Origin of Antiferroelectricity in ${\mathrm{NH}}_4{\mathrm{H}}_2{\mathrm{PO}}_4$ from First Principles

The low-temperature antiferroelectric (AFE) phase of ${\mathrm{NH}}_4{\mathrm{H}}_2{\mathrm{PO}}_4$ corresponds to H ordering in O-H-O bridges leading to ${\mathrm{H}}_2{\mathrm{PO}}_4$ group polarizations perpendicular to the tetragonal $c$ axis and alternating in chains. We determine the microscopic origin of such order by means of first-principles calculations in the framework of the density functional theory. The formation of $\mathrm{N}\mathrm{\text{−}}\mathrm{H}\cdots \mathrm{O}$ bridges with correlated charge transfers and $\mathrm{NH}_4{}^{+}$ group distortions turn out to be essential in stabilizing the AFE configuration against a $c$-polarized ferroelectric (FE) phase, as well as other FE states polarized perpendicular to the $c$ axis. These FE states lie only a few meV above the AFE phase, which explains the observation of FE-AFE phase coexistence near the AFE transition.

Figure 1

Schematic representation of (a) ADP (AFE) and (b) KDP (FE) structures from a top ($z$ axis) view. In the ADP case, short and long $\mathrm{N}\mathrm{\text{−}}\mathrm{H}\cdots \mathrm{O}$ bonds are indicated by long-dashed and dotted lines, respectively.

Figure 2

(a) Energy as a function of the acid H displacement $u_{{\mathrm{H}}_{\mathrm{O}}}$ for different patterns of atomic displacements corresponding to the FE and AFE distortions depicted in Figs. 2b, 2c, respectively. $u_{{\mathrm{H}}_{\mathrm{O}}}^{\min }$ denotes the ${\mathrm{H}}_{\mathrm{O}}$ displacement at the corresponding energy minimum. In addition to the full FE or AFE modes, other curves show the effect of imposing different constraints while performing the FE or AFE modes: N fixed or $\mathrm{NH}_4{}^{+}$ moved rigid as in the PE phase. Lateral views of the ADP formula unit indicate the atomic displacements in the FE (b) and AFE (c) modes. White arrows correspond to displacements imposed according to each mode, dashed arrows to concomitant relaxations.

Figure 3

Ab initio energy of the AFE (solid squares) and the FE (open squares) phases relative to the PE phase, as a function of the rotation angle $\theta$ of the $\mathrm{NH}_4{}^{+}$ ion, as explained in text. $\theta =0$ is the ammonium angular position corresponding to the minimum-energy relaxed states.

Figure 4

(a) Charge density differences ${\rho }^{\mathrm{AFE}}(r)-{\rho }^{\mathrm{PE}}(r)$ (top) and ${\rho }^{\mathrm{FE}}(r)-{\rho }^{\mathrm{PE}}(r)$ (bottom) in the plane defined by the acid H bond and the short $\mathrm{N}\mathrm{\text{−}}\mathrm{H}\cdots \mathrm{O}$ bond of ADP. (b) Same as (a), but in the plane defined by the acid H bond and the long $\mathrm{N}\mathrm{\text{−}}\mathrm{H}\cdots \mathrm{O}$ bond [see Fig. 1a]. (c) Ab initio energy levels of the PE, $xy$-polarized ferroelectric (${\mathrm{FE}}_1$ and ${\mathrm{FE}}_2$), $z$-polarized FE, and AFE states in ADP (see explanations in text).