The calculated spin-resolved Fermi surface, shown in Fig. 2(d), exhibits a planar d-wave symmetry. -1 1 0 Γ X Y M Γ X Y M -1 1 0 (a) (c) (b) (d) FIG. 3. (a) Spin-projected energy bands and (b) correspond- ing Fermi surface calculated with spin-orbit coupling (SOC) for the N´eel vector pointing along the [100] direction. (c) En- ergy bands and (d) Fermi surface calculated with N´eel vector oriented along the [110] direction. The color scale in all pan- els represents the magnitude of the spin projection. The anti- crossings near the Fermi level are highlighted by light green circles. The inclusion of SOC in our calculations reveals that the altermagnetic order in Fe2 S e2 C l exhibits an easy- plane magnetic anisotropy. We find that the ground-state energy is identical when the N´eel vector points along the [100], [110], and [010] directions. We calculate the electronic band structures and Fermi surfaces with spin projections along the [100] and [110] directions, respec- tively. As shown in Figs. 3(a) and 3(c), the introduc- tion of SOC has a minimal impact on the overall band structure. However, the most striking feature is that anti-crossings appear at distinct points near the Fermi level. Specifically, for the [100] spin orientation, the Weyl point along the X-M path remains gapless, whereas a gap opens at the Weyl point along the M-Y path. In

4 contrast, when the spins are aligned along the [110] di- rection, both Weyl points become gapped. This is due to the fact that different spin quantization axes lead to distinct magnetic space groups: P m′ m2′ for the [100] direction and Cm′ m2′ for the [110] direction. Along the [100] direction, the system preserves the symmetry opera- tions {E, Mx } +T {C2 z , My }, where T is the time-reversal operator. Similarly, the symmetry operations along the [110] direction are given by {E, Md } + T {C2 z , Md ⊥} . The Fermi surfaces and their corresponding spin projec- tions along the [100] and [110] directions, as depicted in Figs. 3(b) and 3(d), strictly obey the aforementioned symmetry constraints. a c b a c b (a) Fe Se Cl (d) E n e r g y ( e V ) E n e r g y ( e V ) Γ M Y X Γ M Y X (b) (c) (e) (f) FIG. 4. (a) Electronic band structure and (b) spin-resolved Fermi surface calculated without spin-orbit coupling (SOC) for the bilayer system (one Fe2 S e2 C l layer on one FeSe layer). (c) Electronic band structure and (d) spin-resolved Fermi sur- face for the trilayer system (one Fe2 S e2 C l layer on two FeSe layers). Motivated by the experimental absence of static long- range magnetic order in bulk and thin-film FeSe, we further investigate the influence of the nonmagnetic un- derlying FeSe layers on the altermagnetism in Fe2 S e2 C l. To circumvent the computational limitation of applying layer-specific hole doping in standard plane-wave frame- works, we explicitly initialize the top Fe2 S e2 C l layer with a checkerboard altermagnetic order, while setting the ini- tial magnetic moments of all underlying FeSe layers to zero. Upon structural relaxation with interlayer van der Waals (vdW) corrections for the bilayer and trilayer sys- tems, the underlying layers reliably converge to a non- magnetic state, whereas the top-layer Fe atoms retain their local magnetic moments. As shown in Fig. 4, the characteristic altermagnetic spin splitting remains re- markably stable in this configuration. Crucially, even when the model is extended to a 10-layer slab to accu- rately simulate the true bulk limit [Fig. S5], this alter- magnetic spin splitting persists robustly. These results unambiguously confirm that the altermagnetic state in this system is an intrinsic surface-driven phenomenon. It is highly robust against interlayer hybridization and, most importantly, completely decoupled from the bulk nonmagnetic state. III. DISCUSSION AND CONCLUSION From an experimental perspective, the realization of Fe2 S e2 C l is highly feasible. The surface functionaliza- tion and halogenation of 2D materials have been widely demonstrated via chemical vapor deposition or controlled surface treatment [46, 47]. Furthermore, hole doping in iron-based superconductors is a mature technique, frequently achieved through non-destructive ionic liquid gating [36]. The doping concentration of 0.25 hole per Fe atom (equivalent to 3.47 × 101 4 hole/cm2 ) is exper- imentally viable, particularly in light of established re- ports demonstrating that doping concentrations up to 3.5 × 101 5 e/cm2 can be realized through electrochemical gating techniques [48]. Indeed, recent theoretical stud- ies have extensively highlighted the tremendous poten- tial of surface decoration in tailoring the physical prop- erties of FeSe-based systems. For instance, it has been demonstrated that surface fluorine (F) adsorption on a superconducting FeSe monolayer can effectively control its magnetic anisotropy and induce ferroelasticity [49]. Beyond halogenation, decorating iron-based supercon- ductors with lithium (Li) has been predicted to real- ize high-temperature quantum anomalous Hall insulators [50], while the introduction of metal atoms (Tl, In, Ga) to form 2D MFeSe systems can yield tunable Weyl half- semimetals [51]. These compelling theoretical precedents strongly validate the paradigm of reconstructing the elec- tronic and magnetic structures of FeSe via surface func- tionalization. The potential coexistence of altermagnetism and proximity-induced superconductivity in Fe2 S e2 C l opens a fascinating frontier. In conventional superconductors, magnetic order typically acts as a pair-breaker. However, the unique d-wave symmetry of the altermagnetic spin polarization in momentum space can lead to novel super- conducting states. Specifically, the lifted spin degeneracy in the normal state of Fe2 S e2 C l naturally biases the sys- tem toward equal-spin triplet pairing (∆↑ ↑ or ∆↓ ↓) . This potential for intrinsic triplet superconductivity is a key requirement for realizing Majorana zero modes, position- ing this material as a promising candidate for topological quantum computation. During the preparation of this manuscript, we be- came aware of two contemporaneous studies. One pro- posed that single-sided hydrogenation, oxidation, and fluorination can transform spin-degenerate antiferromag- netic FeSe into a d-wave altermagnet with pronounced momentum-dependent spin splitting [52]. The other re- ported the coexistence of d-wave altermagnetism and nontrivial topology in Janus FeSeX (X = S, Te) mono- layers [53]. Although these results are consistent with the symmetry analysis presented here, observing alter- magnetic spin splitting in a prescribed checkerboard con-

5 figuration does not by itself establish that this config- uration is the true magnetic ground state. The former study does not report a systematic total-energy compari- son among competing magnetic orders, whereas the latter compares only the ferromagnetic, checkerboard altermag- netic, and nonmagnetic states within the primitive cell. Consequently, magnetic states with longer periodicities cannot be excluded. By explicitly comparing the relevant magnetic con- figurations in a 2 √ 2 × 2 √ 2 × 1 supercell, we find that the ideal undoped Fe2 S e2 C l monolayer instead adopts a dimer-ordered ground state, which lies 24.186 meV/Fe below the checkerboard order. Hole doping reverses this energy hierarchy at approximately 0.175 hole/Fe, and at 0.25 hole/Fe the checkerboard order becomes lower than the dimer order by 12.19 meV/Fe. In realistic sam- ples, epitaxial strain, substrate hybridization, interfa- cial charge transfer, defects, nonuniform adsorption, and finite-temperature effects may alter the relative stability of the competing magnetic orders and thereby stabilize the checkerboard altermagnetic order even without in- tentional carrier doping. Our results therefore do not exclude the realization of altermagnetism in nominally undoped experimental samples. Rather, they identify hole doping as a controllable and reliable route to ener- getically stabilize the checkerboard altermagnetic ground state, whereas asymmetric surface functionalization cre- ates the symmetry environment required for altermag- netic spin splitting. In summary, our first-principles study identifies the hole-doped Fe2 S e2 C l system as a stoichiometric, bulk- compatible 2D altermagnetic platform. We thereby pro- vide a concrete material platform that integrates alter- magnetism with potential high-temperature supercon- ductivity. 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