Strong ferroelectricity in one-dimensional materials self-assembled by superatomic metal halide clusters

Abstract

Cluster-assembled materials have long been pursued as they can create some unprecedented and desirable properties. Herein, we assemble a class of one-dimensional (1D) ReNX₄ (X = F, Cl, Br and I) and MF₅ (M = V, Nb and Ta) nanowires by covalently linking their superatomic clusters. These assembled 1D nanowires exhibit outstanding energetic and dynamic stabilities, and hold sizable spontaneous polarization, low ferroelectric switching barriers and high critical temperature. Their superior ferroelectricity is originated from d⁰-configuration transition metal ions generated by the hybridization of empty d orbitals of metal atoms and p orbitals of non-metal atoms. These critical insights pave a new avenue to fabricate 1D ferroelectrics toward the development of miniaturized and high-density electronic devices using building blocks as cluster with precise structures and functionalities.

Graphical abstract

Keywords

ferroelectricity / superatom / cluster-assembled materials / electronic properties / first-principles calculations

1 Introduction

Ferroelectric (FE) materials with the emergence of spontaneous electric polarization, have a wide range of technological applications, such as non-volatile memories, field effect transistors, sensors, and photovoltaics [1−5]. However, miniaturizing FE devices suffers from size limitation of the FE materials due to internal depolarizing electrostatic fields [6]. To overcome this issue, significant progress has been made in two-dimensional (2D) ferroelectrics. The ferroelectric polarization in 2D materials of atomic thickness can be strong enough to subsist, offering a natural solution for nanoscale ferroelectric applications [7, 8].

The lateral dimensionality of 2D ferroelectrics is formally infinite. In reality, however, the ferroelectricity may be weakened by edge reconstruction and boundary [9]. Alternatively, one-dimensional (1D) materials with “no-boundary” feature might be more appropriate for ferroelectrics. So far, several 1D FE nanostructures have been prepared in the laboratory, such as tetrabromo-p-benzoquinone chain [10, 11], water molecules in quasi-1D beryl crystal [12], BaTiO₃ and PbTiO₃ nanotubes [13], which, however, intrinsically contain nonnegligible structural defects. Therefore, it is still desirable to explore 1D ferroelectrics with structurally perfect “boundary” and high stability.

Atomically precise nanoclusters offer new opportunities for exploring excellent properties and can serve as building blocks with tunable electronic structures for assembling materials and devices [14]. Among them, “superatomic clusters” (namely, “superatoms”) possess outstanding stability and are promising for self-assembling [15, 16]. Indeed, some superatomic cluster assembled nanomaterials have already been synthesized. For instance, Re₆Se₈ clusters can be assembled into a 2D hierarchical semiconductor via strong interaction by substitutionally labile Cl atoms, whose transport properties are tunable from semiconducting to metallic and to superconducting upon n-type doping through Cl dissociation [17−19]. C₆₀ together with Co₆Se₈/Cr₆Te₈/Ni₆Te₈ clusters were patterned into three-dimensional crystalline array with CdI₂ or NaCl type [20]. On the theoretical side, Guo et al. [21] proposed a strategy to construct stable 2D lattices using superatomic tetrahedral clusters (i.e., B₄, Al₄, Ga₄, In₄, Cr₄, Mo₄, and Te₄) covalently linked by oxygen atoms. Du et al. [22] examined 27 dimers of endohedral cage clusters and predicted that M@X₁₆ (M = Ti, Zr, or Hf; X = Si, Ge, or Sn) are potential zero-dimensional vdW Lego blocks. Xing et al. [23, 24] presented a joint experiment-theory investigation of a rationally designed layered superatomic crystal of Au₆Te₁₂Se₈ cubes stacked by noncovalent intercube quasibonds, finding a sequential-emerged anisotropic triple-cube charge density wave and polarized metallic states below 120 K. Zhao et al. [25] designed a series of fullerene-based 1D chains, namely U₂C@C₈₀-M (M = Cr, Mn, Mo, and Ru) 1D chains, with both ferroelectric and ferromagnetic properties.

ReNCl₄ cluster with nearly ideal C_4v symmetry has been synthesized in a facile synthesis from perrhenate, sodium azide and HCl gas [26−28]. Inspired by the aforementioned cluster assemblies with extraordinary properties, herein we design 1D nanowires of ReNX₄ (X = F, Cl, Br, and I) by cluster self-assembling and extend them to 1D nanowires of MF₅ (M = V, Nb, and Ta) by isoelectronic substitution. The cluster-assembling rule takes into account both the closed electronic shells for ReNX₄ and MF₅ clusters as well as the binding strength between metal and N/F atoms. The molecular orbitals and superatomic characters of these clusters with 40 valence electrons were identified for the first time. Owing to second-order Jahn−Teller effect, these assembled nanowires intrinsically hold superior ferroelectricity with Curie temperature above 300 K, thereby paving a new route for the design of intrinsic 1D ferroelectrics from self-assembling.

2 Computational methods

Density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP) [29], with planewave basis set (energy cutoff of 500 eV), projector augmented wave potentials [30], and Perdew‒Burke‒Ernzerhof (PBE) exchange–correlation functional [31]. Based on equilibrium structures, a hybrid HSE06 functional [32] was further used to compute the electronic band structures. The convergence criteria for total energy and force were set to 10⁻⁷ eV and 0.01 eV·Å⁻¹, respectively. Uniform k-point meshes with spacing of ~0.015 Å⁻¹ were adopted to sample the Brillouin zones. Phonon dispersion analysis was performed using the Phonopy code [33] based on the density functional perturbation theory. The frontier molecular orbitals and natural population of individual ReNX₄ and MF₅ clusters were analyzed using the PBE functional accompanied with 6-311+G(d) [34] and SDD [35] basis sets, implemented in Gaussian16 suite [36].

3 Results and discussion

We firstly investigate the atomic structure and electronic properties of an individual ReNCl₄ cluster. As shown in Fig.1(a), four equivalent Cl^– atoms and one N^3– atom are bonded with one Re⁷⁺ atom to form a stable N–Re–Cl₄ unit with C_4v symmetry, with N–Re and Re–Cl bond length of 1.67 and 2.30 Å, respectively, and Cl–Re–N angle of 81.24°. According to the valence electronic configurations of Re (5d⁵6s²), N (2s²2p³) and Cl (3s²2p⁵) atoms, each ReNCl₄ cluster carry totally 40 valence electrons and achieves a closed electronic shell of 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁶, which is evidently demonstrated in Fig.1(b). For the first time, the superatomic characteristics [37] for valence molecular orbitals of ReNCl₄ cluster are identified, suggesting its great potential as a building block to assemble nanomaterial.

According to the geometric feature of ReNCl₄ cluster, Re atom is prone to bond with another N atom in adjacent ReNCl₄ cluster to form distorted corner-sharing ReN₂Cl₄ octahedra without tilt. In this manner, ReNCl₄ units can be self-assembled to construct a ReNCl₄ wire along the z axial direction with P4 symmetry and 1D lattice parameter of 4.08 Å. Here, each N^3– ion is bonded in a distorted linear geometry to two Re⁷⁺ atoms and each Cl⁻ ion is bonded to one Re⁷⁺ atom with bond length of 2.31 Å, resulting in invariable valence states of Re, N and Cl atoms as confirmed via the analysis of on-site Bader charge [38] (Re: ‒2.1e; N: 0.9e; Cl: 0.3e). There are one shorter (1.69 Å) and one longer (2.30 Å) Re–N bond with bond overlap population [39] of 0.93 and 0.11, corresponding to nature of strong and weak covalent bond respectively.

To verify the energetic stability of ReNCl₄ nanowire, we calculate its formation energy ΔH defined as ΔH = E_wire – E_cluster, where E_wire and E_cluster are the energy for one unit of 1D nanowire and an individual cluster, respectively. ReNCl₄ nanowire shows negative ΔH of −0.22 eV per formula (Tab.1), indicating that its formation is exothermic. The kinetic stability of ReNCl₄ nanowire is also confirmed by the phonon dispersions in Fig.2(b).

In light of the stability of self-assembled ReNCl₄ nanowire, Cl atoms can be substituted by other halogens (X = F, Br and I) and a series of hypothetic 1D ReNX₄ compounds might possess analogous structure as ReNCl₄ nanowire. More importantly, all these ReNX₄ clusters exhibit superatomic characters. Additionally, isoelectronic substitution is another effective strategy to design isostructural materials. Note that MX₅ (M = V, Nb and Ta; X = Cl, F, Br and I) hold same number of valence electrons with that of ReNCl₄ (40e), resulting in similar geometric structure for both types of clusters, that is, MX₅ cluster also displays X–M–X₄ arrangement like ReNCl₄ cluster. Therefore, 1D distorted MX₅ nanowires can be also constructed by self-assembling of MX₅ clusters (see Fig.2). The energetic and dynamical stabilities of these predicted nanowires are systematically assessed by their formation energies and phonon dispersions [Fig. S1 of the Electronic Supplementary Materials (ESM)]. Eventually, we screen out ReNF₄, ReNCl₄, ReNBr₄, ReNI₄, VF₅, NbF₅ and TaF₅ nanowires with exothermic formation energies ranging from ‒0.01 to ‒0.43 eV per formula, suggesting experimental feasibility for the synthesis of these 1D structures via cluster self-assembling. These results also support that self-assembling superatomic clusters is beneficial for thermodynamic stability. Specifically, the lattice parameters of ReNX₄ nanowires in the range of 3.88−4.10 Å are smaller than 4.11−4.63 Å for MF₅ nanowires (Tab.1). In addition, the lattice constant of ReNX₄ (MF₅) nanowire decreases with increasing atomic number of X (M) element. In all situations, metal ions show an off-center displacement along z axial direction by 0.20−0.82 Å. The electronic band structures of ReNX₄ and MF₅ nanowires are depicted in Fig. S2 of the ESM. Expect ReNI₄, all assembled nanowires are semiconductors with moderate or wide band gaps, which allows switching of the polarization a ferroelectric by applying an external field.

Due to non-centrosymmetry of ReNX₄ and MF₅ nanowires, there is spontaneous polarization along z axial direction. In order to explore the ferroelectric feature of these 1D nanowires, the centrosymmetric phase (P4/m symmetry) without displacement between metal and halide atoms along z axis is firstly identified as the paraelectric (PE) configuration (Fig.2). As a representative, Fig.2(c) displays the phonon dispersion of 1D PE ReNCl₄. Here, three imaginary branches including acoustic and optical phonon modes are throughout the entire Brillouin zone, indicating the geometric instability of PE configuration and a tendency of phase transition from ferroelectric state to a paraelectric state below Curie temperature (T_C). In addition, PE phase has higher energy than that of FE phase by 0.09‒0.85 eV per formula. Taking ReNCl₄ and VF₅ nanowires as examples, the scanned free-energy contour is plotted with different values of d₂‒d₁ and d₃ in Fig.3 (d₁ and d₂ represent the bond length of metal-linked atoms, and d₃ represents displacements of metal and halogen atoms along z chain direction). FE and ‒FE phases are equivalent states with lowest energy, separated by the nonpolar PE state (d₂ ‒ d₁ = d₃ = 0) located at the diagonal direction. These indicate the higher stability of FE and ‒FE phases compared with PE phase. The energy maps of other nanowires are presented in Fig. S3 of the ESM, showing similar phenomena.

The central symmetry of 1D FE ReNX₄ and MF₅ nanowires is eliminated due to the cooperative displacements between metal and halogen atoms, resulting in an evident spontaneous polarization P_FE along the chain direction. According to Berry phase through the modern theory of polarization [40], the calculated P_FE of 1D FE ReNX₄ and MF₅ nanowires are (25.64‒52.03)×10⁻¹⁰ C/m and (24.64‒55.50)×10⁻¹⁰ C/m, respectively, which are comparable and even larger than the values of many FE materials, such as transition-metal dichalcogenides [41], group-IV monochalcogenides [42, 43], bulk BaTiO₃ [44, 45] and lead-zirconate-titanate (PZT) [46, 47].

We further explore the origin of ferroelectricity in these nanowires. 1D ReNX₄ and MF₅ are semiconductors with band gaps in range of 1.43‒1.25 eV and 4.94−6.60 eV, respectively, and display similar features of electronic structure (Fig. S2 of the ESM). Note that ReNF₄ and VF₅ possess direct band gaps. Taking 1D FE ReNCl₄ nanowire as representative, the projected density of states for each element are displayed in Fig.4. The hybridization between Re‒d_xz/d_yz, N‒p_z and Cl‒p_z near the Fermi level is originated from Re–Cl and Re–N bonding. Here, the cooperation of empty d orbitals for Re⁵⁺ and p orbitals for N³⁻ along the polar direction regulates the existence of FE states in 1D ReNCl₄, resulting in the second-order Jahn‒Teller effect aroused by d⁰-configuration [48, 49], which is similar with the well-known FE perovskite oxides [44, 50]. Analogously, the ferroelectricity of VF₅ nanowire also results from d⁰ principle generated by V⁵⁺ empty d orbitals. Furthermore, more remarkable pdπ interaction of Re−d_xz/yz/N–p_x/y than pdσ interaction signifies the strong ferroelectric effect, which is also appeared in BaTiO₃ and PbTiO₃ [44]. Fig.4(c, d) and Fig. S4 of the ESM present the –COOP (Crystal Orbital Overlap Population) integrals for Re−N and M−F bonds, where a positive –COOP denotes favorable bonding interaction and a negative –COOP indicates unfavorable antibonding interaction. The results reveal that the occupied states are bonding states, while the unoccupied states belong to antibonding ones, further confirming that the FE states is stabilized by Re−N and M−F bonding.

Within the Landau−Ginzburg theory [51], the free energy and polarization should satisfy E=\sum _i\left[\frac{\alpha }{2}(P_i{)}^2+\frac{\beta }{2}(P_i{)}^4\right]+ \frac{\gamma }{2}\sum _{i,j}( P_i{-P_j)}^2. The first two terms are related to the energy contribution to polarization in each unit cell, which can be described by anharmonic double-well shape of the potential profile. α and β parameters are obtained by fitting the double-well potentials in Fig.5 and Fig. S5 of the ESM. The third term reflects the nearest-neighbor dipole−dipole coupling within the nanowire, and coefficient γ is fitted using the mean-field theory within nearest-neighbor approximation, which can be plotted as a parabola shape in second-order approximation shown in Fig.5(b) and Fig. S6 of the ESM. The energy barrier E_B for the transition from ferroelectric to paraelectric phases of ReNX₄ and MF₅ nanowires can be determined as 0.74‒0.85 eV and 0.09‒0.50 eV, respectively. It is noteworthy that E_B is one order of magnitude larger than that of other frequently used ferroelectrics such as BaTiO₃ and PbTiO₃ [44], suggesting high Curie temperature for these ferroelectric nanowires.

Ab initio molecular dynamic (AIMD) simulations [52] with 1×1×8 supercells are also performed to evaluate the Curie temperature of these nanowires. Fig.5(c) and Fig. S7 of the ESM show P_FE as a function of temperature. Taking ReNCl₄ and VF₅ nanowires as representatives, the static P_FE values of 25.64 C/m and 55.50 C/m are maintained at finite temperature up to about 300 and 100 K, respectively. Then the Curie temperature for transition of FE to PE phases can be fitted as the temperature-dependent P(T) = a/(1+e^{-k(T-T_C)}), where a and k are constants. Importantly, T_C value is usually related to the energy barrier E_B and the dipole‒dipole coupling between the adjacent unit cells, that is, T_C increases with increasing E_B. Here, ReNX₄ nanowires with larger E_B results in higher T_C value (224−321 K) compared with MF₅ nanowires (72−95 K), which also can be obtained from the pyroelectric response defined as p = ‒(dP/dT). Moreover, the piezoelectric response e₁₁ is dependent on a linear fitting of 1D polarization changes with respect to the uniaxial strains ε₁₁ along the z direction. A linear relation between polarization change and the strain within ±1% for ReNX₄ and MF₅ nanowires has been demonstrated in Fig.5(d) and Fig. S8 of the ESM. The obtained e₁₁ is as high as 61×10⁻¹⁰ C/m, which is an order of magnitude larger than that of MoS₂ monolayer (3.64×10⁻¹⁰ C/m) [53]. The active pyroelectric and piezoelectric responses in these nanowires suggest their broad applications in sensors and energy conversion devices. Particularly, the giant pyroelectric coefficients of ReNX₄ and MF₅ nanowires in range of (0.02‒0.13)×10⁻¹⁰ C/(K·m²) (Tab.1) are larger than those of most ferroelectric crystals, for instance, 2.0, 8.3, and 1.8×10⁻⁴ C/(K·m²) for BaTiO₃, LiNbO₃ and LiTaO₃, respectively [54].

4 Conclusion

In summary, we have designed a series of ReNX₄ (X = F, Cl, Br and I) and MF₅ (M = V, Nb and Ta) nanowires by self-assembling superatomic clusters, based on the criteria of superatomic orbital characters within the shell model and orbital interaction between adjacent clusters. Self-assembling superatomic clusters can strengthen the stability of these 1D structures and achieve ferroelectric effect. These cluster-self-assembled 1D materials are all dynamically stable and possess a moderate or wide band gap of 1.43‒6.60 eV (expect for metallic ReNI₄ nanowire). Notably, ReNX₄ and MF₅ nanowires exhibit sizable spontaneous polarization and low switching barrier, and ReNX₄ nanowires hold high T_C above room temperature that is essential for ferroelectric devices. The extraordinary ferroelectric properties in these assembled materials are derived from an electronic mechanism, i.e., the second-order Jahn‒Teller effect with d⁰-configuration transition-metal ions in the materials. These theoretical results open unprecedented opportunities for the discovery of new ferroelectric materials and point to a feasible route for the exploration of exotic 1D physics from cluster assemblies.

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