Theoretical study of ferroelectric potassium nitrate

We present a detailed study of the structural behavior and polarization reversal mechanism in phase III of $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$, an unusual ferroelectric material in which the nitrate groups rotate during polarization reversal. This material was one of several studied in a previous work [O. Diéguez and D. Vanderbilt, Phys. Rev. Lett. 96, 056401 (2006)] where methods were described for computing curves of energy versus electric polarization. In the present work, we extend and systematize the previous first-principles calculations on $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ and analyze in detail a two-parameter model in which the energy of the system is written as a low-order expansion in the polarization and the nitrate group orientation. We confirm that this model reproduces the first-principles results for $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ very well and construct its parameter-space phase diagram, describing regions where unusual triple-well potentials appear. We also present first-principles calculations of $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ under pressure, finding that its energy-versus-polarization curves change character by developing a first-derivative discontinuity at zero polarization.

Figure 1

(Color online) Top and side views of the 15-atom conventional hexagonal cell (outlined in black) for ferroelectric $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ in (a) the ground state with negative polarization, (b) a metastable paraelectric state, and (c) the ground state with positive polarization. Blue lines indicate the equivalent five-atom rhombohedral cells. Panels (d)–(f) show top views of the same structures as in (a)–(c), clarifying the near-neighbor environment of a K atom. Neighbors in the plane above and below are indicated with black and blue lines, respectively; first K-O neighbors are drawn as dashed lines, while second K-O neighbors are designated by dotted lines.

Figure 2

(Color online) Phase diagram of the model given by Eq. (2) including a paraelectric phase $\left(R32\right)$ and two ferroelectric phases ($R3m$ and $R3$). Each thick (thin) continuous line represents a first-order (second-order) phase transition. The broken lines enclose areas of the diagram mentioned in the text. The empty circle (square) corresponds to a fit of the exact (SRV) $E\left(P\right)$ fixed-cell first-principles calculations for $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ to Eqs. (1, 2); the filled symbols and the arrows indicate how the situation changes when stress in the cell is relaxed (zero pressure).

Figure 3

Energy-versus-polarization curves in area IIa (top curve), area IIc (bottom curve), and on the boundary separating them (middle curve). The value of $\alpha$ is the same in all three cases; the system goes from paraelectric to ferroelectric with increasing $\beta$.

Figure 4

Energy versus polarization, and $\mathrm{N}{\mathrm{O}}_3$ rotation angle versus polarization, for the ferroelectric phase of $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ without strain relaxation. The squares and circles represent SRV and exact first-principles calculations, respectively (from Ref. 3), while the curves have been fitted to these data using Eqs. (1, 2), as described in the text.

Figure 5

Energy versus polarization, and $\mathrm{N}{\mathrm{O}}_3$ rotation angle versus polarization, for the ferroelectric phase of $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ with strain relaxation. The squares and circles represent SRV and exact first-principles calculations, respectively, while the curves have been fitted to these data using Eqs. (1, 2), as described in the text.

Figure 6

(Color online) Zero-polarization first-principles calculations of the value of the $\mathrm{N}{\mathrm{O}}_3$ rotation angle and of the N-O distance in $\mathrm{K}\mathrm{N}{\mathrm{O}}_3$ as functions of the reduction in the lattice parameter. The empty symbols correspond to calculations in which the $R32$ structure is imposed, while the filled symbols correspond to calculations in which this restriction is removed. All calculations were done using the exact method of Ref. 3.