Axiality-Induced Chirality via Surface Polarization

• Axiality-induced chirality via surface polarization is a symmetry-driven phenomenon coupling chirality (G₀), axiality (𝐆) and polar fields (𝐐) to stabilize unique interfacial domains.
• A minimal s–p hybridized model with spin–orbit interaction demonstrates that surface dipole fields lower energy barriers for creating single-domain chiral or axial states.
• This mechanism offers tunable domain control and enantioselectivity, providing practical implications for spintronics, molecular recognition, and chiral catalysis.

Axiality-induced chirality via surface polarization is a symmetry-driven phenomenon in which the interplay between axial, chiral, and polar multipole moments at an interface dictates the stabilization or induction of chiral or axial domains, with key consequences for domain control, interfacial functionalities, and surface-enhanced responses. This mechanism, underpinned by precise symmetry coupling and supported by theoretical models, generalizes the mutual induction processes between chirality (G₀: electric toroidal monopole), axiality (𝐆: electric toroidal dipole), and surface polarization (𝐐: electric dipole), and has broad implications in the context of condensed matter physics, spintronics, and molecular recognition (Hayami et al., 21 Oct 2025).

1. Unified Multipole Symmetry Framework

The phenomenon is defined in terms of the coupling among three fundamental even–time-reversal multipole degrees of freedom:

• Chirality (G₀): Electric toroidal monopole, a pseudoscalar that encodes the handedness (left vs. right) of the underlying structure.
• Axiality (𝐆 = (Gₓ, G_y, G_z)): Electric toroidal dipole, an axial vector representing monoaxial order.
• Polarity (𝐐 = (Qₓ, Q_y, Q_z)): Electric dipole, a polar vector reflecting broken spatial inversion and surface fields.

These multipoles are coupled by symmetry. The lowest-order couplings are: $$G₀ \leftrightarrow \mathbf{Q} \cdot \mathbf{G}, \quad \mathbf{G} \leftrightarrow G₀\,\mathbf{Q}, \quad \mathbf{Q} \leftrightarrow G₀\,\mathbf{G}$$ This means that at a surface where a polar field 𝐐 is necessarily present, the presence of chirality in the bulk (G₀ ≠ 0) will, by symmetry, select and stabilize a particular axial moment (𝐆), and conversely, axiality in the bulk (𝐆 ≠ 0) will, at the surface, select a particular sign of chirality (G₀) (Hayami et al., 21 Oct 2025).

2. Mechanism of Chirality-Induced Axiality via Surface Polarization

In a chiral system with bulk G₀ ≠ 0 (e.g., a chiral substrate or phase), the surface always exhibits a native polar field 𝐐 due to broken inversion at the boundary. The interfacial energy contains a term

$$\mathcal{H}_{\text{coupling}} \sim G₀\, \mathbf{Q} \cdot \mathbf{G}$$

such that a finite G₀ and polar surface field 𝐐 lower the energy for a preferred orientation of the axial vector 𝐆 (e.g., by favoring Gₓ > 0 or Gₓ < 0). As a result, only one domain of axiality is stabilized at the surface—a mechanism referred to as chirality-induced axiality via surface polarization (CIAS).

Model calculations—using a minimal s–p hybridized tight-binding chain with spin–orbit coupling—demonstrate that near the interface, the surface-induced electric dipole (Qₓ) couples to the bulk chirality (G₀) via this symmetry-allowed term, producing an axial moment (e.g., Gₓ) localized at the boundary. The explicit dependence of this stabilization energy difference on the magnitude of the coupling fields and the filling provides guidance for linking material parameters to observable domain control (Hayami et al., 21 Oct 2025).

3. Inverse Effect: Axiality-Induced Chirality via Surface Polarization

The mechanism is fundamentally reciprocal. In a material with strong axiality (𝐆 ≠ 0, e.g., a monoaxial or ferroaxial system), the same interfacial polar field 𝐐 at the surface produces a coupling

$$\mathcal{H}_{\text{coupling}} \sim \mathbf{Q} \cdot \mathbf{G}\, G₀$$

This term stabilizes a specific sign of the chiral order parameter (G₀) at the surface, a process denominated as axiality-induced chirality via surface polarization (AICS). The surface thus becomes chiral (even if the axial bulk is not), with the sign of chirality directly dictated by the orientation of the axial moment 𝐆 and the surface field 𝐐.

This reciprocal nature provides a powerful tool for engineering single-domain states: by selecting an appropriate combination of substrate (chiral or axial) and surface termination (polarity), one can deterministically control the sign of axiality or chirality in a target layer or domain (Hayami et al., 21 Oct 2025).

4. Model System and Theoretical Analysis

The theoretical analysis is grounded in a minimal model of a linear s–p orbital chain (with spin–orbit interaction), analyzed via mean-field theory including external or internally stabilized coupling fields h_{G₀} (chirality mean field), h_{Gₓ} (axial mean field), and boundary-localized polar fields 𝐐. Calculations clarify:

• When only G₀ and 𝐐 are finite, 𝐆 emerges at the boundary (CIAS).
• When only 𝐆 and 𝐐 are finite, G₀ emerges at the boundary (AICS).

The energy difference between competing domain configurations (e.g., Gₓ > 0 vs. Gₓ < 0) is consistently found to scale with the product |𝐐| |G₀| (or |𝐐| |𝐆| in AICS), thus confirming the general symmetry analysis. The predicted sign dependence and sensitivity to chemical potential strongly constrain experimental realizations (Hayami et al., 21 Oct 2025).

5. Single-Domain Stabilization and Interfacial Functionalities

The explicit coupling between chirality (G₀), axiality (𝐆), and surface-induced polarity (𝐐) fundamentally alters the energetic landscape at interfaces and domain boundaries:

• Single-domain stabilization: By leveraging the surface-polarity-mediated CIAS/AICS couplings, one can energetically select and stabilize a domain with a unique sign of chirality or axiality at the interface, suppressing domain walls and mixed states.
• Interfacial functionalities: These reciprocal couplings underpin selective adsorption phenomena. For example, an axial surface (with finite 𝐆) is predicted to selectively adsorb a given enantiomer, while a chiral surface will energetically distinguish different orientations of an axial molecule. Such selectivity can be exploited in enantioselective catalysis, crystallization, and molecular recognition (Hayami et al., 21 Oct 2025).

6. Implications and Potential Applications

The CIAS/AICS mechanisms provide several opportunities and suggest new device functionalities:

• Tunable domain control: The magnitude of single-domain stabilization energy can be modulated via external means (e.g., electrostatic gating, applying external fields, or engineering polar layering and surface terminations).
• Spintronics and molecular electronics: Control of chirality or axiality at interfaces, without external magnetic fields, enables the design of devices leveraging nonreciprocal transport effects, chirality-induced spin selectivity (CISS), and cross-correlation optical phenomena.
• Enantioselective separation: The non-magnetic, multipole-mediated interfacial selectivity could provide a route to high-fidelity separation of chiral and axial molecules at the solid–liquid or solid–gas interface, with controllable substrate properties.

A plausible implication is that such effects would allow for novel approaches to enantioselective catalysis and next-generation resettable chiral/axial memory devices.

7. Experimental Prospects

While the analysis is predominantly theoretical, several experimentally accessible consequences are identified:

• Energy splittings between competing domain configurations at surfaces/interfaces are predicted to scale with |𝐐| and with the intrinsic multipole fields (h_{G₀} or h_{Gₓ}), suggesting observable signatures in domain stabilization and switching experiments.
• Candidate materials exhibiting strong axial or chiral order (e.g., RbFe(MoO₄)₂, NiTiO₃, Ca₅Ir₃O₁₂, K₂Zr(PO₄)₂) are already known to feature interfacial or single-domain phenomena, potentially related to these multipolar couplings.
• Surface-sensitive probes (such as scanning tunneling microscopy, nonlinear optics, or transport measurements) and controlled modifications of surface polarization via gating or adsorbate engineering represent experimental approaches for verifying CIAS/AICS predictions (Hayami et al., 21 Oct 2025).

Summary Table: Couplings and Outcomes

Bulk Order Present	Surface Field (𝐐)	Induced Order at Surface	Coupling Symmetry
Chirality (G₀)	Yes	Axiality (𝐆)	G₀ ↔ 𝐐·𝐆
Axiality (𝐆)	Yes	Chirality (G₀)	𝐆 ↔ G₀𝐐

This structural symmetry principle enables cross-coupling between different types of multipolar order and introduces a robust platform for tuning chiral and axial responses at interfaces.

Conclusion

Axiality-induced chirality via surface polarization embodies a reciprocal, symmetry-driven mechanism in which surface-induced dipole fields select and stabilize chiral or axial domains at an interface via symmetry-allowed multipolar couplings. This process, substantiated by theoretical modeling and symmetry analysis, underlies new avenues for single-domain stabilization, interfacial enantioselectivity, and tunable device functionalities, with broad implications for condensed matter systems, spintronics, and chiral molecular recognition (Hayami et al., 21 Oct 2025).