Altermagnetic Fe₂Se₂O Multilayers

• Altermagnetic Fe₂Se₂O multilayers are layered transition-metal oxychalcogenides exhibiting d-wave spin splitting and symmetry-protected non-relativistic altermagnetism.
• They are engineered through precise crystalline design and first-principles screening, resulting in tunable quantum spin Hall phases marked by multiple spin-filtered edge states.
• Their integrated control over spin, valley, and layer dynamics offers promising prospects for advanced applications in topological spintronics, valleytronics, and ultrafast quantum devices.

Altermagnetic Fe$_2$Se$_2$O multilayers are a class of layered transition-metal oxychalcogenide systems exhibiting symmetry-compensated, non-relativistic spin band splitting—termed "altermagnetism"—and exotic topological phases such as a multi-channel quantum spin Hall (QSH) effect. These systems are characterized by d-wave altermagnetic ordering, robust layer-by-layer tunability, and a cross-disciplinary relevance spanning spintronics, valleytronics, and topological quantum matter. The Fe$_2$Se$_2$O multilayer paradigm demonstrates how magnetic, spintronic, and topological functionalities can be integrated through careful crystalline engineering and symmetry control.

1. Altermagnetic Ordering and d-Wave Spin Splitting

Fe$_2$Se$_2$O multilayers realize a compensated collinear magnetic configuration that differs fundamentally from conventional antiferromagnets and ferromagnets. The defining property is a momentum-dependent, symmetry-protected spin polarization: in the absence of net magnetization, electronic bands with opposite spin moments are split in reciprocal space, a non-relativistic effect not reliant on strong spin–orbit coupling (Wei et al., 18 Oct 2024, Chen et al., 5 Aug 2025).

The spin splitting $\mathbf{S}_k$ displays d$_{x^2-y^2}$-wave form factor,

$\mathbf{S}_k \propto (k_x^2 - k_y^2),$

meaning the splitting vanishes along $k_x = \pm k_y$ and is maximal along the principal axes. This d-wave altermagnetism causes unique nodal structures in both the spin and band-resolved density of states, sharply distinguishing Fe$_2$Se$_2$O multilayers from conventional collinear magnets (Wei et al., 18 Oct 2024, Chen et al., 5 Aug 2025).

2. Structural Features and Material Design

Fe$_2$Se$_2$O multilayers belong to a broader family of layered tetragonal oxychalcogenides with transition metal (TM) square lattices sandwiched between chalcogenide and oxide layers. Their weakly coupled van der Waals layers and high crystalline anisotropy make them suitable for multilayer engineering (Wei et al., 18 Oct 2024, Chen et al., 5 Aug 2025).

The design of altermagnetic order in these systems is guided by:

• Symmetry Analysis: Space and layer group identification, followed by division of atomic positions (Fe, Se, O) into orbits under appropriate subgroup operations. Magnetic sublattices are engineered via operations (rotations, mirrors) that map one set of spins to the other, ensuring "collinear-compensated" order (Peng et al., 22 Feb 2025).
• First-Principles Screening: Structures and candidate magnetic orderings are verified by density functional theory (DFT) and phonon spectrum calculations to confirm both the magnetic ground state and dynamical stability (Peng et al., 22 Feb 2025).
• Realization and Analogy: Fe$_2$Se$_2$O exhibits structural analogy to experimentally realized layered d-wave altermagnets such as La$_2$O$_3$Mn$_2$Se$_2$ (Wei et al., 18 Oct 2024) and is closely related to 3$d^5$/3$d^6$-based heterostructures such as LiFeO$_2$Fe$_2$Se$_2$ (Heil et al., 2014), where Fe$^{2+}$ (3$d^6$) forms robust Hund’s metal sheets embedded in a correlated (Mott-like) matrix.

3. Topological Phases: Quantum Spin Hall Effect Beyond $\mathbb{Z}_2$

A haLLMark of Fe$_2$Se$_2$O altermagnetic multilayers is the emergence of a robust QSH phase, characterized by multiple pairs of spin-filtered, gapless helical edge states protected by mirror-spin symmetry (Chen et al., 5 Aug 2025, Mazin et al., 2023). Unlike conventional TRS-protected QSH insulators (restricted to a $\mathbb{Z}_2$ index), the presence of d-wave altermagnetism circumvents this topological constraint.

Key features include:

• Linear Scaling of Edge Modes: The number of helical edge state pairs and the quantized spin Hall conductance scale exactly with the number of Fe$_2$Se$_2$O layers: for $N$ layers, $N$ pairs of edge modes, yielding spin Hall conductance $\sigma_{xy} = 2Ne / 4\pi$ (Chen et al., 5 Aug 2025).
• Mirror-Spin Chern Number: The topological invariant is not simply the spin Chern number $\mathcal{C}_s$, but a mirror-spin Chern number $$\mathcal{C}_m = (\mathcal{C}_+ - \mathcal{C}_-) / 2$$, where $\pm$ indicate eigenvalues under a horizontal mirror reflection. This symmetry protects edge states even in the presence of significant perturbations.
• Hamiltonian Structure: The bilayer tight-binding Hamiltonian includes a combination of anisotropic hopping, d-wave exchange, and SOC terms,

$$[m - (t_m^x + t_m^y)(\cos k_x + \cos k_y)]\,\tau_0 \sigma_z s_z,$$

with $\sigma$ and $s$ denoting sublattice and spin spaces. The QSH phase arises from the interplay of d-wave altermagnetic order and SOC-induced gaps (Chen et al., 5 Aug 2025).

• Experimental Accessibility: The quantized plateau in spin Hall conductance, robust even under moderate disorder, is detected by electrical edge transport without external magnetic fields.

4. Control of Spin, Valley, and Layer Degrees of Freedom

Fe$_2$Se$_2$O multilayers exhibit strong interrelation between spin, valley, and layer dynamics:

• Spin-Layer Coupling: The spin splitting and its spatial distribution in multilayers critically depend on magnetic order, layer number (odd/even), and external perpendicular electric field $E_z$. Odd-layer systems can show coexistence of spin-split and spin-degenerate bands, whereas even-layer systems may enforce global spin degeneracy unless symmetry is explicitly broken through stacking, gating, or field effects (Tian et al., 21 Oct 2024).
• Valleytronics and Ferrovalley Physics: Interlayer sliding—lateral shift between adjacent Fe$_2$Se$_2$O layers—breaks specific mirror or glide symmetries, inducing tunable valley polarization between X and Y points in the Brillouin zone (Li et al., 4 Oct 2024). This generates switchable ferrovalley states with linear dichroism and enables the anomalous valley Hall effect (AVHE), where layer, valley, and spin polarization are locked.
• Electrical and Optical Modulation: Application of out-of-plane electric fields, chemical janusization, or uniaxial strain permits active control over band splitting, valley polarization, and topological properties, offering rapid and reversible manipulation of the altermagnetic state (Mazin et al., 2023, Tian et al., 21 Oct 2024, Li et al., 4 Oct 2024).

5. Magnetic Correlations, Correlation Effects, and Quantum Fluctuations

The magnetic sector in Fe$_2$Se$_2$O multilayers is marked by:

• Nearly Degenerate Magnetic Configurations: Multiple antiferromagnetic and altermagnetic arrangements are energetically close, leading to fragile long-range order and strong amplitude of quantum spin fluctuations—a regime favorable for unconventional magnetic, topological, or even superconducting phases (Heil et al., 2014).
• Role of Correlations: In related systems such as LiFeO$_2$Fe$_2$Se$_2$, there is clear separation between strongly correlated, nearly Mott-insulating layers and robust metallic FeSe-like layers, as evidenced by DFT+DMFT calculations. For Fe$_2$Se$_2$O and its analogs, strong Hund’s coupling and Coulomb interactions selectively suppress contributions from half-filled 3$d^5$ subsystems, leaving the 3$d^6$-derived fermiology intact (Heil et al., 2014).
• Persistence of 2D Magnetic Correlations: As shown in La$_2$O$_3$Mn$_2$Se$_2$, 2D short-range order can survive above the Néel temperature, an effect likely to manifest in Fe$_2$Se$_2$O, influencing both transport and topological response (Wei et al., 18 Oct 2024).

6. Experimental Techniques and Optical Switching

Probing and manipulating the altermagnetic state in Fe$_2$Se$_2$O multilayers involves:

• Magnetooptical Probes: Magnetooptical Kerr effect (MOKE) measurements are sensitive to the band off-diagonal dielectric response induced by momentum-dependent spin splitting. Substantial Kerr angles (up to $0.1$–$0.4^\circ$) are predicted, comparable to ferromagnets (Mazin et al., 2023).
• Angle-Resolved Photoemission Spectroscopy (ARPES): Direct observation of the spin-resolved band structure, including momentum-dependent (d-wave or higher) splitting and lifting of Kramers degeneracy, verifying both compensated magnetization and symmetry-breaking (Vita et al., 27 Feb 2025).
• Optical Switching: In related layered altermagnets, ultrafast laser pulses have been demonstrated to quench or switch the altermagnetic phase nonthermally, monitored by time-resolved reflectivity. This illustrates the potential of Fe$_2$Se$_2$O multilayers for ultrafast, low-power control of magnetic and topological states ("altertronics") (Vita et al., 27 Feb 2025).

7. Potential Applications and Future Directions

Fe$_2$Se$_2$O multilayers represent a platform for:

• Topological Spintronics: Linearly scaling, exactly quantized spin Hall conductance enables robust, high-speed, and miniaturized spin current channels, surpassing limitations of conventional $\mathbb{Z}_2$ QSH insulators (Chen et al., 5 Aug 2025).
• Valleytronics and Multilayer Logic: The ability to tune, switch, and read out valley and spin states via optical and electrical means suggests applications in valley-based memory and logic devices (Li et al., 4 Oct 2024).
• Correlated Quantum Matter: The interplay of strong correlations, short-range magnetic order, and multi-channel edge modes suggests further exploration of quantum criticality, unconventional superconductivity (as analogized in FeSe-based systems), and proximity effects in heterostructures (Heil et al., 2014, Mazin et al., 2023).
• Ultrafast Devices: Optical control of altermagnetic order—with net-zero stray fields and minimal thermal dissipation—positions Fe$_2$Se$_2$O as a promising component for ultrafast, energy-efficient magnetic switching and quantum information processing circuits (Vita et al., 27 Feb 2025).

In summary, altermagnetic Fe$_2$Se$_2$O multilayers exemplify an integrated quantum material system where symmetry-protected collective spin phenomena, topologically robust transport, and multilayer engineering converge, offering a pathway to a new generation of quantum technologies.