Molecular ferroelectric with low-magnetic-field magnetoelectricity at room temperature

The study addresses the challenge of realizing single-phase materials that exhibit coupled magnetic and electric polarizabilities (magnetoelectric coupling) at room temperature under low magnetic fields. Traditional multiferroics like BiFeO3 and hexagonal RMnO3 show room-temperature behavior but molecular ferroelectrics often suffer from low ordering temperatures, weak polarization, and low melting points, with ME coupling typically observed only at very low temperatures. The authors hypothesize that effective ME coupling can be achieved in a paramagnetic ferroelectric molecular solid by exploiting magnetostriction to modulate internal dipoles. They target [MX4]− (M = transition metal, X = halide) molecular complexes, proposing that the softer molecular framework enhances magnetostrictive responses and thus ME coupling. The specific research goal is to demonstrate low-field, room-temperature ME coupling in the paramagnetic ferroelectric (TMCM)[FeCl4] and elucidate the mechanism via structural changes and DFT.

The paper situates the work within efforts to realize room-temperature ME coupling for applications in data storage, spintronics, and low-power electronics. Prior room-temperature ME materials include BiFeO3 and hexagonal RMnO3, while molecular materials are attractive due to tunability via functional groups. Limitations of molecular ferroics include low ordering temperatures and weak polarization, and most ME coupling in molecular systems occurs at low temperature. A pivotal precedent is a 2020 report by Long et al. showing that ME coupling can arise in a paramagnetic molecular ferroelectric via magnetostriction, indicating long-range magnetic order is not required. The authors build on this by focusing on [MX4]− complexes, which are prone to ferroelectricity and magnetostriction, as promising candidates for room-temperature ME behavior.

• Structural and ferroelectric characterization: Single-crystal X-ray diffraction (room temperature; space group Cm; polar point group m). Temperature-dependent second harmonic generation (SHG) on powders (300–338 K) to detect non-centrosymmetry and phase transition. Differential scanning calorimetry (DSC) at 10 K/min to identify thermal anomalies. P–E hysteresis loops measured using a double-wave method to remove non-hysteretic components. Piezoelectric force microscopy (PFM: DART-SS-PFM and SS-PFM OFF-field) for local domain imaging, switching characterization, and amplitude/phase mapping.
• Magnetostriction measurements: Atomic force microscopy (AFM) under in-plane magnetic fields (±2 kOe) to map vertical displacement along the a-axis and acquire local magnetostriction loops. Physical Property Measurement System (PPMS-9) measurements of vertical displacement versus parallel magnetic field up to ~2.5 kOe at room temperature. In-situ single-crystal XRD under an external magnetic field (~10 kOe applied along c-axis) to quantify lattice parameter changes and intermolecular distances.
• Magnetic characterization: DC susceptibility χMT under 1 kOe from 2–370 K to confirm paramagnetism and detect subtle changes across the structural transition (~323 K).
• Magnetoelectric coupling characterization: In situ PFM under magnetic fields (±2 kOe) to monitor domain redistribution and intrinsic piezoelectric response (resonance and dΦ/dV slopes). Field-dependent ferroelectric loops and temperature-dependent polarization under various magnetic fields to quantify ΔP/P0.
• DFT calculations: VASP with PAW potentials; PBE-GGA + U (Dudarev, Ueff = 4 eV on Fe 3d); energy cutoff 500 eV; k-point grid 2×2×4; DFT-D3 vdW correction. Polarization via Berry phase method. Considered FM and three AFM orders; identified G-AFM ground state; estimated exchange J ≈ 0.3 meV. Simulated magnetostrictive trends via differences between FM and G-AFM optimized lattices; calculated band structure and DOS (band gap ~2.2 eV).

• Crystal structure and phase transition: (TMCM)[FeCl4] is monoclinic, polar (space group Cm, point group m) at room temperature. SHG shows non-centrosymmetric signals below ~320 K with a sharp change near 320–323 K; DSC shows first-order peaks at ~321.5 K, indicating a discontinuous structural transition to a centrosymmetric phase above this temperature.
• Ferroelectricity: P–E hysteresis confirms switchable polarization: Ps ≈ 0.32 μC cm−2 along a-axis and ≈ 6.1 μC cm−2 along c-axis. PFM reveals intrinsic piezoelectric responses along both a and c axes, 180° phase switching beyond coercive field, butterfly amplitude loops, and domain reversal upon poling.
• Magnetostriction: AFM under 2 kOe reveals ~10 nm thickness increase along a-axis in many regions, with heterogeneous responses (both positive and negative magnetostriction indicating multiple equivalent states). Local magnetostriction loops show displacement change ~2×10−5 at 2 kOe; PPMS corroborates ~2×10−5 at 2.5 kOe at room temperature. In-situ XRD under ~10 kOe (H//c) shows lattice changes: a from 13.0043(7) Å to 13.0808(5) Å, b from 14.8164(7) Å to 14.7898(5) Å, c from 6.4817(3) Å to 6.5327(2) Å, β from 98.881(4)° to 98.706(4)°. The intermolecular Cl···Cl distance increases from 3.422 Å to 3.451 Å; [FeCl4]− anion volume slightly decreases.
• Magnetoelectric tensor and coupling: The ME tensor component a31 reaches approximately 89 mV Oe−1 cm−1 (reported magnitude also noted as −89 mV Oe−1 cm2 in the abstract context). Magnetic fields suppress ferroelectric polarization along a, modifying loop symmetry, amplitude, and coercive fields. Relative polarization change ΔP/P0 along a is −7% at 10 kOe and −12% at 40 kOe at room temperature.
• Magnetism and theory: χMT at room temperature is 4.401 cm3 mol−1 K, close to Fe(III) S = 5/2 expectation (4.375). A transition near 323 K in χMT aligns with the structural (ferroelectric) transition. DFT finds G-AFM ground state with very weak exchange J ≈ 0.3 meV, consistent with experimental paramagnetism at room temperature. Calculated polarizations: ~0.31 μC cm−2 (a-axis) and ~8.23 μC cm−2 (c-axis), close to experiment. Differences between FM and G-AFM optimized lattices (a +0.15%, b +0.036%, c −0.083%) indicate a moderate magnetostrictive effect; band gap ~2.2 eV.
• Comparison: The measured ME response magnitude exceeds typical multiferroic BiFeO3 bulk values (≈0.6–7 mV Oe−1 cm−1), highlighting strong low-field, room-temperature ME behavior in a molecular ferroelectric.

The findings demonstrate that magnetostriction in a soft molecular ferroelectric framework can effectively couple magnetic and electric degrees of freedom in a paramagnetic state at room temperature. In (TMCM)[FeCl4], low magnetic fields stretch Cl···Cl contacts and slightly contract the [FeCl4]− anions, altering lattice parameters and local dipole configurations. This mechanically driven structural change suppresses ferroelectric polarization along the a-axis and yields a sizable ME tensor component a31, enabling low-field control of polarization. The heterogeneous magnetostriction response (multiple equivalent states) is consistent with a single-ion dominated mechanism in a soft lattice. DFT supports the mechanism, reproducing polarization magnitudes and indicating that small changes in magnetic configuration can produce measurable lattice distortions. Overall, the results validate a strategy for achieving room-temperature ME coupling in molecular ferroelectrics without requiring long-range magnetic order, with performance surpassing classic oxide multiferroics in ME coefficient magnitude under low fields.

This work establishes a design methodology for room-temperature, low-field magnetoelectric coupling in molecular ferroelectrics by leveraging magnetostriction of halide-coordinated transition-metal anions. The paramagnetic ferroelectric (TMCM)[FeCl4] exhibits robust ferroelectricity, significant low-field magnetostriction, and a large ME response (a31 ~89 mV Oe−1 cm−1; polarization reduction up to −12% at 40 kOe). Structural tuning under magnetic fields—particularly Cl···Cl stretching and [FeCl4]− volume change—directly modulates dipole configurations to couple magnetism and ferroelectricity. Future research could explore broader [MX4]− families and related molecular frameworks to optimize ME strength, stability across phase transitions, and device-relevant performance, as well as engineering domain and microstructural uniformity for reproducible responses.

• Molecular ferroics generally exhibit lower ordering temperatures, weaker spontaneous polarization, and lower melting points; although this system operates at room temperature, these broader material constraints may affect robustness.
• Magnetostriction is spatially nonuniform with both positive and negative responses at different regions, indicating multiple equivalent states and potential hysteresis/variability.
• A first-order structural transition occurs near 320–323 K (close to room temperature), which may influence stability and device operation across this temperature range.
• The material remains paramagnetic at room temperature with very weak magnetic exchange; while sufficient for magnetostriction-driven coupling, it precludes functionalities relying on long-range magnetic order.
• DFT simulations approximate the paramagnetic state (using ordered spin configurations), providing qualitative rather than fully quantitative descriptions of magnetostrictive responses.