Prediction of a multifunctional hexagonal Fe₂O₃ monolayer with chiral antiferromagnetism and piezoelectricity

Abstract

Two-dimensional (2D) materials that exhibit magnetism and piezoelectricity offer exciting opportunities for next-generation spintronic and multifunctional devices. The recently synthesized 2D hexagonal Fe₂O₃ provides a promising platform [Nat. Mater. 20, 1073 (2021)], yet its atomic structure remains unidentified. Herein, we report that high-throughput first-principles screening reveals a viable monolayer structure that can serve as a candidate for experimental realization. The proposed hexagonal Fe₂O₃ monolayer features a large direct band gap of 3.1 eV and hosts a robust chiral antiferromagnetic order stabilized by the interplay between triangular-lattice-induced geometric frustration and strong magnetic anisotropy. The absence of inversion symmetries gives rise to a pronounced in-plane piezoelectric response, with a d₁₁ coefficient of −29.51 pm/V. Remarkably, these key electronic, magnetic, and piezoelectric properties remain robust under biaxial strain, highlighting the hexagonal Fe₂O₃ monolayer as a multifunctional candidate for piezoelectrically engineered spintronic applications.

Graphical abstract

Keywords

chiral AFM Fe₂O₃ monolayer / magnetic anisotropy energy / biaxial strain / piezoelectric effect / first-principles calculations

1 Introduction

Two-dimensional (2D) magnetic materials have rapidly emerged as a vibrant research frontier owing to their fundamental scientific significance and potential device applications [1−4]. Unlike their bulk counterparts, magnetic order in 2D systems arises from the interplay between reduced dimensionality, exchange interactions, and magnetic anisotropy, which stabilizes long-range spin alignment against thermal fluctuations even in monolayers [5]. A broad spectrum of 2D magnets, including ferromagnets [6−9], ferrimagnets [10, 11], and antiferromagnets [12−14], has been discovered, each exhibiting distinct spin configurations and tunable magnetic properties. Recent advances have revealed rich physical phenomena in two-dimensional magnetic materials, including multiferroicity, valley polarization, and altermagnetic behavior [15−18]. Among these, antiferromagnetic (AFM) materials, characterized by antiparallel spin alignment and vanishing net magnetization, offer unique advantages such as negligible stray fields and ultrafast spin dynamics, rendering them ideal platforms for next-generation high-speed and high-density spintronic devices [19−21]. Moreover, the pronounced sensitivity of 2D magnets to external stimuli such as electric fields or strain enables strong magnetoelectric coupling, opening promising avenues for investigating microscopic mechanisms and designing multifunctional spintronic architectures.

In triangular lattices, intrinsic magnetic exchange frustration often gives rise to noncollinear spin configurations. In particular, the 120° coplanar chiral AFM order has drawn particular attention because it simultaneously breaks time-reversal symmetry [22, 23]. Such chiral spin textures underpin a broad spectrum of emergent quantum phenomena including spin-liquid behavior, improper ferroelectric polarization, magnetoelectric coupling, anomalous Hall effects, and topological spin structures [24−26], many of which have been experimentally observed in materials such as Mn₃Pt [27] and NiGa₂S₄ [28]. With the rapid advancement of 2D magnetism, room-temperature-stable chiral AFM order has recently been realized in layered systems such as Hf₂VC₂F₂ [29], marking an important step toward integrating frustrated magnetism into low-dimensional materials. Notwithstanding significant progress, genuinely robust chiral AFM in the atomically thin limit remains scarce. Achieving this goal hinges on a fundamental understanding of the synergy between magnetic frustration and anisotropy in reduced dimensions, underscoring the imperative to explore intrinsically frustrated 2D magnets with strong anisotropy and tunable coupling.

On the other hand, achieving efficient and low-power electric-field switching remains a major challenge for practical applications. Conventional ferroelectric strategies suffer from hysteresis, fatigue, and limited switching speeds, which restrict their reliability and scalability [30]. Piezoelectric strain engineering offers an alternative route by exploiting noncentrosymmetric materials to convert external voltages into linear, hysteresis-free, and ultrafast in-plane strains. These strains can directly and efficiently tune magnetic order through magnetoelastic coupling, providing a robust and energy-efficient means of electric-field-driven magnetic control. 2D piezoelectrics further enhance this capability owing to their flexibility, large surface-to-volume ratio, and strong surface charge response, leading to remarkable piezoelectric efficiencies [31−34]. For example, monolayer MoS₂ exhibits a piezoelectric coefficient of about 3.71 pm/V [35, 36], comparable to bulk α-quartz [37], while the predicted d₂₂ of monolayer SnSe can reach approximately 250 pm/V [38]. These exceptional properties position 2D piezoelectrics as key enablers for the next generation of energy-efficient and tunable electronic devices.

Fe-based 2D magnets have attracted significant attention due to their abundance, environmental benignity, and technological compatibility. Typical examples such as FePS₃ [12], FeSe [39], Fe₃GeTe₂ [7], Fe₃GaTe₂ [40], Fe₂O₃ [41], Fe₃O₄ [42], and FeO₂ [43] exhibit rich crystal configurations alongside diverse magnetic and electronic properties, making them model systems for investigating spin, charge, and orbital coupling phenomena. Recently, 2D hexagonal Fe₂O₃ was experimentally synthesized, though its precise crystal structure remains unresolved. Here, high-throughput structural screening identifies an possible experimental hexagonal Fe₂O₃ monolayer with Fe ions forming a triangular lattice. This phase exhibits a large magnetic anisotropy energy of 3.88 meV/Fe, stabilizing a chiral AFM order robust under −6% to 2% biaxial strain, and an exceptionally high, strain-tunable piezoelectric coefficient d₁₁, modifiable by more than a factor of two. These results provide a concrete material target and a theoretical foundation for piezoelectrical AFM spintronic devices.

2 Results and discussion

Experimentally, Fe₂O₃ has been confirmed to adopt a hexagonal symmetry, although the precise atomic positions remain unresolved [44]. Based on the 2:3 stoichiometry, we performed a high-throughput screening of binary compounds with hexagonal structures from the C2DB [45] materials database, considering both interatomic interactions and chemical bonding rationality. Twelve candidate parent structures with potential stability were thus identified. The dynamical stability of the structure was assessed by phonon spectrum calculations (see Supplementary Materials Fig. S1). Among these, one structure [Fig. 1(a)] emerged as the energetically most favorable and exhibited no imaginary frequencies in its phonon spectrum [Fig. 1(b)]. The simulated high-resolution transmission electron microscopy (HRTEM) image of this configuration shows a distinct hexagonal pattern, consistent with observations (see Supplementary Materials Fig. S2) [46], offering strong evidence for its validity as the experimental 2D Fe₂O₃. Structurally, the monolayer consists of an O−Fe−O−Fe−O stacking sequence, where Fe atoms form a triangular lattice within sublayers. Each Fe atom is bonded to six surrounding O atoms, resulting in distorted FeO₆ octahedral characteristic of the hexagonal lattice framework. Slight structural deformation after 5 ps AIMD simulations at 300 K demonstrates thermal stability [Fig. 1(c)]. Mechanical stability is evidenced by the elastic constants, which satisfy C₁₁, C₁₂ > 0 and C₁₁ > |C₁₂|. The monolayer exhibits isotropic mechanical behaviors, as shown in Figs. 1(e) and (f), with a Young’s modulus of 100 N/m, a value that lies between those of MoS₂ monolayer (120.10 N/m) [47] and black phosphorus (92.13 N/m) [48], and a Poisson’s ratio of approximately 0.6, indicating a large capacity for lateral deformation.

To determine the magnetic ground state of the Fe₂O₃ monolayer, we systematically considered six representative magnetic configurations [Fig. 2]. The collinear configurations are selected to include both FM and AFM coupling states between in-plane and out-of-plane nearest-neighbor Fe ions. In addition, the 120° chiral AFM state is included to capture the key noncollinear order arising from geometric frustration in this system. Energy comparisons of these magnetic configurations indicate that the Fe₂O₃ monolayer adopts a chiral AFM ground state, characterized by interlayer FM coupling and intralayer 120° coplanar AFM spin arrangements. In octahedral ligand field [Fig. 3(a)], the Fe 3d orbitals split into triply degenerate t_2g states (d_xy, d_xz, and d_yz) and doubly degenerate e_g states (d_{x^2-y^2} and d_{z^2}). The half-filled Fe 3d orbitals contribute a large magnetic moment of 5 μ_B/Fe.

Moreover, the chiral AFM Fe₂O₃ monolayer possesses easy-plane magnetization with a sizeable magnetic anisotropy energy (MAE) of 3.88 meV/Fe [Fig. 3(b)], which is significantly larger than that of the CrI₃ monolayer (~0.84 meV/Cr) [49] and ensures robust in-plane magnetization. The large MAE, zero net magnetization, and frustration-stabilized spin chirality ensure robustness of spin arrangement against small perturbations, although minor spin canting cannot be entirely excluded. The orbital-resolved analysis of the magnetic anisotropy energy (MAE) within the framework of second-order perturbation theory is shown in Fig. S3. The calculated magnetic shape anisotropy of 0.394 meV/Fe also favors in-plane magnetization. The preference for in-plane magnetization is maintained across U values ranging from 4.00 to 7.89 eV (Table S2).

To reveal the temperature-dependent magnetism, the coupling strength between Fe atoms was analyzed using the Heisenberg spin Hamiltonian:

(1)\mathrm{H}=-{\displaystyle \sum _{⟨ij⟩}{J}_1{\mathit{S}}_i{\mathit{S}}_j-{\displaystyle \sum _{⟨mn⟩}{J}_2{\mathit{S}}_m{\mathit{S}}_n-A{\displaystyle \sum _i{\left(S_i^{ab}\right)}^2.}}}

Here, J₁ and J₂ represent the interlayer nearest-neighbor (NN) and intralayer next-nearest-neighbor (NNN) exchange interaction, respectively [Figs. 1(a) and S4], ⟨ij⟩ and ⟨mn⟩ correspond to the site of NN and NNN Fe ions, respectively, S is the normalized spin operator, taken as 5/2 here, S_i^{ab} represents the in-plane spin component magnitude of Fe ion at i site, defined as

(2)S_i^{ab}=\sqrt{{\left(S_i^x\right)}^2+{\left(S_i^y\right)}^2},

where S_i^x and S_i^y are the components of the spin operator along the in-plane x- and y-directions, respectively. A is the magnetocrystalline anisotropy coefficient. The J₁ and J₂ are calculated to be 0.84 and −2.80 meV. The positive J₁ indicates interlayer FM coupling, whereas the negative J₂, which dominates the in-plane interactions, originates from the geometric frustration inherent in the triangular lattice. In this lattice, the geometry leads to magnetic frustration, preventing the simultaneous satisfaction of antiparallel alignment among all three neighboring magnetic atoms in an AFM Néel state [43, 50]. Consequently, the ground state stabilizes into a chiral AFM order characterized by a magnetic propagation vector \mathit{q}=(\pi /3,\pi /3,0).

Monte Carlo simulations based on the Heisenberg model at different temperatures determined that the chiral AFM order in the Fe₂O₃ monolayer can persist below a Néel temperature (T_N) of 40 K, higher than the previously reported 2D non-collinear materials, such as MnRe₂O₈ monolayers (31 K) [51] and MnSi monolayers (27.7 K) [52]. Figures 3(c)−(e) show the real-space distribution of magnetic moments at different temperatures. At 10 K, the spin directions in the triangular lattice mainly remain within the ab-plane, exhibiting a spin-frustrated state with a 120° angle between adjacent Fe atoms. When the temperature rises to 40 K, the spin-frustrated state persists (see Supplementary Materials Fig. S5). As the temperature rises above 40 K, the 120° spin order between in-plane neighbors degrades, and the parallel alignment of spins between adjacent layers is progressively destroyed, showing a clear trend toward interlayer decoupling. At 200 K, disordered regions dominate the entire lattice, and the Fe₂O₃ monolayer transitions to a paramagnetic state. The magnetic moment snapshots with the U values ranging from 4 to 7 eV are shown in Fig. S6, and the corresponding J values are provided in Table S3.

To investigate the spin-related physical properties in the chiral AFM Fe₂O₃ monolayer, we calculated the spin-resolved band structure with considering SOC. The Fe₂O₃ monolayer is a semiconductor with a direct band gap of 3.10 eV [Figs. 3(f)−(h)]. Such a wide gap ensures its semiconducting behavior at room temperature. Furthermore, the x, y, and z magnetization components exhibit highly non-trivial distribution patterns in momentum space. Specifically, As the k-point traverses the high-symmetry path M→K→Γ, the intensity of the spin z-component gradually increases, while the spin intensities of other components gradually decrease and even change sign. This characteristic, where the spin direction undergoes continuous, smooth, and large-amplitude rotation with momentum, is direct evidence of “non-trivial spin-momentum locking” and a hallmark electronic structure feature of such coplanar antiferromagnets under strong SOC [53]. This phenomenon indicates an intimate coupling between spin and orbital degrees of freedom, providing the intrinsic structural basis for potential emerging transport properties like the anomalous Hall effect [26].

The non-centrosymmetric Fe₂O₃ structure and intrinsic semiconducting feature allow the piezoelectric effect. Here, a \sqrt{\text{3}} × \text{3} × 1 supercell was selected for piezoelectricity calculations [Fig. 2(f)]. The polarization induced by strain or stress in non-centrosymmetric crystals can be characterized by third-rank piezoelectric strain (e_ijk) and stress (d_ijk) tensors. The piezoelectric tensor can be characterized by the first-order derivative, with specific equations:

(3)e_{ijk}={\displaystyle \frac{\mathrm{\partial }{P}_i}{\mathrm{\partial }{\epsilon }_{jk}}}=e_{ijk}^{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}+e_{ijk}^{\mathrm{i}\mathrm{o}\mathrm{n}},

(4)d_{ijk}={\displaystyle \frac{\mathrm{\partial }{P}_i}{\mathrm{\partial }{\epsilon }_{jk}}}=d_{ijk}^{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}+d_{ijk}^{\mathrm{i}\mathrm{o}\mathrm{n}}.

Here, P_i, ε_jk, and σ_jk represent the polarization vector, strain, and stress, respectively. i, j, and k correspond to the x, y, and z directions. The sum of the piezoelectric stress and strain tensors reflects the ionic and electronic contributions. The piezoelectric coefficients e_ijk and d_imn are related to the elastic tensor C_mnjk:

(5)e_{ijk}=\left({\displaystyle \frac{\mathrm{\partial }{P}_i}{\mathrm{\partial }{\epsilon }_{jk}}}\right)\left({\displaystyle \frac{\mathrm{\partial }{P}_i}{\mathrm{\partial }{\sigma }_{jk}}}\right)=d_{imn}{C}_{mnjk}.

For the Fe₂O₃ monolayer, it can be simplified by considering only in-plane strain and stress components, and by adopting Voigt notation, leading to

(6)\begin{array}{rl}& \left(\begin{array}{ccc}{e}_{11}& e_{12}& 0\\ 0& 0& e_{26}\\ 0& 0& 0\end{array}\right)\\ & =\left(\begin{array}{ccc}{d}_{11}& d_{12}& 0\\ 0& 0& d_{26}\\ 0& 0& 0\end{array}\right)\times \left(\begin{array}{ccc}{C}_{11}& C_{12}& 0\\ C_{21}& C_{22}& 0\\ 0& 0& C_{66}\end{array}\right).\end{array}

Thus, yielding

(7)d_{12}={\displaystyle \frac{e_{12}\cdot C_{11}-e_{11}\cdot C_{12}}{C_{22}\cdot C_{11}-C_{21}\cdot C_{12}}},

(8)d_{11}={\displaystyle \frac{e_{11}\cdot C_{22}-e_{12}\cdot C_{21}}{C_{11}\cdot C_{22}-C_{21}\cdot C_{12}}},

(9)d_{26}={\displaystyle \frac{e_{26}}{C_{66}}}.

The piezoelectric strain tensor of the chiral AFM Fe₂O₃ monolayer was systematically investigated using density functional perturbation theory (DFPT). Our calculations reveal a piezoelectric stress coefficient e₁₁ of −17.99 × 10⁻¹⁰ C/m, significantly surpassing the value of 3.70 × 10⁻¹⁰ C/m of the MoS₂ monolayer, demonstrating stronger mechano−electric coupling. Combined with its remarkable mechanical stiffness, characterized by elastic constants C₁₁ = C₂₂ = 167.21 N/m and C₁₂ = C₂₁ = 106.82 N/m, the Fe₂O₃ monolayer yields a piezoelectric strain coefficient d₁₁ = −29.51 pm/V. This value exceeds the documented d₁₁ of 3.71 pm/V for the MoS₂ monolayer by a factor of eight [35, 36].

Moreover, the piezoelectric effect in the chiral AFM Fe₂O₃ monolayer is highly sensitive to biaxial tensile strain (Fig. 4). Under 2% tensile strain, the coefficients d₁₁ and e₁₁ increase to −85.52 × 10⁻¹⁰ C/m and −22.06 pm/V, respectively. This enhanced piezoelectricity is primarily attributed to strain-induced relative displacements of the ionic sublattices. Furthermore, the chiral AFM order remains stable throughout the −6% to 2% in-plane biaxial strains (see Supplementary Materials Table S4), ensuring that the enhanced piezoelectric response originates purely from the electronic structure, but not the magnetic phase transitions. The combination of this strain-tunable piezoelectricity with robust chiral AFM order suggests the potential for developing advanced strain-mediated, low-power spintronic devices and non-volatile magnetic memory with piezoelectric write capabilities.

3 Conclusion

In summary, we propose a viable experimental candidate for a 2D hexagonal Fe₂O₃ monolayer that simultaneously exhibits chiral AFM order, wide direct band gap, and pronounced piezoelectric response. The intrinsic Fe triangular frustrated lattice, along with a high magnetic anisotropy energy of 3.88 meV/Fe, jointly stabilizes the chiral AFM configuration. The interplay between structural inversion symmetry and magnetic time-reversal symmetry breaking gives rise to nontrivial spin-momentum locking and accounts for the in-plane piezoelectric response. Remarkably, the Fe₂O₃ monolayer exhibits a superior piezoelectric coefficient d₁₁ of −29.51 pm/V, significantly exceeding that of the canonical MoS₂, with its performance further enhanced under tensile strain. These findings establish the hexagonal Fe₂O₃ monolayer as a promising platform for exploring magneto-electric coupling and potential applications in spintronic and multifunctional devices.

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