Pressure-induced ferroelectric transition in LiBC

Ferroelectricity is usually suppressed by pressure. Here, we establish a general phenomenological theory to describe pressure-induced ferroelectrics and then relate it to real materials. Based on first-principles calculations, we identify a pressure-induced ferroelectric transition in which the nonpolar LiBC in the ZrBeSi structure type transforms into the polar state in the LiGaGe structure type at about 108 GPa. The pressure-induced ferroelectric LiBC has a larger polarization of $1.95\mathrm{C}/{\mathrm{m}}^2$ and band gap of 3.27 eV at 110 GPa. A ferroelectric multiple-well energy as a function of polar distortion is found. The pressure-induced ferroelectric transition is driven by the softness of one of the $A_{2u}$ modes in the nonpolar LiBC above 60 GPa. We also find an enhancement of a dynamic transfer of charge along the B–C bond under pressure, which indicates that the ionic electrostatic interactions become stronger. Our work demonstrates the existence of pressure-induced ferroelectrics and thus provides opportunities to design devices with ferroelectrics working on high-pressure conditions.

Figure 1

Enthalpy as a function of the polar distortion $u$ for (a) $b>0$ and (b) $b<0$.

Figure 2

Schematic picture of hysteresis in ferroelectric crossing critical points.

Figure 3

(a) Crystal structure of the nonpolar LiBC with the $P{6}_3/mmc$ ZrBeSi structure type at ambient pressure. Arrows indicate the displacement of one of the $A_{2u}$ modes. (b) The crystal structure of the polar LiBC with the $P{6}_{3}mc$ LiGaGe structure type at 110 GPa. (c) Enthalpies of the polar phase relative to the nonpolar phase as a function of pressure.

Figure 4

The energy band structures of the nonpolar LiBC at (a) ambient pressure and (b) 100 GPa. The energy band structures of the polar LiBC at (c) 60 GPa and (d) 110 GPa. The color lines indicate the projection to the B $p_{\mathrm{z}}$ (red), C $p_{\mathrm{z}}$ (blue), B $p_{x/y}$ (green), and C $p_{x/y}$ (orange) states.

Figure 5

Schematic pictures of bonding characters in nonpolar LiBC. (a) σ bonding (left) and π bonding (right) in two-dimensional planar B-C hexagons. (b) Intralayer antibonding and interlayer bonding (left); intralayer antibonding and interlayer antibonding (right). (c) Intralayer bonding and interlayer bonding (left); intralayer bonding and interlayer antibonding (right).

Figure 6

Multiple-well energy of LiBC as a function of polar distortion obtained by linear interpolation between the polar and nonpolar structures at (a)100 GPa and (b) 110 GPa. Red lines indicate the fitting data with the phenomenological theory.

Figure 7

Frequencies of the (a) $A_{2u}$ and (b) $E_{1u}$ models as a function of pressure in nonpolar LiBC. The inset shows frequencies of the $A_1$ mode as a function of pressure in polar LiBC.

Figure 8

Born charges $Z_{C,\alpha \beta }^{*}$ as a function of pressure for the (a) nonpolar and (b) polar LiBC.

Figure 9

(a) Ion-clamped contributions and (b) ionic dielectric coefficients as a function of pressure in nonpolar LiBC.