Orbital ordering, ferroelasticity, and the large pressure-induced volume collapse in PbCrO${}_3$

We predict a tetragonal ground state for perovskite-structured PbCrO${}_3$ from density functional theory (DFT) $+$ $U$ calculations, and explain its anomalously large volume. The predicted structure is stabilized due to orbital ordering of Cr $d$ in the presence of a large tetragonal crystal field, mainly due to off-centering of the Pb atom. At higher pressures (smaller volumes) there is a first-order transition to a cubic phase where the Cr-$d$ orbitals are orbitally liquid. This phase transition is accompanied by a ∼11.5% volume collapse, one of the largest known for transition-metal oxides. The large ferroelasticity and its strong coupling to the orbital degrees of freedom could be exploited to form potentially useful magnetostrictive materials.

Figure 1

Total energy difference with GGA $+$ $U$ ($U$ $=$ 3 eV and $J$ $=$ 0.87 eV) as a function of Pb displacements in an otherwise cubic structure with $a$ $=$ 4.0 Å (i.e.,$V_0=64$ Å${}^3$) and $a$ $=$ 3.713 Å, i.e., 20% compression with respect to $V_0$ (in red). Without compression Pb off-centering is energetically favorable with displacements along the tetragonal direction giving the lowest energy. Under a 20% compression the cubic phase has the lowest energy.

Figure 2

Energy vs volume curve for the cubic and the fully relaxed tetragonal structure using GGA $+$ $U$ and LDA $+$ $U$. (a) Data from Fig. 4 of Ref. 11 was inverted to obtain the energy vs volume curve for SrCrO${}_3$. (b) Enthalpy of the two phases using GGA $+$ $U$ showing a predicted transition pressure of ∼7 GPa and the accompanying volume change of ∼11.5%.

Figure 3

Band structure plots for the tetragonal ($P$4$\mathit{mm}$) and the cubic (Pm-3$m$) phases at the experimentally measured anomalously large volume under ambient conditions of 64.0 Å${}^3$. Fat bands are plotted for the majority-spin Cr-$d$ orbitals along the path: (0.5,0,0)$\to$(0,0,0)$\to$(0,0.5,0.5)$\to$(0.25,0.5,075)$\to$(3/8,3/8,3/4) $\to$(0.5,0,0)$\to$(0.25,0.5,0.75)$\hspace{0.5em}\to$(0.5,0.5,1.0)$\to$(3/8,3/8,3/4)$\to$(0,0,0) in the Brillouin zone. The insets show corresponding partial density of states plots with units of states/eV/cell from a separate FP-LMTO calculation. There is large splitting of the $t_{\mathit{xy}}$ orbitals in the tetragonal phase compared to the cubic phase, and they form a dispersionless band. This leads to full occupancy of this orbital. This orbital ordering is responsible for stabilizing the experimentally observed large volume in ambient conditions.