Ab initio study of pressure-induced structural and electronic phase transitions in ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$

${\mathrm{Ca}}_2\mathrm{Ru}{\mathrm{O}}_4$ is a compound with a Mott insulating ground state, which responds to external pressure in a variety of ways, some of which are expected (an insulator-metal transition) while others are more surprising (an expansion of the $c$ lattice constant). We provide here a comprehensive study of these pressure-induced structural and electronic changes using DFT$+U$ calculations, and demonstrate generally good agreement with experiment. The insulator-metal transition is reproduced and coincides with an isostructural transition, the $c$ lattice expansion, $\mathrm{Ru}{\mathrm{O}}_6$ octahedral distortions, and associated changes to the Ru $4d$ orbital order. The metallic part of the phase diagram features several competing phases. The high-pressure $Bbcm$ phase is found to be unstable in the ground state over a broad pressure range and suggested to be thermally stabilized instead.

Figure 1

(a) Optimized lattice parameters of ${\mathrm{Ca}}_2\mathrm{Ru}{\mathrm{O}}_4$ at atmospheric pressure as function of $U$. Left axis is for $a$ and $b$, right axis for $c$. (b) DOS at the Fermi energy (left axis) and average Ru spin moment (right axis) as a function of $U$ at atmospheric pressure. (c) Spin-resolved DOS near the Fermi energy for $U=0.0\mathrm{eV}$ (a half-metallic phase) and $U=1.5\mathrm{eV}$ (an insulating phase). (d) The experimental S-$Pbca$ crystal structure. Blue spheres are Ca, brown polyhedra are the $\mathrm{Ru}{\mathrm{O}}_6$ octahedra. (e) The Fermi surface for $U=0.0\mathrm{eV}$. (f) The Fermi surface viewed along $k_z$.

Figure 2

(a) Phase diagram of the ${\mathrm{Ca}}_2\mathrm{Ru}{\mathrm{O}}_4$ ground state in $(P,U)$ space, based on analysis of $Pbca$ structures. Four phases are identified: insulating S-$Pbca$, half-metallic $Pbca$-1 (HMe1), half-metallic $Pbca$-2 (HMe2), and a fully metallic $Pbca$ (FMe). Color scale indicates the length of the $c$ axis. (b): The magnitude of the Ru spin moment in $(P,U)$ space. Overlaid points show the grid of calculations used to build both diagrams.

Figure 3

(a) DOS of the FMe phase at $P=15\mathrm{GPa}$ for $U=0.0\mathrm{eV}$. (b) The corresponding Fermi surface and (c) the Fermi surface viewed along $k_z$. (d)–(f) The same for the HMe2 phase at $P=17.5\mathrm{GPa}$ for $U=1.5\mathrm{eV}$.

Figure 4

Pressure dependence of the lattice parameters for a range of representative $U$ values. Experimental data at two different temperatures are marked by filled black symbols, and vertical lines indicate the pressure-driven structural phase transitions identified in experiment at 295 K by Steffens et al. [3]. For clarity, only the experimental data in the $Pbca$ phases are shown [3, 34].

Figure 5

(a) Labeling convention for O sites and distortion angles in $\mathrm{Ru}{\mathrm{O}}_6$. Purple dashed line is the [110] direction. $\mathrm{\Theta }$ and $\mathrm{\Phi }$ are the tilt and rotation angles, respectively. (b)–(g) Octahedral bond lengths and distortion angles as a function of pressure for $U=0.0$, 1.25, and $1.75\mathrm{eV}$.

Figure 6

Ru $4d$ orbital occupancies for $U=0.0$, 1.25, and $1.75\mathrm{eV}$ as a function of pressure. Top: Majority spin channel (up spins). Middle: Minority spin channel (down spins). Bottom: Total orbital occupancies (up $+$ down). Vertical lines mark phase transitions.

Figure 7

(a) Enthalpy, energy, and pressure-volume differences between the $Bbcm$ and FMe L-$Pbca$ phases as a function of pressure. $\mathrm{\Delta }X=X_{Bbcm}-X_{Pbca}$. (b) Octahedral distortion angles of the FMe L-$Pbca$ phase under high pressure. See Fig. 5 for definitions of $\mathrm{\Theta }$ (tilt) and $\mathrm{\Phi }$ (rotation).