The reaction of Dy(NO3)3.5H2O, L1, and CoBr2 in MeOH at ambient temperature in the presence of triethylamine yields block-shaped brown-colour single crystals (Supplementary Fig. 1). The single crystal data collection was performed at both low-temperature (150 K) and RT (300 K). The structure solution unveiled the molecular formula of the complex as [CoIII3DyIII(L1)6].4MeOH (Co3Dy; Fig. 1a). Co3Dy is crystallized in the tetragonal, polar P43 space group. The unit cell parameters remain unchanged at low and RTs (Supplementary Table 1), indicating that the polar space group is well maintained up to RT, which is a highly challenging process for the discrete molecular system.16–18 As no drastic structural changes are observed in the data collected at two different temperatures, the structural description of Co3Dy collected at RT is detailed in the Supplementary text.
The thermal stability of complex Co3Dy was assessed by thermogravimetric (TGA) analysis, showing a weight loss of ~ 6.2% between 320–340 K due to solvent MeOH departure (Supplementary Fig. 2). This loss of solvent molecule did not affect the structure of Co3Dy, confirmed by variable temperature PXRD (Supplementary Fig. 3). No thermal anomaly was observed up to 350 K in differential scanning calorimetry (DSC) (Supplementary Fig. 4). To determine the accurate FE transition temperature (Tc; FE to paraelectric) we performed the temperature-dependent dielectric measurement of Co3Dy, where a distinct dielectric anomaly was observed around ~ 330 K in the plot of the real part of the dielectric constant (εr) as a function of temperature (Supplementary Fig. 5a). The εr values in different frequencies (e.g., εr = 43.1 at 1.2 kHz and 330 K) are in the expected range for the discrete molecular FE, which is consistent with the other literature reports.16,18 However, the observed tangent loss (tanδ ~ 0.85 at 1.2 kHz) value is relatively high (Supplementary Fig. 5b) as compared to the traditional piezoceramics (tanδ ~ 0.02) and some of the other discrete molecular systems. This is presumably due to the (semi)conducting metal ions present in Co3Dy (such as CoIII/DyIII).20 The temperature-dependent εr in ferro- and para-electric phases were linearly fitted using the Curie-Weiss law. We noticed that the ratio of Cpara to Cferro is close to 1 for all the frequencies measured (Supplementary Fig. 5c).21 This suggests a second-order phase transition mechanism is operational in Co3Dy, a common phenomenon for discrete molecular complexes supported by the broad Gaussian-like anomaly in the εr plot. The changes in the entropy (ΔS = 15.03 J K⁻¹ mol⁻¹) and enthalpy (ΔH = 2.47 J g⁻¹) values from DSC further support this proposal.22 Hence, the Tc of Co3Dy is above RT (Tc >330 K), which is unusual for discrete molecular complexes.23
To assess the FE characteristics of Co3Dy pellet, we measured the polarization versus electric field (P-E) loop at a frequency of 20 Hz at RT. We observed a well-saturated hysteresis loop with a polarization (Ps) value of 0.35 µC/cm² (Fig. 1b). To unambiguously confirm the FE signature of Co3Dy, the local FE response was probed with the help of piezo-response force microscopy (PFM), performed at RT. Amplitude and phase shifts were recorded at different points of the sample, which afforded a typical butterfly loop (amplitude vs. voltage) and phase loop (phase vs. voltage; Fig. 2a). Both of these hysteresis loops confirm the ferroelectricity and polarization reversibility of Co3Dy. The piezoelectric coefficient (d33) value calculated from the butterfly loop is 123 ± 0.5 pC/N, the highest value reported in all the discrete molecular complexes, hybrid organic-inorganic systems, and even most of the well-known bulk oxide systems (Fig. 2b). Such a large value of d33 is attributed to the high amplitude values in the butterfly loop, which originates from the more remarkable strain inducing in the presence of the applied voltage (Figs. 2c and 2d), which is presumably assisted by the elastic structural flexibility offered by Co3Dy in the presence of electric field. The "propeller-shaped" arrangement of the metal ions (3 CoIII and one DyIII) linked by the chiral ligands facilitates polarizing the molecule (vide infra). Also, the high color contrast in the PFM phase images indicates mixed domain patterns with different polarization directions of the dipoles (Figs. 2e and 2f).
The FE behavior of Co3Dy is well established, and we turned our attention to investigating the slow relaxation of magnetization (SMM) behavior in the DyIII ions of Co3Dy. The variable temperature DC magnetic susceptibility was measured from 2.0 K to 300 K in the presence of 1 kOe (Supplementary Fig. 6). The observed RT magnetic susceptibility (χMT) value of 14.01 cm3 K mol− 1 matches with the theoretical value for DyIII ion (14.17 cm3 K mol− 1), indicating the high purity of Co3Dy.38 AC magnetic susceptibility showed out-of-phase signals below 6.2 K without an external DC field, suggesting magnetic bi-stability due to the strong orbital momentum of DyIII in Co3Dy (Supplementary Fig. 7–9). Ab initio CASSCF calculations on the X-ray structure of Co3Dy revealed the magnetization easy axis is perpendicular to the molecule's plane (Supplementary Fig. 10). LoProp-Charge analysis confirmed delocalized charge density on metal ions (Supplementary Fig. 11), resulting in switchable polarization, leading to an unprecedented piezoelectric d33 coefficient of 123.5 ± 0.5 pC/N. Further details on magnetization reversal energy barriers are in the supplementary information (Supplementary Figs. 12–13 and Tables 2–4). Magnetic hysteresis showed weak coercivity at 2.0 K (Supplementary Fig. 14) and a paramagnetic behavior at RT (Fig. 3a). Molecular engineering enables precise chemical adjustment of materials, allowing the integration of the FE phenomenon with anisotropic metal ions, as seen in Co3Dy. Such synergy is difficult to achieve in conventional bulk oxides due to the counterbalancing of FE and FM properties in the same phase.
The coexistence of FE and paramagnetic responses at RT suggests the possibility of an ME effect in Co3Dy.36 Materials exhibiting ME coupling demonstrate a close connection between magnetic ordering and electric polarization, consequently impacting dielectric properties. Magneto-dielectric (MD) coupling in MF materials can be confirmed when a noticeable and consistent change in εr occurs as a function of an external DC magnetic field. The frequency-dependant real εr and tan(δ) behaviour of Co3Dy at RT is illustrated in Supplementary Fig. 15. The higher εr at a lower frequency (ꞷ) can be understood from the Maxwell–Wagner (MW) model.39 At higher frequency regions, the relaxation time (τ) of the interfacial dipoles exhibits a notable decrease (ꞷ < 1/τ). Consequently, the dipoles lag behind the applied electric field, reducing the εr.40 This phenomenon is also reflected in tan(δ) behavior, which follows a similar trend with increasing frequency. The study of the MD effect, characterized by a change in the εr due to the application of an external magnetic field, has been the subject of extensive research to identify MF phases in bulk oxides, while such investigation lacks in the literature for discrete molecular based MFs.41,42 The MD effect is computed as follows:
MD (%) = \(\frac{{{\epsilon }}_{r}\left(H\right)-{{\epsilon }}_{r}\left(0\right)}{{{\epsilon }}_{r}\left(0\right)}\) × 100 …………………..Eq. 1
where, εr (H) and εr (0) represent the dielectric constant in the presence of an external magnetic field H and zero fields, respectively.
The frequency-dependent MD (%) was calculated in the presence of 5 and 8 kOe magnetic fields (Fig. 3b). The negative amplitude of MD (%) refers to a decrease in εr (MD % = -2.0% and − 3.0%, respectively in 5 kOe and 8 kOe magnetic fields), which is higher in the low-frequency region and increases with an applied external magnetic field. A similar MD (%) effect has been noted in other materials (Supplementary Table 5). The observed MD effect likely occurs due to the intrinsic spin-lattice effect.23 This demonstrates the presence of an inherent coupling among spin and dipolar order; given that DyIII ground state anisotropy is strongly axial, relatively strong dipolar coupling is also expected.
To extract the α, we fabricated an ME nanogenerator (MENG) device based on Co3Dy (Co3Dy-MENG), and the purity of the active component (Co3Dy) of the device was further confirmed through PXRD (Supplementary Figs. 16–17). We employed a semi-dynamic method to determine the α between spin and dipoles (Supplementary Fig. 18). A linear relationship between the generated voltage and the HAC indicates a well-established linear ME coupling effect (Fig. 3c).7 This phenomenon is also widely recognized in bulk oxide/composite materials.43
Furthermore, we varied the frequency of HAC within the range of 100 Hz to 10 kHz while maintaining a constant amplitude of 2 Oe, and we measured the induced voltage. Applying Eq. 2, we calculated α for different frequencies (Fig. 3d).
α = \(\frac{V}{{H}_{AC} \times t}\) …………………..Eq. 2
Where, V and t represent the induced voltage and thickness of the film, respectively.
Remarkably, we observed the maximum α value of ~ 250 mV Oe− 1 cm− 1 registered at 1 kHz. The observed α value for Co3Dy-MENG is the largest reported compared to the other literature reports, including Long and co-workers' recent ZnII-YbIII molecular complex.36 This value is also surpassed by the several conventional oxides of single-phase and/or multi-phase materials reported in the literature (Fig. 4). Therefore, the molecular-based MFs are observed to be an excellent candidate to increase ME coupling to realize the molecular-based memory device, sensor, transducer, actuators, etc.
We used finite element analysis (FEM) simulations to study the induced voltage from the Co3Dy-MENG in response to an applied AC magnetic field.47 The simulation model featured a cylindrical coil with 90 copper wire turns and a DyIII complex thin film (Dy-film) exposed to the AC magnetic field along the z-direction. Experimentally determined parameters like εr and permeability were used as input for this model. An AC of 1 A at 1 kHz was applied to the coil, generating a magnetic field as per Maxwell's first equation (∇ × H = J + ∂D/∂t). This induced an electric field in the Dy-film following Faraday's law (∇ × E = - ∂B/∂t), resulting in electric displacement on the surface according to Gauss's law (∇·D = ρ, D = εE). The simulation showed surface polarization and the generation of surface charge in response to the AC magnetic field.
To validate the magnetoelectric coupling observed from the FEM analysis, we used the Co3Dy-MENG device to convert the magnetic field to electrical energy (Supplementary Figs. 19–20). This coupling, achieved through "strain-mediated magnetoelectric coupling," controls the interactions of magnetic and electrical properties in MF materials by inducing strain,36 often through piezoelectric effects, thereby enhancing functionalities like voltage generation in AC magnetic fields (Fig. 5a).43
An AC voltage regulator powered the Helmholtz coil to produce the AC magnetic field. The Co3Dy-MENG device generated an open circuit voltage (Voc) of about 430 mV and a short circuit current of 0.3 µA with a 24.2 Oe AC magnetic field (Fig. 5b-5c), exhibiting a magneto sensitivity (Sm = Voc/HAC) of 17.7 mV Oe− 1 at ~ 50 Hz.48,49 The harvested power was stored in capacitors with different capacitances (1, 2.3, and 4.7 µF; Fig. 5d and Supplementary Fig. 21). Additionally, we demonstrated a practical application by connecting the Co3Dy-MENG device to a bridge diode rectifier and a 0.3 µF capacitor, powering a red LED (Fig. 5e(i)). This setup efficiently captures weak AC magnetic fields, such as those from household appliances like hair dryers, which are generally challenging for conventional generators. The Co3Dy-MENG device generated an output voltage from an AC magnetic field due to its strong ME coupling. This energy powered a red LED (Fig. 5e(ii)), showcasing the practical application of the ME coupling in Co3Dy at RT. When exposed to the AC magnetic field from a hair dryer, Co3Dy a single-phase molecular-based MF, exhibited strain-induced polarization changes, leading to electricity generation. This sustainable energy can be stored in a battery or capacitor, highlighting a novel energy harvesting method with potential for self-powered molecular-based devices.