Chirality-Induced Spin Polarization

• Chirality-induced spin polarization is the effect where electrons passing through non-mirror symmetric materials acquire a preferred spin orientation via spin–orbit and exchange interactions.
• Theoretical models using non-Hermitian exchange and geometric spin–orbit coupling demonstrate robust spin filtering across molecular, bulk, and knot-like systems.
• Applications span spintronics, enantioselective sensing, and quantum information, driving innovations in tunable chiral materials and device architectures.

Chirality-induced spin polarization describes the phenomenon where electrons traversing chiral systems—materials or molecules lacking mirror and inversion symmetries—emerge with a preferred spin orientation. This effect, commonly summarized under the term chirality-induced spin selectivity (CISS), manifests across multiple platforms, including molecular assemblies, bulk crystals, topological knots, and hybrid optoelectronic architectures. It has significant implications for spintronics, quantum information, molecular sensing, and fundamental questions in chemical and condensed matter physics.

1. Origin and Mechanisms of Chirality-Induced Spin Polarization

The central microscopic mechanism behind chirality-induced spin polarization is the coupling of electron spin to the chiral geometry of matter, fundamentally mediated by spin–orbit or exchange interactions that break mirror (parity) and time-reversal symmetry, while often preserving combined $\mathcal{PT}$-symmetry (Theiler et al., 9 May 2025). In structurally chiral electron systems, the absence of mirror symmetry prohibits independent two-electron exchange; instead, a correlated “twin-pair” exchange emerges, inherently violating both %%%%1%%%% and $\mathcal{T}$ but conserving $\mathcal{PT}$. This requirement imposes a non-Hermitian exchange term in the effective Hamiltonian: $$H = \frac{{\hat{p}}^2}{2m} + \hat{V} - i\alpha\, \hat{\sigma} \cdot \hat{p}$$ with $\alpha = K/(mc)$ derived from the exchange interaction $K$. This term links electron spin to momentum (spin-momentum locking), a generic requirement for robust spin filtering.

In organic molecules and biological electron-transfer processes, the mechanism is often initiated by photoexcitation and subsequent electron hopping: the system evolves from a singlet excited state $|S_1\rangle$ via spin–orbit and exchange couplings to a charge transfer (CT) state prepared as a coherent superposition,

$$|\psi_{\theta}\rangle = \cos\theta\,|S\rangle + i\sin\theta\,|T_0\rangle$$

with chirality-dependent mixing angle $\theta = \arctan(\Lambda_{DA}/(2 V_{DA}))$ (Fay et al., 2021). The exchange coupling in the intermediate state enables an oscillatory conversion of this spin coherence into a real, measurable spin polarization.

In bulk chiral metals and topological knots, geometric curvature and lattice topology further amplify the effect. For example, in trefoil knot molecular systems (“knot-driven spin selectivity”), geometric spin–orbit coupling arises from electrons following three-dimensionally curved paths, generating Berry phase-driven spin transport robust against disorder and temperature (Sun et al., 27 Jul 2025).

2. Theoretical Models and Quantitative Formulations

Analytically tractable models capture the essential elements of chirality-induced spin polarization:

• Non-Hermitian Exchange: The effective Hamiltonian $H = (p^2/2m) + V - i\alpha\, \sigma \cdot p$ captures the non-Hermitian exchange responsible for boundary-localized, spin-polarized states (Theiler et al., 9 May 2025).
• Photo-induced Electron Transfer: The net static spin polarization deposited by hopping between CT states is given by

$$\langle \Delta P_z \rangle = -\frac{k_{ET2} (2J/\hbar) \sin(2\theta)}{k_{ET2}^2 + \Omega^2}$$

with $$\hbar\Omega = \sqrt{4J^2 + \delta\epsilon^2 + 4J \delta\epsilon\cos(2\theta)}$$, encapsulating contributions from exchange $J$, SOC $\Lambda_{DA}$, and diabatic coupling $V_{DA}$ (Fay et al., 2021).

• Diffusive Chiral Metals: For bulk, diffusive systems characterized by a “hedgehog” spin–orbit interaction $H = (k^2/2m) + \alpha \sigma\cdot k$, Boltzmann-transport formalisms yield bulk and boundary spin polarization,

$$s_z^{(1)}(z, t) = \frac{1}{3} \frac{e E_0 \tau}{\pi^2} m^2 \alpha \cos(\omega t)$$

$$j_{s;zz}^{(2)}(z, t) = -\frac{7}{15} \frac{(eE_0\tau)^2}{\pi^2} m \alpha \cos^2(\omega t)$$

These responses manifest as current-induced magnetization and, at higher order, spin currents and antiparallel accumulation at boundaries (Kato et al., 8 Aug 2024).

• Topological Knots: In knot systems, geometric SOC arises from the molecular curvature,

$$H_{geo} = \frac{\hbar}{4m} \sum_i [-\kappa_i (N_i \times p_i) \cdot \sigma]$$

where $\kappa_i$ is the local curvature and $N_i$ the normal vector of the path. The discretized form accurately quantifies robust, topology-protected spin polarization (Sun et al., 27 Jul 2025).

• Electron Correlation Enhancement: In chiral molecular wires with strong electron–electron interactions, spin polarization is significantly enhanced—up to $46.5\%$—by correlation-driven suppression of kinetic energy and effective amplification of the SOC (Xu et al., 7 May 2024).

3. Experimental Signatures and Robustness

Multiple experimental platforms provide high-confidence signatures of chirality-induced spin polarization:

• Bulk and Polycrystalline Systems: Robust, millimeter- and centimeter-scale spin polarization is detected in both single-crystalline and polycrystalline samples of chiral disilicides (NbSi$_2$, TaSi$_2$) using inverse spin Hall voltage conversion techniques. The effect is resilient against grain boundaries and sample fragmentation, with a “sum rule” verifying that nonlocal spin signals add up across distant domains (Shishido et al., 2021, Kousaka et al., 2022).
• Nonlocality and Device Engineering: Nonlocal spin polarization extends over macroscopic distances, and simultaneous injection of charge currents at multiple contacts allows spatial “gating” of spin polarization domains. The splitting of spin-dependent chemical potentials, $\Delta\mu = \mu_\uparrow - \mu_\downarrow$, describes the phenomenology (Shishido et al., 2023).
• Magnet-Free Spin Generation: Injection of charge from a nonmagnetic electrode through a self-assembled chiral molecular layer (e.g., $\alpha$-helix AHPA-L) into $n$-doped GaAs yields a detectable spin accumulation, governed by a universal temperature dependence $\Delta V(T)/\Delta V(0) = 1 - (T/T_0)^{5/2}$ and a log-normal scaling with current (Liu et al., 27 Mar 2024).
• Topological Robustness: Trefoil knot molecules sustain ultra-high spin polarization (often $>60\%$, approaching $90\%$ experimentally) and metallic conductivity that is stable against molecular lattice distortions, strain, and high temperature (to 350$^\circ$C). The disappearance of the effect upon topological trivialization underscores the unique protection afforded by knot topology (Sun et al., 27 Jul 2025).

4. Role of Spin–Orbit, Phononic, and Vibrational Interactions

The magnitude and efficiency of chirality-induced spin polarization depend fundamentally on the interplay of molecular structure, SOC, nuclear vibrations, and, in solids, atomic-scale symmetry breaking:

• Spin–Orbit Conversion: Organic molecules typically possess weak SOC, but adjacent heavy-metal electrodes or intrinsic SOC in inorganic chiral crystals are critical for converting orbitally polarized currents into net spin polarization (Adhikari et al., 2022, 2208.00043, Yang et al., 2023).
• Phononic and Vibronic Effects: Chiral phonons—lattice vibrations with noncollinear polarization vectors—carry angular momentum and generate spin currents in nonmagnetic conductors through phonon-assisted SOC. The kernel of the induced polarization,

$$\langle M_k \rangle = 4\xi \int f(\epsilon_k) l_q^2 V^2(q) K_{k,q}\,dq/(2\pi)^3$$

captures this angular momentum transfer (Fransson, 2022). Additionally, vibrational circular dichroism modes in chiral molecules can drive time-dependent changes in spin angular momentum ($dS/dt$), especially under applied magnetic fields, resulting in net spin-polarization without net charge current (Miwa et al., 4 Dec 2024).

• Pseudo Jahn–Teller Interactions: In C$_3$ symmetric molecules, pseudo Jahn–Teller coupling enables translational–rotational mixing, setting an angular momentum “barrier” for spin-selective transmission. The resulting spin filtering efficiency is largely independent of the molecular SOC and underpinned by nuclear vibrational quantum number dynamics (Kato et al., 2021).

5. Unified Paradigms and Quantitative Chirality Measures

Recent theoretical work synthesizes CISS effects within a non-Hermitian, quantum statistical framework emphasizing symmetry constraints:

• Non-Hermitian Exchange as Universality: The twin-pair exchange model with a non-Hermitian $i\,\hat{\sigma}\cdot\hat{p}$ term, but conserved $\mathcal{PT}$, explains both robust real eigenvalues and boundary spin accumulation (the “skin effect”). Its applicability spans 1D helices, tetrahedral molecules, crystalline solids, and systems with complex topologies, offering a unified explanation for all observed CISS phenomena and their spin-momentum locking (Theiler et al., 9 May 2025).
• Continuous Chirality Measure (CCM): The degree of chirality, quantified by CCM, linearly tracks SOC-induced spin splitting and orbital moment polarization,

$$B^{in}(\mathbf{k}) = C \cdot \mathbf{k}, \quad C = C_s + C_v + C_t$$

where $C_s, C_v, C_t$ correspond respectively to Weyl, Rashba, and Dresselhaus tensors (Grieder et al., 15 Apr 2025). Hydrostatic pressure, atomic substitution, or molecular strain can tune CCM and thereby control spin filtering, orbital polarization, and chiroptical effects.

• CISS as Spin Polarizer: In two-terminal quantum transport, the correct scattering matrix treatment reveals that chiral molecules are spin polarizers—transmitted and reflected electrons possess the same (not opposite) spin polarization, dictated by chirality and electron incidence (2208.00043). This eliminates the paradox of equilibrium spin current and aligns theory with observed anomalous Hall effects.

6. Applications, Implications, and Future Directions

Chirality-induced spin polarization has inspired rapid innovation in spintronics, quantum information, molecular sensing, and enantioselective catalysis:

• Spintronic Devices: Robust room-temperature spin filtering, kilometer-scale propagation in chiral crystals, nonmagnetic spin injection, and the realization of gate-tunable nonlocal spin polarization suggest realistic pathways to low-power, high-coherence spin transistors, logic gates, and memory architectures.
• Enantio-Selective Chemistry and Sensors: Enantiospecific NMR signals, induced by chirality-dependent spin-spin couplings, point to direct routes for NMR-based chiral discrimination and potentially to the development of molecular quantum logic networks (Georgiou et al., 1 Jul 2024). Devices exploiting chiral vibrationally driven spin polarization may enable magnetic separation of enantiomers using achiral ferromagnetic substrates (Miwa et al., 4 Dec 2024).
• Material Design via CCM: The integration of continuous chirality measure with electronic structure calculations provides a rational strategy for discovering and engineering chiral materials with prescribed optical and spintronic functionalities (Grieder et al., 15 Apr 2025).
• Fundamental and Applied Open Questions: Outstanding challenges involve mapping the impact of electron correlation and many-body dynamics (Xu et al., 7 May 2024), extending models to complex geometries (multi-knot structures, higher-dimensional topological manifolds), and refining theoretical frameworks for non-Hermitian quantum dynamics in open chiral systems. Experimentally, correlating macroscopic device response with molecular-scale chirality and resolving the crossover from molecular to crystalline to topological CISS remains a frontier.

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In summary, chirality-induced spin polarization encompasses a spectrum of mechanisms—all rooted in the interplay between geometric or topological asymmetry, spin–orbit or exchange interactions, and quantum statistics that transcend conventional Hermitian, parity, and time-reversal symmetric frameworks. The phenomenon is now recognized across molecules, crystals, and moiré superlattices, with a unified theoretical treatment converging on non-Hermitian exchange and spin-momentum locking as universal drivers. This conceptual and technological advance underpins ongoing innovation in quantum information, molecular recognition, and the design of synthetic chiral materials for next-generation spintronic devices.