Ferroionic 2D Materials

• Ferroionic 2D materials are atomically-thin van der Waals systems that exhibit coupled ferroelectric, ferromagnetic, and ionic responses, exemplified by Cu⁺ migration in CuCrP₂S₆.
• They enable reversible control of electrical, magnetic, and optical properties via mechanisms like switchable polarization (~10 μC/cm²) and magnetoelectric coupling (α ~10⁻¹⁴–10⁻¹² s/m).
• These materials drive innovations in nonvolatile memory, spin/valley logic, neuromorphic electronics, and integrated photonics, outperforming other 2D alternatives such as WS₂, MoS₂, and graphene.

Ferroionic two-dimensional (2D) materials comprise atomically thin van der Waals systems exhibiting coupled ferroic orders—in particular, the coexistence and cross-coupling of ferroelectric, ferromagnetic, and ionotronic (mobile-ion-driven) phenomena. These materials, typified by transition/rare-earth halides and layered chalcogenides, allow the manipulation of electronic, magnetic, and ionic degrees of freedom via external stimuli. They support spontaneous, switchable polarization and/or magnetization persisting below a ferroic transition temperature, frequently mediated by the long-range rearrangement of light ions such as Cu⁺. This multifunctionality underpins emerging device architectures for nonvolatile memory, spin/valley logic, neuromorphic electronics, and tunable integrated photonics.

1. Fundamental Ferroic Orders and Definitions

Ferroionic 2D materials are characterized by the presence of at least two coupled order parameters:

• Ferromagnetism is spontaneous spin alignment below a Curie temperature, $T_C$, requiring spin-rotation symmetry breaking via magnetocrystalline anisotropy in 2D to evade the Mermin–Wagner theorem. The minimal model is an anisotropic Heisenberg Hamiltonian,

$$H = -\sum_{\langle i,j\rangle} J_{ij}\, \mathbf{S}_i \cdot \mathbf{S}_j - K \sum_i (S_i^z)^2$$

where $J_{ij}$ are exchange couplings and $K$ is the uniaxial anisotropy (An et al., 2020).

• Ferroelectricity is defined by a spontaneous, switchable polarization vector, $\mathbf{P}$, stable in zero field below $T_{FE}$. The Landau-Ginzburg expansion in $P$ reads

$$F(P) = \alpha P^2 + \beta P^4 + \gamma (\nabla P)^2 - \mathbf{E} \cdot \mathbf{P} + \cdots$$

where $\alpha$ changes sign at $T_{FE}$. Ionic displacements or rearrangements (rather than just rigid lattice distortions) can drive $P$ in ferroionic systems (Lai et al., 2018, Dushaq et al., 2023).

• Ferroionic response involves mobile cations (e.g., Cu⁺) whose field-driven redistribution between energetically degenerate (or metastable) sites carries the net dipole, directly controlling both ferroelectric and optoelectronic properties (Lai et al., 2018, Dushaq et al., 2023).
• Multiferroicity arises when multiple ferroic orders coexist and are coupled, notably via spin–dipole or valley–spin–charge couplings.

2. Prototypical Ferroionic 2D Materials and Structures

The principal families of transition/rare-earth halides and selected chalcogenophosphates realize diverse ferroionic phenomena:

Material	Structure/Class	Dominant Ferroic Orders	Structural Motif
CrI₃, CrBr₃	Trihalides (MX₃)	Ferromagnetism	Honeycomb; Cr in I₆/Br₆ octahedra
VOI₂, WO₂Cl₂	Oxyhalides/Chalcogenides	Ferroelectricity, spiral M	Layered; off-centering M ions
CuCrP₂S₆	Chalcogenophosphate	Ferroelectric, FM, valley	Monoclinic, ABPₓ geometry (Lai et al., 2018)
GdI₂	Rare-earth halide (MX₂)	Ferromagnetism	MoS₂ type; 2D FM from 4f electrons

Monolayer and few-layer CuCrP₂S₆ adopts a type-I ABPₓ structure where Cu and Cr alternate at the centers of puckered S hexagons, linked by P₂S₆ dimers. The ferroelectric phase exhibits all Cu⁺ displaced to one side of the chalcogen plane, generating a net out-of-plane dipole, while the antiferroelectric ground state features antiparallel Cu displacements (Lai et al., 2018, Dushaq et al., 2023).

3. Mechanisms and Quantitative Figures of Merit

Ferroionic phenomena are underpinned by field-driven ion motion and strong coupling between crystallographic, electronic, and magnetic subsystems:

• Ferroionic Polarization and Switching:
  • Out-of-plane ferroelectricity in CuCrP₂S₆ is driven by reversible Cu⁺ migration (displacement $d_\text{Cu} \sim 2.65$ Å). The estimated polarization in monolayer is $P_z \approx 10\,\mu\mathrm{C/cm}^2$.
  • The energy barrier for switching is 0.11–0.21 eV/f.u., corresponding to coercive fields $E_c\sim2.5\times10^7$ V/m, enabling room-temperature retention but requiring high field for metastable FE phase realization (Lai et al., 2018).
• Ferromagnetism and Magnetoelectric Coupling:
  • Intrinsic FM (3 μB/Cr³⁺) in CuCrP₂S₆ is stabilized by strong in-plane exchange ($\Delta E_\text{FM–AF}\sim13$ meV/f.u.) and moderate magnetocrystalline anisotropy energy (MAE $\sim0.5$–2 meV/f.u.). The direction of the magnetic easy axis is locked to ferroelectric polarization, yielding large magnetoelectric coefficients ($\alpha\sim10^{-14}$–$10^{-12}$ s/m) (Lai et al., 2018).
• Valley Coupling and Spin–Orbit Effects:
  • Spin–orbit coupling removes valley degeneracy in FE phase; reversal of $P_z$ or $M$ inverts the sign of valley splitting ($\Delta_v\sim20$ meV), supporting all-electric or all-magnetic control of valley polarization (Lai et al., 2018).
• Electro-optic Modulation via Ferroionic Mechanisms:
  • In hybrid silicon photonic microring resonators (MRRs), field-driven Cu⁺ redistribution in CuCrP₂S₆ modulates the local refractive index via the Kramers–Kronig relation. Experimentally, index changes $\Delta n_\text{eff}\approx2.8\times10^{-3}$ are achieved with optical losses of 2.7 dB/cm and voltage–length product $V_\pi L\approx0.25$ V·cm. This performance outstrips that of WS₂, MoS₂, and graphene-based phase shifters (Dushaq et al., 2023).
• Ionotronic and Memristive Dynamics:
  • Cu migration exhibits timescales $\tau_\text{ion}\sim10^{-2}$ s (for micron-scale domains, $D_i\sim10^{-10}$ m²/s). I–V measurements reveal bidirectional resistive switching with ON/OFF ratios $\sim4\times10^3$; nonvolatile, analog "weight" states persist under zero bias, analogous to memristive synapses (Dushaq et al., 2023).

4. Characterization Methodologies

The suite of experimental techniques for probing ferroionic 2D materials includes:

• Ferroelectricity: Piezoresponse force microscopy (PFM) enables nanoscale mapping and switching of polarization, with room-temperature amplitude/phase hysteresis and negligible topographic damage for CuCrP₂S₆ flakes (Lai et al., 2018).
• Ferromagnetism: Superconducting quantum interference device (SQUID), magneto-optical Kerr effect (MOKE), polarized photoluminescence (PL), and vibrating sample magnetometry (VSM) resolve both in-plane and out-of-plane FM loops in monolayer and stacked systems.
• Opto-ionic modulation: Optical transmission and resonance analysis in microring or Mach–Zehnder configurations extract $\Delta n$, extinction ratios, insertion losses, and voltage-driven hysteresis (Dushaq et al., 2023).
• Structural/defect analysis: High-resolution transmission electron microscopy (HRTEM), atomic force microscopy (AFM), and X-ray diffraction assess stacking, domain structure, and defect landscapes.

5. Device Architectures and Applications

Ferroionic 2D materials have enabled diverse device concepts:

1. Spin–filter tunnel junctions: CrI₃ or multiferroic analogues serve as atomically thin barriers for spin-dependent tunneling, yielding tunneling magnetoresistance $>10^4\,\%$ (An et al., 2020).
2. Magnetoelectric spin FETs: Heterostructures such as graphene|CrI₃|graphene allow gate-controlled AFM–FM switching with on/off ratios of $10^3$–$10^4$ (An et al., 2020).
3. Nonvolatile spin–valley memories: CuCrP₂S₆ underpins nonvolatile memory combining electric, magnetic, and valley degrees of freedom, switchable via external fields (Lai et al., 2018).
4. Integrated photonic phase shifters: CCPS/Si hybrid MRRs achieve sub-fJ/bit, compact ($<30\,\mu$m) devices for phase modulation, beam steering, and optical switching, surpassing competing 2D alternatives (Dushaq et al., 2023).
5. Neuromorphic elements: The analog, hysteretic ionotronic response provides a platform for memristive synapses with optical/electrical readout and programmable conductance states (Dushaq et al., 2023).

6. Theoretical Perspectives and Comparison with Other 2D Materials

Compared to strictly electronic or magnetic 2D systems, ferroionic materials harness the mobility of ionic sublattices. Distinctive features include:

• High polarization values: $P_z\sim10\,\mu\mathrm{C/cm}^2$ enabled by full-ion displacements (Cu, in CCPS) (Lai et al., 2018).
• Tunable, multistate analog memory: Ion migration energy barriers (0.1–0.2 eV) are intermediate between fast electronic and slow atomic rearrangements, facilitating both fast switching and long retention (Lai et al., 2018, Dushaq et al., 2023).
• Low-voltage, low-loss electro-optic tuning: CCPS devices exhibit $V_\pi L=0.25$ V·cm and propagation loss $<3$ dB/cm, outperforming WS₂, MoS₂, and graphene modulators in comparable waveguide or MRR architectures (Dushaq et al., 2023).

A summary table of key performance metrics is provided:

Material	Device	$L$ ($\mu$m)	$V_\pi L$ (V·cm)	Loss (dB/cm)	Voltage Range (V)
CCPS	Si MRR	30	0.25	2.7	±7
WS₂	SiN MZI	800	1.5	~5	±10
MoS₂	SiN MRR	30	0.69	4.2	±10
Graphene	Si EO mod	450	2.2	6–10	<5

(Dushaq et al., 2023)

7. Prospects, Limitations, and Directions

Ferroionic 2D materials, especially those based on mobile cations in van der Waals chalcogenides and halides, represent a versatile platform for the study and exploitation of strongly coupled ferroic orders at the atomic limit. They offer precise, reversible control of electric, magnetic, and refractive properties via applied fields and exploit spin, charge, and ion migration on comparable energy scales. Speed is currently limited by ionic drift ($\tau_{\rm ion}\sim10$–100 ms for micron domains), but device miniaturization and interface engineering may accelerate switching to sub-ms regimes (Dushaq et al., 2023). The analog, multistate functionality coupled with direct optical readout points to applications in neuromorphic photonics, nonvolatile multiferroic memory, and highly integrated quantum-classical platforms.

A plausible implication is that further development of synthesis methods (e.g., molecular beam epitaxy, encapsulation), alongside first-principles modeling, will be required to approach room-temperature operation and scalability for commercial optoelectronic and spintronic devices (An et al., 2020). The field remains actively driven by advances in high-sensitivity measurement, theoretical understanding of coupled ferroic domains, and applied device prototyping.