Yinglu
Jia
^{ab},
Min
Zhao
^{a},
Gaoyang
Gou
*^{a},
Xiao Cheng
Zeng
*^{b} and
Ju
Li
*^{c}
^{a}Frontier Institute of Science and Technology, and State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi' an 710049, China. E-mail: gougaoyang@mail.xjtu.edu.cn
^{b}Department of Chemistry and Department of Mechanical & Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA. E-mail: xzeng1@unl.edu
^{c}Department of Nuclear Science and Engineering and Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. E-mail: liju@mit.edu
First published on 4th May 2019
Two-dimensional (2D) ferroelectric (FE) materials displaying spontaneous polarizations are promising candidates for miniaturized electronic and memory devices. However, stable FE orderings are only found in a small number of 2D materials by experiment so far. In the current work, based on high-throughput screening of a 2D van der Waals layered materials database and first-principles calculations, we demonstrate niobium oxide dihalides NbOX_{2} (X = Cl, Br and I), a group of experimentally synthesized yet underexplored van der Waals layered compounds, as a new family of 2D materials that simultaneously exhibit intrinsic in-plane ferroelectricity and antiferroelectricity. Similar to FE perovskite oxides, polar displacement of Nb cations relative to the center of the anion octahedral cage can lead to experimentally measurable FE polarizations up to 27 μC cm^{−2} in layered NbOX_{2}. The presence of low-lying antiferroelectric (AFE) phases can effectively reduce the energy barrier associated with polarization switching, suggesting switchable ferroelectricity is experimentally achievable. In addition, the mechanism driving FE phase transitions in NbOX_{2} monolayers around Curie temperature T_{C} is clearly revealed by our finite-temperature simulations. NbOCl_{2} monolayer is predicted to be a stable ferroelectric with T_{C} above room temperature. Moreover, application of NbOBr_{2} and NbOI_{2} monolayers as 2D dielectric capacitors is further developed, where electrostatic energy storage of nearly 100% efficiency can be achieved in the 2D single-layer regime.
New conceptsTwo-dimensional (2D) ferroelectric (FE) materials with stable spontaneous polarizations above room temperature hold great promise in miniaturized electronic and memory devices. Here, we demonstrate a new strategy to uncover a wide spectrum of experimentally synthesizable yet unreported 2D FE materials. Combining high-throughput screening of a 2D layered materials database and first-principles calculations, layered NbOX_{2} (X = Cl, Br and I), have been identified as a new family of 2D FE materials. The 2D NbOX_{2} layers can be readily obtained through exfoliation of bulk NbOX_{2} which were synthesized decades ago. In particular, NbOCl_{2} monolayer with atomic thickness can exhibit room temperature stable ferroelectricity with sizable spontaneous polarization. Moreover, coexistence of FE and antiferroelectric (AFE) phases and the associated AFE/FE phase transition can enable practical applications of layered NbOX_{2} as 2D dielectric capacitors, with the potential to achieve nearly 100% efficiency for electrostatic energy storage. |
Guided by first-principles calculations, a number of 2D FE materials have been successfully synthesized and demonstrated with stable FE orderings by experiment. Typically, in-plane ferroelectricity and FE phase transitions were predicted in group-IV monochalcogenide (GeS, SnS and SnSe, etc.) monolayers,^{11–14} and then experimentally demonstrated in atomic-thick SnTe.^{15,16} Computational discovery of 2D FE α-In_{2}Se_{3} layers^{17} initiated the extensive experimental studies on intercorrelated in-plane and out-of-plane ferroelectricity within this system.^{18–22} Spontaneous symmetry breaking in the 1T phase of MoS_{2} monolayers can lead to robust in-plane ferroelectricity,^{23} while its structural polarity was detected by second harmonic generation measurement very recently.^{24} The material discoveries mentioned above largely relied on researchers' experience or chemical intuition, which was usually restricted to identifying 2D FE materials with structure or composition analogous to the known ones. For example, group-IV monochalcogenide monolayers were investigated as structural analogues to phosphorene.^{11} Therefore, providing rational strategies for a wide spectrum of new 2D FE material discovery will largely accelerate research progress within this field, which is also beneficial for a complete and insightful understanding regarding the unique properties of 2D ferroelectricity at the nanoscale.
In this work, instead of using a traditional intuition guided material design approach, we demonstrate a new strategy for discovering experimentally synthesizable 2D layered FE materials. Recent data-mining studies have provided the complete database covering almost all experimentally reported 2D van der Waals layered materials (including 2D layered FE materials).^{25,26} Further screening of these 2D materials databases for acentric layered semiconductors or insulators with switchable polarizations can lead to the discovery of new classes of 2D layered FE materials which are not simply composition or structural analogues to any experimentally reported ones. After searching the 2D weakly bonded layered materials database provided by Cheon et al.^{25} using basic structural and energetic criteria (Fig. 1), we identified niobium oxide dihalides NbOX_{2} (X = Cl, Br and I) as long-sought-after 2D van der Waals layered FE materials.
Bulk NbOX_{2} have been synthesized since the 1960s,^{27,28} and they can be potentially exfoliated into 2D layered forms. Despite their structural polarities at room temperature,^{28–31} NbOX_{2} have not been considered or investigated as 2D layered ferroelectrics. Except for earlier tight-binding band structure calculations,^{32} accurate predictions regarding electronic and FE properties for NbOX_{2} bulk and 2D layers have never been reported. In our work, based on first-principles calculations, model Hamiltonian and molecular dynamics simulations, we identify the presence of stable FE and metastable antiferroelectric (AFE) phases in both 3D bulk and 2D layered forms of NbOX_{2}. The coexistence of FE and AFE phases can lead to unique polarization switching and structural phase transition features in NbOX_{2}, distinct from the currently known 2D FE materials. Our findings demonstrate NbOX_{2} as a practical system to study the intrinsic ferroelectricity and antiferroelectricity down to the monolayer limit, and to explore the novel functionalities associated with 2D FE/AFE phase transitions.
NbOCl_{2} | NbOBr_{2} | NbOI_{2} | ||||
---|---|---|---|---|---|---|
Bulk | Monolayer | Bulk | Monolayer | Bulk | Monolayer | |
E _{b} (meV Å^{−2}) | 12.19 | — | 12.77 | — | 13.40 | — |
d _{Nb} (Å) | 0.15 | 0.14 | 0.14 | 0.14 | 0.13 | 0.13 |
ΔE_{FE} (meV f.u.^{−1}) | 13.31 | 13.63 | 10.64 | 11.00 | 8.12 | 9.08 |
P (μC cm^{−2}) | 26.86 | 26.50 | 22.28 | 22.32 | 17.78 | 17.66 |
E _{g} (eV) | 1.84 (3.73) | 1.88 (3.99) | 1.79 (3.07) | 1.87 (3.01) | 1.69 (1.83) | 1.77 (1.84) |
As determined by experimental structural characterizations,^{29–31} bulk NbOX_{2} can crystalize in a ferroelectric C2 phase with monoclinic symmetry, where Nb cations exhibit non-zero off-center displacement along the Nb–O–Nb atomic chain direction (b axis). In our work, in order to explore all possible NbOX_{2} polar configurations, we choose the Nb polar-distortion free, centrosymmetric C2/m phase (ground state structures for MoOCl_{2}^{34} and TaOI_{2}^{35}) as the paraelectric (PE) reference for bulk NbOX_{2}. Fig. 2(a) displays the crystal structure for the PE bulk phase (crystallographic parameters shown in Table S1 of the ESI†), in which there exits one-dimensional Peierls distortion^{36} of Nb atoms in each NbO_{2}X_{4} octahedra, leading to an alternation of two unequal Nb–Nb distances along the Nb–X–Nb direction (a axis). As we will discuss later, Nb–Nb Peierls distortion is crucial for determining the electronic structures and band gaps of NbOX_{2}. After examining the phonon spectra of PE phases, the soft phonon modes and corresponding polar structural instabilities for bulk NbOX_{2} can be identified.
We use bulk NbOI_{2} as an example and display the calculated phonon spectrum of its PE phase in Fig. 2(b). Three types of soft optical phonon modes with imaginary frequencies at the Γ point (ω = i 83, 82 and 71 cm^{−1}) are identified, corresponding to FE (all Nb atoms have exactly the same polar displacement), antipolar (two neighboring monolayers have anti-parallel Nb polar displacement) and AFE (Nb atoms from neighboring octahedra within each monolayer displace oppositely) Nb polar displacement patterns relative to the center of the NbO_{2}I_{4} octahedra. It is noted that Nb polar displacement in all three modes is restricted along the Nb–O–Nb direction. We next inject each soft mode into PE NbOI_{2}, followed by structural optimization to obtain lower symmetry polar phases. FE phases with C2 symmetry (Table S2 in the ESI†) are obtained after relaxation of FE-mode related structure. Cooperative displacement of all Nb atoms (polar displacement amplitude d_{Nb} ≈ 0.14 Å) in the FE phase can break inversion symmetry and generate non-zero spontaneous polarizations along the b axis, which can be qualified using Berry phase calculations. The typical polarization-energy double well curves are obtained for bulk NbOX_{2} FE phases (Fig. S1 in the ESI†), after recording the variation of polarization and total energy of the system with respect to the amplitude of the FE mode connecting the FE C2 and PE C2/m phases. Based on our calculations, bulk NbOCl_{2} exhibits the largest spontaneous polarization, highest FE potential depth and largest Nb polar displacement amplitude (Table 1), due to the significant electronegativity of the Cl anion. Besides the FE phase, antipolar phases with P2/c symmetry and AFE P phases (crystallographic parameters shown in Tables S3 and S4 of the ESI†) with anti-parallel interlayer or intralayer Nb polar displacement are also identified. Each Nb cation in the antipolar or AFE phases has non-zero polar displacement, but their contributions to the overall polarization of the system cancel out.
After investigation of bulk NbOX_{2}, we now turn to 2D NbOX_{2} multi-layers and monolayers, where we will demonstrate these NbOX_{2} layers as intrinsic 2D FE (AFE) materials. The soft-mode adopted structural optimization scheme is also used to obtain the polar ground state structures for 2D NbOX_{2} layers. FE, antipolar and AFE soft modes are found in the PE phase of NbOX_{2} multi-layers, while the monolayers only have FE and AFE modes (Fig. S2 and Table S5 in the ESI†). Without a vertical stacking sequence and out-of-plane periodicity, all 2D NbOX_{2} layers are optimized into orthorhombic symmetry. Fig. 3(a) summarizes our calculated energetic results for all polar phases in NbOI_{2} (results for NbOCl_{2} and NbOBr_{2} are provided in Fig. S3 of the ESI†). The FE phase is the most stable structure for all NbOX_{2} layered systems, independent of the layer numbers. Except for the monolayer, the antipolar phase is the next most stable phase, and is very close to the FE phase in energy. Even the less stable AFE phase has a small energy difference (<2 meV f.u.^{−1}) relative to the FE phase.
FE phases of NbOX_{2} also show weak layer-dependent in-plane ferroelectricity due to the van der Waals interlayer interactions.^{37} Shown in Fig. 3(b) are the calculated double-well potential curves for FE NbOI_{2}, where NbOI_{2} monolayer, bilayer and bulk exhibit almost identical Nb polar displacement amplitude and FE potential depth in their FE phases (similar results are also found in NbOCl_{2} and NbOBr_{2}). Based on layer-independent energetic stability and ferroelectricity, it is expected that in-plane FE polarization of almost the same magnitude (Table 1) can be obtained in all structural forms of NbOX_{2}, including 3D bulk and 2D layers. This unique feature makes 2D NbOX_{2} distinct from group-IV monochalcogenides (e.g. GeS, SnS and SnTe), a well studied 2D FE material class with in-plane ferroelectricity. As it is demonstrated by experiment, 2D orthorhombic SnTe layers (γ phase) exhibit strong antipolar interlayer coupling, leading to a vanishing of ferroelectricity in the bulk phase and those multi-layers containing even numbers of layers.^{16}
NbOX_{2} monolayer can be stabilized into two polar phases, either a stable FE or metastable AFE phase, which contain two NbO_{2}X_{4} octahedra in their unit cell. To evaluate the possibility of FE-to-AFE transition, we calculate 2D energy contour plot of NbOI_{2} monolayer as a function of polar displacement of two Nb atoms within a single unit cell. As shown in Fig. 3(c), two degenerate FE (AFE) phases locate along the diagonal directions, separated by the PE phase. Transition between two FE phases with opposite polarizations does not need to go through the high-energy PE phase. Instead, it will cross a low-lying AFE phase, where the polar displacement of one Nb atom is reversed, while keeping the other almost unchanged.
Fig. 4 displays our calculated energy band structures and projected density of states (PDOS) for FE NbOX_{2}, obtained from HSE hybrid density functional calculations. All NbOX_{2} systems, including 3D bulk and 2D monolayer, are predicted to be indirect semiconductors with nominal E_{g} (the energy difference between the filled and empty band edges, shown in Table 1) around 1.8 eV. Due to the hybridization of Nb-4d with anion p orbitals, largely dispersed energy bands around the conduction band minimum (CBM) in NbOX_{2} are mainly contributed to by empty Nb-4d states. Below the Fermi level, the highest occupied valence band is almost dispersionless through the entire Brillouin zones of the monoclinic bulk and orthorhombic monolayer. For NbOCl_{2} and NbOBr_{2}, such a flat band is isolated from other valence bands of hybridized anion p orbitals. Further orbital component analysis indicates that the dispersionless valence bands (marked as green circles in the energy bands of the monolayers) originate from localized Nb-d_{z2} states. Meanwhile, similar weakly dispersed energy bands also appear in conduction states (above CBM), corresponding to empty Nb-d_{z2} orbitals.
Fig. 4 Electronic structures for FE NbOX_{2}. HSE calculated energy band structures and projected density of states (PDOS) for FE bulk NbOX_{2} with C2 monoclinic symmetry (upper panel) and FE NbOX_{2} monolayer with Pmm2 orthorhombic symmetry (lower panel). Fermi energy level is set as energy zero. The choice of k-point path for the monoclinic Brillouin zone follows the convention from ref. 40. For NbOX_{2} monolayer, the contribution of Nb-d_{z2} orbital to energy bands are highlighted by green circles. The variation of the energy separation between the occupied and empty Nb-d_{z2} orbitals at Γ point (ΔE_{Nb-d}) as a function of Nb–Nb paring distance (d_{Nb–Nb}) in FE NbOX_{2} monolayers is also presented. NbOCl_{2} monolayer with the shortest d_{Nb–Nb} has the strongest Peierls distortion intensity and therefore the largest ΔE_{Nb-d}. |
Formation of the energy gap between the filled and empty Nb-d_{z2} states (ΔE_{Nb-d}) is a direct consequence of 1D Peierls distortion.^{36} Each Nb^{4+} cation in NbOX_{2} has one unpaired 4d electron. Paring of two 4d electrons simultaneously occurs in the NbOX_{2} single unit cell, after periodic dimerization of neighboring Nb cations created by the 1D Peierls distortion. The energy gap is then formed as two paired electrons are favored to fully occupy the low-energy Nb-d_{z2} orbital, leaving the high-energy d_{z2} orbital empty. We double checked the electronic structures for NbOX_{2} using spin polarized calculations, which also predict nonmagnetic ground states with paired electrons on the Nb-d_{z2} orbitals. In fact, the intensity of the 1D Peierls distortion in NbOX_{2} can be well qualified by energy separation between the occupied and empty Nb-d_{z2} orbitals (ΔE_{Nb-d}). As shown in the last plot of Fig. 4, the strongest Peierls distortion with the shortest Nb–Nb distance in NbOCl_{2} monolayer leads to the largest ΔE_{Nb-d}. The overall extraordinarily large ΔE_{Nb-d} in all three systems indicates that 1D Peierls distortion in NbOX_{2} is ultra-stable, able to survive over thermal fluctuations at high temperature.
In layered NbOX_{2}, Nb-d_{z2} orbitals can hardly hybridize with any planar anion p orbitals. As a result, Nb-d_{z2} states correspond to the dispersionless energy bands that are quite localized in energy. More importantly, optical transitions from the localized Nb-d_{z2} valence band to other empty Nb-d orbitals from conduction bands are completely forbidden. The effective optical absorption in NbOX_{2} comes from the transition between hybridized anion-p orbitals of the valence band and hybridized Nb-4d orbitals (except d_{z2}) of the conduction bands. Therefore, as far as optical absorption properties are considered, NbOCl_{2} and NbOBr_{2} are insulators with optical transition allowed E_{g} > 3.0 eV (Table 1). Due to the weak electronegativity of the I anion, bulk and monolayer NbOI_{2} can exhibit semiconducting electronic and optical properties. Typically, as a ferroelectric semiconductor with an indirect E_{g}, bulk NbOI_{2} can effectively absorb visible light with a photon energy above 2.0 eV (Fig. S4 in the ESI†), making it suitable for FE photovoltaic applications.^{41,42}
2D NbOX_{2} layers have orthorhombic symmetry with anisotropic planar crystal structures, where Nb atoms bond with X–X edges along one planar direction and O atoms along the other. Similarly to many other 2D FE materials,^{12,43} strong anisotropy in crystal structures of 2D NbOX_{2} will be reflected in their energy bands and optical absorption properties as well. Using semiconducting monolayer NbOI_{2} as an example, we will illustrate its highly anisotropic and strongly coupled electronic and optical absorption properties. Fig. 4(a) shows the band structure for FE NbOI_{2} monolayer, where all the energy bands around the Fermi energy level are marked by colored circles whose radii are proportional to the contribution of the corresponding atomic orbitals. I anion has a weaker electronegativity than O, therefore the valence bands around the Fermi level mainly come from I-p orbitals. Except for the localized d_{z2} bands, most valence and conduction bands show anisotropic dispersion along two planar directions: valence I-p_{y} bands and low-lying conduction Nb-d_{yz} bands are highly dispersed along Γ–Y (reciprocal lattice equivalent of the crystallographic b axis), but weakly dispersed along the Γ–X direction.
Besides electronic structures, we have also investigated the anisotropic optical properties of NbOI_{2} monolayer by simulating its optical absorption coefficient α, excited by incident light polarized along the x and y directions (corresponding to the a and b axes, respectively). As shown in Fig. 5(b), both α_{x} and α_{y} have optical absorption edges around 2.0 eV. Above the absorption edge, a strong optical absorption peak appears at 3.15 eV, when incident light is polarized along the x direction. The strength of this absorption peak in α_{x} is larger than that of α_{y} by almost 10 times, indicating a strong direction-dependent photo-absorption in NbOI_{2} monolayer. As energy bands around the Fermi level are mainly contributed to by hybridized I-p and Nb-d orbitals, the low-energy optical absorption in NbOI_{2} can be assigned to optical transitions from I-p to Nb-d orbitals. When NbOI_{2} monolayer is excited by incident light polarized along the x direction, optical transitions between all weakly dispersed Nb-d_{yz} and I-p_{y} energy bands along the whole Γ–X direction (indicated by dashed red arrows in Fig. 5(a)) can contribute to optical absorption at 3.15 eV in α_{x}. While along the y direction, the weaker absorption at 3.15 eV comes from the optical transition (blue dashed arrow) of Nb-d_{yz} and I-p_{y} bands around the Γ point only. As a result, when monochromatic light with photon energy of 3.15 eV is incident on FE NbOI_{2} monolayer, optical absorption along the nonpolar a axis is significantly larger than that along the polar axis, leading to a nearly linearly polarized optical absorption selectivity in NbOI_{2} monolayer.^{39}
During the polarization reversal (switching) process, FE domain-walls between oppositely orientated FE mono-domains will be formed in NbOX_{2} monolayers. Meanwhile, the polarization reversal process can be carried out through the motion of FE domain-walls.^{44,45}Fig. 6(a) displays the supercell configuration containing two FE mono-domains with opposite polarization directions, separated by a 180° FE domain-wall located along the I–I lattice plane in NbOI_{2} monolayer. Each mono-domain is composed of four NbOI_{2} unit cells, stacking along the a axis. To preserve the periodic boundary condition required by first-principles plane wave calculations, we must include two coherent FE domain-walls (twin walls) in one supercell, so that the whole supercell can be repeated periodically along both axes.
In order to evaluate how polarization is reversed across the FE domain-wall, we analyze the evolution of Nb polar displacement amplitude (d_{Nb}) as a function of Nb distance (r) away from the domain-wall. As shown in Fig. 6(a), polarization is reversed as d_{Nb} changes its sign abruptly across the domain-wall. d_{Nb} of each Nb cation almost fully recovers to its mono-domain value (indicated by dashed lines). As a result, the 180° FE domain-wall supercell configuration is geometrically similar to a NbOI_{2} superlattice, where AFE phases are sandwiched between two FE phases with opposite polarizations. As the energy difference between AFE and FE phases of NbOI_{2} monolayer is as low as 1.24 meV f.u.^{−1}, the 180° FE domain-wall has a very small domain wall energy. The d_{Nb}–r curve shown in Fig. 6(a) can be quantitatively described using a function corresponding to the soliton solution of one-dimensional fourth-order Landau–Ginzburg domain wall theory^{44} as:
(1) |
We then explore the kinetic process for domain-wall motion by simulating the corresponding minimum energy pathway (MEP) trajectory and the associated energy barrier height, using a generalized solid-state NEB method.^{46} Such a method allows both atomic positions and lattice parameters to relax along the pathway. As shown in Fig. 6(b), transition from the initial to the final domain-wall configurations resembles the motion of the domain wall from one I–I lattice plane to the next, accompanied by the reversal of polarization direction of one group of Nb cations by 180°. At the saddle point configuration along the MEP, the domain-wall moves to the lattice plane where Nb cation is located. This very Nb cation is then constrained to have zero d_{Nb}, while d_{Nb} of other Nb cations remain unchanged. As a result, the MEP associated with domain-wall motion is similar to the energy pathway for transition from single FE to AFE phase, as we obtained earlier from the energy contour plot in Fig. 3(c). The overall barrier height for polarization reversal of the Nb cation in the NbOI_{2} monolayer is predicted to be 14.9 meV, which is much smaller than the polarization rotation barrier (∼40 meV) in FE perovskite PbTiO_{3}.^{47} Therefore, the presence of the low-lying AFE phase can lead to a small energy barrier, which is beneficial for easy domain-wall motion and polarization switching in NbOI_{2} monolayer.
Using the simulated energy barrier, we can estimate how large the electric field needs to reverse FE polarization in NbOI_{2} monolayer. The critical electric field E_{C} is given by: E_{C} ≃ E_{barrier}/P·V, where P is the spontaneous polarization and V is the normalized cell volume for NbOI_{2} monolayer. The estimated critical electric field E_{C} ≃ 0.63 MV cm^{−1}, which is readily accessible by experiment.^{48} Therefore, electric field induced switching of FE polarization can be achievable under laboratory conditions.
The geometry of 2D NbOX_{2} monolayers can be represented by a 2D lattice grid containing a number of Nb cations, where each Nb cation at 2D grid point i [i is a collapsed index of its 2D position (m, n)] has a unique polar displacement d_{i}. Due to the 1D nature of polarization, d_{i} of Nb cations are collinearly arranged into columns along the polar axis. Using polar displacement d_{i} as the order parameter, the configuration of NbOX_{2} monolayer at any condition can be unambiguously specified. Therefore, we can express the free energy of NbOX_{2} monolayer as Landau–Ginzburg expansion of order parameter d_{i} as:^{13}
(2) |
A | B | C _{ x } | C _{ y } | T _{C} (K) | |
---|---|---|---|---|---|
NbOCl_{2} | −1.29 × 10^{3} | 3.03 × 10^{4} | 48.23 | 6.08 × 10^{3} | 396 |
NbOBr_{2} | −1.11 × 10^{3} | 2.74 × 10^{4} | 38.68 | 4.28 × 10^{3} | 283 |
NbOI_{2} | −1.01 × 10^{3} | 2.85 × 10^{4} | 19.14 | 4.82 × 10^{3} | 242 |
Based on the effective Hamiltonian we developed for NbOX_{2} monolayers, we can investigate temperature induced structural transition using MC simulations (computational details in the ESI†). For comparison, we also perform parameter-free ab initio MD simulations, where the time evolution of the instantaneous temperature, total energies and cation polar displacement of NbOX_{2} can be obtained (Fig. S6 in the ESI†). Due to the large computational cost, we restrict our MD simulations of NbOX_{2} monolayers to selected target temperature. Fig. 7 shows our simulated temperature dependent macroscopic average polar displacement 〈d(T)〉 in NbOX_{2} monolayers. The structural transition from FE to PE phase is identified, as the simulated 〈d(T)〉 drops abruptly to zero around T_{C}. Moreover, at the selected temperature, ab initio MD predicted ensemble average 〈d(T)〉 are in overall good agreement with MC results (the largest derivation occurs in NbOI_{2}, with ΔT ∼ 60 K), which validates the effective Hamiltonian and parameters we used for MC simulations. Curie temperature T_{C} can be quantitatively determined after fitting MC simulated 〈d(T)〉 as follows:^{13}
(3) |
Fig. 7 Structural phase-transitions and Curie temperatures of NbOX_{2} monolayers. Upper panel: Temperature dependence of the average Nb polar displacement obtained from MC and ab initio MD simulations for NbOCl_{2}, NbOBr_{2} and NbOI_{2} monolayers. Average polar displacement 〈d(T)〉 is normalized with respect to the corresponding 0 K value. Black lines are fitted to MC data based on eqn (3). The error bars of Nb polar displacement highlight the thermal fluctuations during the MD simulations. Lower panel: MD simulated polarization reversal process in NbOI_{2} monolayer. The normalized polar displacements (d_{i}(T)/|d(0 K)|) for each Nb cation in a 8 × 8 lattice grid are presented when the temperature is below, approaching and above Curie temperature T_{C}. Polarization reversal occurs when T ≈ T_{C}, and is initiated by switching d_{i} of a single Nb from one cation column along the polar axis (y direction). |
In order to understand the microscopic mechanism governing FE–PE phase transition, we further examine temperature dependent cation displacement evolution. The lower panel of Fig. 7 plots the real space mapping of d_{i} from the whole NbOI_{2} lattice grid during MD simulations after the system reaches thermal equilibrium at target temperature below, approaching and above T_{C}, respectively. Below T_{C}, the magnitude of d_{i} starts to decrease from its zero temperature value as temperature increases. The polarization reversal event (changing sign of d_{i}) does not occur until T ≈ T_{C}, where |d_{i}| of some Nb cations become small enough so that thermal energy is comparable with the energy cost to form a head-to-head/tail-to-tail polar configuration. The polarization reversal process around T_{C} is initiated by switching d_{i} of a single Nb cation from one cation column. Then the whole column simultaneously switches its polarization to the opposite direction, to avoid the unfavorable head-to-head/tail-to-tail configuration. The FE–PE phase transition is achieved through dynamic reversal of column polarization as mentioned above. As AFE phase in NbOX_{2} is more stable than the distortion-free PE phase. Even when T > T_{C}, the system stays in a thermal-equilibrium PE state, where the overall polarization is almost zero, but individual columns can still have non-zero and randomly oriented polarization along the polar axis. As a result, PE state above T_{C} is more like a disordered AFE phase. Moreover, the energy cost associated with “collective” reversal of whole column polarization is negligible compared to the “isolated” cation dipole switching energy (C_{y} ≫ C_{x}, Table 2), thus T_{C} of NbOX_{2} monolayer is mainly determined by “isolated” rather than “collective” cation dipole switching events.^{49} Therefore, T_{C} is not simply proportional to the energy difference associated with “collective” polarization reversal (FE-to-AFE phase transition). Even though AFE phase is close to FE phase in energy, NbOX_{2} monolayers can still have T_{C} around or even above room temperature.
The 1D polarization nature and coexistence of FE/AFE phases make 2D NbOX_{2} exhibit the unique polarization reversal and structural phase-transition features. In experiment, AFE perovskite oxides have been widely used as dielectric capacitors for electrostatic energy storage through electric charging and discharging processes.^{52} In particular, high energy densities are achieved in perovskite solid solutions near the phase boundaries where FE and AFE phases coexist.^{53} We therefore propose the application of NbOX_{2} monolayers as 2D dielectric capacitors.
Fig. 8(a) displays a schematic diagram for a 2D single-layered capacitor obtained by lateral growth of a heterostructure between a NbOX_{2} monolayer and another 2D metallic material, where an electric field can be applied along the polar axis through a metal electrode. In order to evaluate the performance of a 2D NbOX_{2} based capacitor, we choose NbOI_{2} monolayer as an example, and investigate the electric-field induced phase transition by simulating its P–E loop around room temperature using MC simulations. When electric field E is applied along the polar axis, the additional energy term −(E·P)V will be incorporated into the effective Hamiltonian in eqn (2). The effective polarization P can be computed from Nb polar displacement d_{i} and Born effective charge Z_{i}* by: . Therefore, the electric field related energy term can be simplified as: −E(Σ_{i}d_{i}·Z_{i}*). Based on our predictions, NbOI_{2} monolayer adopts a disordered AFE (PE) phase at room temperature. The simulated P–E loop in Fig. 8(b) shows that under the charging process (increasing E) P increases abruptly around 0.15 MV cm^{−1}, indicating that a small critical field E_{C} can trigger the AFE-to-FE transition in NbOI_{2} monolayer at room temperature. Above E_{C}, P increases linearly within FE phase upon further charging. Remarkably, an almost identical P–E curve associated with the FE-to-AFE transition is obtained under the discharging process (decreasing E). As a result, under the applied electric field, NbOI_{2} monolayer possesses P–E loops with almost no hysteresis, which is consistent with its small FE/AFE energy difference and low polarization switching energy barrier at room temperature.^{54} Similarly to NbOI_{2}, NbOBr_{2} monolayer also crystalizes in a disordered AFE phase at room temperature and exhibits nearly hysteresis-free P–E loops. While NbOCl_{2} monolayer has a non-zero FE polarization at room temperature, it features P–E double hysteresis loops of typical ferroelectrics. Due to the energy loss associated with the hysteresis, NbOCl_{2} monolayer is less suitable for electrostatic energy storage than NbOBr_{2} or NbOI_{2}. A 2D capacitor based on NbOBr_{2} or NbOI_{2} monolayers can exhibit nearly zero energy loss during the charging and discharging processes, yet has the advantage of operating at a low electric field, which can potentially enable nearly 100% efficiency for electrostatic energy storage in the 2D monolayer.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9nh00208a |
This journal is © The Royal Society of Chemistry 2019 |