Magnetoelectric (ME) materials, possessing coupled magnetic and electric polarizabilities, are highly sought after for applications in magnetically controlled electronics and electric-field controlled spintronics. However, creating ideal ME materials is challenging due to the inherent competition between ferroelectricity and magnetism in their symmetry and electronic structure. While perovskite-type bismuth ferrite (BiFeO3) and hexagonal RMnO3 (R = rare earth elements) show ME coupling at room temperature, their limitations drive the search for alternative materials. Molecular materials offer advantages like tunability through functional group manipulation, but typically suffer from low ordering temperatures and weak spontaneous polarization. Recent research highlights that effective ME coupling can be achieved even in the paramagnetic phase through magnetostriction, where an applied magnetic field induces structural deformation, affecting internal dipoles. This paper focuses on [MX4]⁻ complexes (M = transition metal; X = halide ion), known for their potential ferroelectric properties and magnetostrictive effects. The study investigates (TMCM)[FeCl4] (TMCM = trimethylchloromethylammonium), a Fe(III)-based molecular complex, to demonstrate room-temperature ME coupling in its paramagnetic-ferroelectric phase.

The field of magnetoelectric coupling has primarily focused on multiferroics exhibiting coexisting ferroelectric and ferromagnetic orders. However, achieving this coexistence in single-phase molecular materials is difficult due to challenges in magnetic ordering within molecular complexes. A significant breakthrough was the 2020 report by Long et al., demonstrating room-temperature, low-field switching in a molecular ME material, [Zn(OAc)(L)Yb(NO3)2]. This study revealed two crucial aspects: effective ME coupling can occur even without long-range magnetic ordering (in the paramagnetic phase), and magnetostriction provides a viable pathway for demonstrating ME coupling in ferroelectrics. The sensitivity of transition metal ion magnetic interactions to coordination environment deformation makes molecular ferroelectrics potentially more responsive to magnetostriction than inorganic materials due to their softer crystalline frameworks. Previous works on molecular materials demonstrating magnetoelectric effects, including [N(C2H5)3CH3][FeCl4] and others, highlighted the potential but also the challenges in achieving robust room-temperature coupling at low fields. This study builds upon this foundation, aiming to demonstrate a robust ME coupling at room temperature and under low magnetic fields in a molecular system.

The study characterized the ferroelectricity and magnetostriction of (TMCM)[FeCl4] using various techniques. Ferroelectricity was investigated through structural analysis (revealing a polar monoclinic structure with space group Cm), second harmonic generation (SHG) measurements (confirming a non-centrosymmetric structure below 320 K), polarization-electric field (P-E) hysteresis loops (showing saturated polarization along the a- and c-axes), and piezoelectric force microscopy (PFM) (visualizing ferroelectric domains and their switching behavior). Magnetostriction was explored using atomic force microscopy (AFM) under an applied magnetic field, revealing non-uniform mechanical deformation with a magnitude of ~2 × 10⁻⁵ at 2.5 kOe. Physical property measurement system (PPMS) measurements confirmed the AFM results. In-situ single-crystal X-ray diffraction examined structural changes under magnetic fields, observing changes in intermolecular distances and [FeCl4]⁻ anion volume. Density functional theory (DFT) calculations qualitatively simulated the magnetostrictive effect, determining the magnetic ground state and predicting polarization values close to experimental results. The ME coupling was investigated using in-situ PFM measurements under magnetic fields, observing changes in ferroelectric domain distribution and P-E loop characteristics, further quantified through temperature-dependent polarization measurements under various magnetic fields. Specific methods used include differential scanning calorimetry (DSC), SHG, powder X-ray diffraction (PXRD), single-crystal X-ray diffraction, scanning electron microscopy (SEM), transmission electron microscopy (TEM), AFM, PFM, and direct current (dc) magnetic susceptibility measurements. The DFT calculations employed the Vienna ab initio Simulation Package (VASP) with the Perdew-Burke-Ernzerhof parameterization of the generalized gradient approximation (GGA) and Hubbard U correction.

The key findings of this study are: 1. (TMCM)[FeCl4] exhibits robust ferroelectricity at room temperature, confirmed by structural analysis, SHG, P-E loops, and PFM. The saturated polarization reached up to 0.32 µC cm⁻² along the a-axis and 6.1 µC cm⁻² along the c-axis. 2. The material displays significant magnetostriction at room temperature, with a deformation of ~10⁻⁴ along the a-axis under a 2 kOe magnetic field, confirmed by AFM and PPMS measurements. 3. A strong magnetoelectric coupling is observed at room temperature and under low magnetic fields. The magnetoelectric tensor component α31 is estimated to be approximately -89 mV Oe⁻¹ cm², much larger than values reported for BiFeO3. Under a 40 kOe magnetic field, the polarization along the a-axis decreases by -12%. 4. The magnetostrictive effect stems from the change in halogen Cl…Cl bond lengths and the volume of [FeCl4]⁻ anions, directly influencing the ferroelectric polarization. This is further supported by DFT calculations showing qualitative agreement with the experimental observations. 5. The DFT calculations confirm the experimental observation of a paramagnetic state at room temperature and provide a theoretical framework for understanding the magnetostrictive behavior. 6. The in situ PFM measurements clearly show the redistribution of ferroelectric domains under the applied magnetic field, providing direct evidence of the magnetoelectric coupling.

The results demonstrate the successful realization of a room-temperature magnetoelectric material with significant coupling at low magnetic fields. The observed ME coupling is directly linked to the magnetostrictive effect, providing a clear mechanism for the interplay between magnetic and electric properties. The magnitude of the magnetoelectric coupling observed in (TMCM)[FeCl4] is remarkably high, surpassing that of many conventional multiferroic materials. This finding offers a new design strategy for ME materials, highlighting the potential of molecular systems to achieve efficient ME coupling at room temperature and low magnetic fields. The successful combination of ferroelectricity and a significant magnetostrictive effect in a molecular system opens up possibilities for exploring similar molecular complexes for improved magnetoelectric devices. The quantitative agreement between experimental findings and DFT calculations strengthens the understanding of the underlying mechanisms.

This study successfully demonstrates room-temperature magnetoelectric coupling under low magnetic fields in the molecular ferroelectric (TMCM)[FeCl4]. The combination of ferroelectricity and a substantial magnetostrictive effect leads to a strong ME coupling, primarily due to changes in Cl…Cl distances and [FeCl4]⁻ anion volume under magnetic fields. This design strategy offers a promising avenue for creating efficient room-temperature magnetoelectrics with applications in spintronics and related fields. Future research can explore variations of the TMCM cation and other [MX4]⁻ complexes to further optimize ME coupling strength and explore novel functionalities.

The non-uniformity of magnetostriction observed in some regions of the crystal suggests that further investigation is needed to understand the origin of this inhomogeneity and its impact on the overall magnetoelectric properties. While DFT calculations provide valuable insights, they are qualitative and could be further refined to quantitatively model the paramagnetic state at room temperature. The current study focuses primarily on the a-axis; further investigation is needed to fully characterize the ME coupling along other crystallographic axes.