The model of ZB, RS and CsCl structures are displayed in Fig. 1(a), where the ZB lattice can either adopt an 8-atom cubic cell (left) or a smaller 4-atom unit cell (right). First, we select superalkali NH4 and superhalogen BCl4 for constructing a supersalt NH4BCl4, where both superatoms are non-centrosymmetric compared with isotropic single atoms, as shown in Fig. 1(b). After an extensive structure search using the CALYPSO code, we obtain the ground state structure of supersalt NH4BCl4 displayed in Fig. 1(c), which is non-centrosymmetric with independent superalkali NH4 and superhalogen BCl4 ions. It is a distorted zinc-blende (dZB) structure where the lattice constants (|a|:|b|:|c|=\(\sqrt{2}\):\(\sqrt{2}\):1) are relatively doubled in |a| and |b| (or contracted by half in |c|) compared with the 4-atom unit cell of standard ZB (|a|:|b|:|c|=1:1:\(\sqrt{2}\)). This structure is 0.08 and 0.44 eV/f.u. lower in energy compared with corresponding RS and CsCl structures, respectively. Similar to ZB phase, each superalkali cation in the dZB supersalt is tetrahedrally bonded with four adjacent superhalogen anions and vice versa, akin to sp3 hybridization of covalent bonding, which are also connected by weak H…Cl hydrogen bonds (with bond length ~ 2.4 Å). The energy release computed for a hypothetical reaction BN + 4HCl→ NH4BCl4, is as high as 1.10 eV/f.u. (i.e., ΔE=-1.10 eV/f.u.), which may enable its solution-processed synthesis via etching of boron nitride by acid. We also examined the following reactions:
NH4BCl4→NH4Cl + BCl3, ΔE = 0.14 eV/f.u.,
NH4BCl4→NH3BCl3 + HCl, ΔE = 0.41 eV/f.u.,
These hypothetical decompositions are all endothermal, which confirms the chemical stability of NH4BCl4 and impedes the formation of other products like NH4Cl or NH3BCl3 during the synthesis. However, the strong covalent B-N bonding of BN may lead to high energy cost to break those bonds, so we cannot guarantee the formation BN + 4HCl→ NH4BCl4 would spontaneously proceed at ambient conditions. On the other hand, the reaction NH4Cl + BCl3→ NH4BCl4 might be a more feasible route for the fabrication of NH4BCl4. For the same group pnictides like BP, AlN, the bondings are weaker and the larger hollow space may enable protons or halogen anions to permeate from the surface to inside, which should facilitate similar formations of supersalts. Hence, we further searched a series of low-energy structures for NH4MX4/PH4MX4 supersalts. As shown in Fig. 1(c), the ground state of NH4BBr4 shares the same type of dZB structure with NH4BCl4, which is similar to the case for PH4BCl4, PH4AlCl4, PH4BBr4, PH4BBr4, with a slight difference in the relative angles between the cation tetrahedrons and anion tetrahedrons. 3d metal like Fe may also be used to construct superhalogen like FeCl4, and the corresponding supersalts like PH4FeCl4, PH4FeBr4 turn out to possess similar dZB ground state structures. Their formations are all energetically favorable, with positive energy releases as listed in Table 1. There are a few exceptions like NH4BF4 and NH4AlCl4 that prefer to form structures where each superalkali cation is hydrogen-bonded to 8 adjacent superhalogen anions and vice versa, while NH4AlF4 forms a layered perovskite structure, as shown in the right panel of Fig. 1(c).
Next, we focus on the polar dZB structures in Fig. 1(c), which could be ferroelectric as long as their polarizations are switchable. In previous studies, 32, 33 the computed switching barriers for ZB structures like CuCl and ZnO can be over 0.30 eV/f.u., so their polarizations are difficult to reverse under ambient conditions. Compared to the breaking of covalent bonds in those structures during polarization switching, the energy barrier for ion displacement in ionic supersalts should be much lower. Taking NH4BCl4 shown in Fig. 2(a) as the paradigmatic case, if all the NH4 cations at the initial ground state (I) are simultaneously displaced by 2.63 Å along –y direction, with the rotation of all superatoms by a certain angle along –y axis, an equivalent structure (III) with a reversed polarization can be obtained. The reversed polarization turns out to be of a considerable value, namely, 13.8 µC/cm2 as listed in Table 1. Its band structure in Fig. 2(b) reveals that the system is insulating with a large bandgap over 5 eV, which should result in high dielectric breakdown voltage. The ferroelectric switching pathway is computed by SSNEB calculations in Fig. 2(c), with a symmetric state as the intermediate state (II), revealing a switchable barrier of only 0.13 eV/f.u. (0.013 eV/atom). Such a high ion displacement with such a small switching barrier is unimaginable in traditional ferroelectrics. For example, the ion displacement in PbTiO3 during ferroelectric switching is far below 1 Å, while the barrier is even larger (~ 0.15 eV/f.u., i.e., 0.03 eV/atom).34
The dynamical stability of the polar ground state for NH4BCl4 is further verified by the phonon spectra in Fig. S1, which shows no imaginary frequencies in all vibration spectra. For the nonpolar intermediate state II (paraelectric phase), the imaginary soft optical modes will lead to both rotation and translational displacement of NH4 cations and BCl4 anions away from the centrosymmetric position, giving rise to the spontaneous symmetry-breaking below the Curie temperature. Born-Oppenheimer molecular dynamics (BOMD) simulations are also performed to check its thermal stability. Snapshots of the equilibrium structure for NH4BCl4 at 300 K and at the end of 5 ps are shown in Fig. S2, suggesting the robustness of its ferroelectricity at ambient conditions. Similar mechanism of ferroelectric switching can be applied to other supersalts like PH4BBr4 via the displacement of cations and anions (2.86 Å along –y direction). The switching barrier in this case is also around 0.13 eV/f.u. (i.e., 0.013 eV/atom, as shown in Fig. 3(c)). The only difference is the rotational mode of superatoms during ferroelectric switching, as displayed in Fig. S3.
We note that the dZB structure is relatively elongated in two directions, i.e., contracted in the third direction compared with standard ZB phase, which is actually a spontaneous strain that might be switched via stress. The pathway for such ferroelastic switching for NH4BCl4 is calculated by SSNEB method, where a symmetrical non-polar state P(0) can be the intermediate state as its polarization switched from –z direction at the initial P(-z) state to –x/–y direction at the final state P(-x)/P(-y), as shown in Fig. 3(a) and (b). Here, the superiority of ionic ferroelastics with long-range Coulomb interactions between ions can be highlighted, as a barrier of only 0.065 eV/f.u. (i.e., 0.0065 eV/atom) is required for reversing such a high ferroelastic strain (defined as (|b|/|c|-1) × 100%) more than 40%. For high-strain (> 20%) ferroelastics predicted in previous reports, 35, 36, 37, 38 the switching barriers (up to 0.5 eV/atom) are almost orders of magnitude higher, which can be attributed to the distinct features of covalent bonds in those systems. Moreover, the ferroelectric polarization is also rotated by 90 degree upon ferroelastic switching. Such 90-degree polarization switching can also be achieved if an external electric field is applied along –x or –y direction. Hence, the ferroelectricity and ferroelasticity are coupled, so we can use strain to control the polarization direction and electric field to control strain. Due to the low barrier, the required electric field or stress for reversing such a large strain can be greatly reduced.
Supersalts with 3d magnetic ions like PH4FeBr4 also possess similar coupled ferroelectricity and ferroelasticity. Moreover, their magnetism can also be coupled. We have checked different possible spin configurations (see Table S1) for PH4FeBr4.Tthe ground state is displayed in Fig. 4(a), which is antiferromagnetic where the spins of two Fe ions in the unitcell are of opposite direction, while the spins on the same lines along –x, –y or –z direction are of the same direction. Further, spin non-collinear calculations reveal a magnetic anisotropy energy of 0.4 meV for the spin of each Fe atom, where the spins prefer to be aligned along –y direction, the “contracted” direction in Fig. 4(a). However, as the “contracted” direction is switched to –x direction upon ferroelastic switching, i.e., 90-degree ferroelectric switching, the magnetization easy axis is also switched from –y to –x direction. Equivalently, it might also be switched to –z direction via a strain or electric field along –z direction. Compared with NH4BCl4, the switching barrier of PH4FeBr4, according to the calculated pathway in Fig. 4(b), is larger (~ 0.13 eV/f.u.), while the bandgap is much more reduced (~ 1 eV, see Fig. 4(c)) to a desirable range for nanoelectronics. Hence, magnetism is also coupled with ferroelectricity and ferroelasticity in PH4FeBr4, which can be viewed as a multiferroic material with “triferroic” coupling. Such coupling may render electrically-controlled giant anisotropic magnetoresistance for non-volatile memories, which is highly desirable but still challenging in the current developing field of antiferromagnetic spintroincs.39