Electron doping in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$: Collapse of band gap and magnetic order

The electron-doping-driven collapse of the charge gap and staggered magnetization of the spin-orbit-assisted Mott insulator ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ is explored via first-principles computational methods. In the antiferromagnetic phase, the gap and magnetization are observed to decrease slowly with increasing doping, with an abrupt collapse of both the gap and the magnetization at an electron concentration corresponding to 4.8% substitution of Sr with La, in excellent agreement with experiment. Additionally, we describe the structural effects of electron doping in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ via a competition between the steric effect from smaller La atoms substituted within the lattice and the dominant doping-driven deformation-potential effect. Curiously, our first-principles calculations fail to capture the low-temperature structural distortion reported in the low-gap phase of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, supporting the notion that this distortion arises as a secondary manifestation of an unconventional electronic order parameter in this material.

Figure 1

Structural visualizations of (a) ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and (b) ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. Sr-214 takes a tetragonal structure (space group $I{4}_1/acd$) [32], and slight deviations from tetragonal make Sr-327 monoclinic (space group $C2/c$) [11]. The first Brillouin zone for Sr-327 is shown in (c), with high-symmetry points labeled [33].

Figure 2

$\text{DFT}+U$ band structure of Sr-327. Solid lines show the undoped (insulating) case, and dashed lines show the band structure after the collapse of the gap (at a doping level $x=0.08$). The energy of the bands is referenced to the VBM in both cases. Occupied states (Ir $5d$ states with a mix of $J_{\text{eff}}=3/2$ and $J_{\text{eff}}=1/2$) are shown in blue, and unoccupied states (Ir $5d$ states with $J_{\text{eff}}=1/2$) are shown in orange. The gap in the undoped case is 0.27 eV, indirect between $\mathrm{\Gamma }$ and a point 81% of the way from $\mathrm{\Gamma }$ to $X$. The smallest direct gap is 0.44 eV, 78% of the way from $\mathrm{\Gamma }$ to $X$. In the doped case, the indirect gap has collapsed to only 7 meV. The CBM is at the same point of the Brillouin zone as in the undoped case, and the VBM is at the $C$ point. Also shown is the Fermi level in the doped case, represented by a gray dashed line 218 meV above the CBM.

Figure 3

(a) Indirect band gap and (b) out-of-plane magnetization as a function of the number of doping electrons per strontium atom ($x$). Lowest-energy structures for each doping level are shown in blue circles, connected by lines as a guide to the eye. Calculated metastable structures are shown in red triangles. In (a), experimental gap values from Ref. [19] are shown as green diamonds for comparison. Inset (c): Energy difference between the small-moment state and antiferromagnetic (AF) state. The crossover at $x=0.048$ is the critical doping level for the phase transition.

Figure 4

Percentage change of (a) out-of-plane lattice parameter $c$ and (b) cell volume as a function of doping. Note the tendency of the lattice to contract on calcium doping (or incorporation of ${\mathrm{La}}^{+}$), driven by steric effects, and the tendency toward lattice expansion on electron doping, driven by the deformation-potential effect. Lines connecting data points are a guide to the eye. Electron doping (without ionic substitution) is shown in red triangles, ${\mathrm{La}}^{+}$ (lanthanum substitution without the donated electron) is shown in green diamonds, and ${\mathrm{La}}^{+}+e^{-}$ (lanthanum substitution including the donated electron) is shown in blue circles. Experimental data for lanthanum doping [14, 24] are shown as solid black circles. For comparison, calculated results for calcium substitution are shown as orange squares, and experimental results as black squares.