Electronic reconstruction and charge transfer in strained ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$ double perovskite

The electronic, magnetic, and optical properties of the double perovskite ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$ (SCIO) under biaxial strain are explored in the framework of density functional theory, including a Hubbard $U$ term and spin-orbit coupling in combination with absorption spectroscopy measurements on epitaxial thin films. While the end member ${\mathrm{SrIrO}}_3$ is a semimetal with a quenched spin and orbital moment and bulk ${\mathrm{SrCoO}}_3$ is a ferromagnetic (FM) metal with spin and orbital moment of 2.50 and 0.13 ${\mu }_B$, respectively, the double perovskite SCIO emerges as an antiferromagnetic Mott insulator with antiparallel alignment of Co, Ir planes along the [110] direction. Co exhibits a spin and enhanced orbital moment of $\sim 2.35–2.45$ and $0.31–0.46{\mu }_B$, respectively. Most remarkably, Ir acquires a significant spin and orbital moment of 1.21–1.25 and 0.13 ${\mu }_B$, respectively. Analysis of the orbital occupation indicates an electronic reconstruction due to a substantial charge transfer from minority to majority spin states in Ir and from Ir to Co, signaling an ${\mathrm{Ir}}^{4+\delta }$, ${\mathrm{Co}}^{4-\delta }$ configuration. Biaxial strain, varied from $-1.02\%$ $\left(a_{{\mathrm{NdGaO}}_3}\right)$ through 0% $\left(a_{{\mathrm{SrTiO}}_3}\right)$ to $1.53\%$ $\left(a_{{\mathrm{GdScO}}_3}\right)$, affects the orbital polarization of the $t_{2g}$ states and leads to a nonmonotonic change of the band gap between 163 and 235 meV. The absorption coefficient reveals a two-plateau feature due to transitions from the valence to the lower-lying narrow $t_{2g}$ and the higher-lying broader $e_g$ bands. Inclusion of many-body effects, in particular, excitonic effects by solving the Bethe-Salpeter equation, increases the band gap by $\sim 0.2\mathrm{eV}$ and improves the agreement with the measured spectrum concerning the position of the second peak at $\sim 2.6\mathrm{eV}$.

Figure 1

Structure of (a) ${\mathrm{SrCoO}}_3$, (b) ${\mathrm{SrIrO}}_3$, and (c) double perovskite ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$. Sr, Co, Ir, and O ions are shown in green, yellow, blue, and red, respectively. Note that the DP is modeled in a 40-atom unit cell, rotated by ${45}^{\circ }$ and twice the size of those of the end members.

Figure 2

The total energy of ${\mathrm{SrCoO}}_3$ with FM and AFM order for different symmetry for $U$ = 1.5 eV, 3.0 eV, and 4.52 eV.

Figure 3

$\mathrm{DFT}+U$ band structure (a), (b) without, and (c), (d) with SOC, element-projected density of states (PDOS) and (e), (f) spin density of ${\mathrm{SrCoO}}_3$ for FM (top panels) and G-type AFM coupling (bottom panels). Majority and minority bands in (a) and (b) are shown in dark gray and orange, respectively.

Figure 4

$\mathrm{DFT}+U$ band structure and element-projected density of states of ${\mathrm{SrIrO}}_3$ (a) without and (b) with SOC. For the band structure the same color scheme was used as in Fig. 3.

Figure 5

$\mathrm{DFT}+U$ band structure, projected density of states (PDOS), and spin density of ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$ (a)–(c) without and (d)–(f) with SOC strained at (a) and (d) $a_{\mathrm{NGO}}$, (b) and (e) $a_{\mathrm{STO}}$, (c) and (f) $a_{\mathrm{GSO}}$. For the band structure the same color scheme was used as in Fig. 3.

Figure 6

Orbitally projected DOS of Co $3d$ states in ${\mathrm{SrCoO}}_3$ and strained ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$ (a) without and (b) with SOC, and Ir $5d$ states in ${\mathrm{SrIrO}}_3$ and ${\mathrm{Sr}}_2{\mathrm{CoIrO}}_6$ (c) without and (d) with SOC. For better visibility, the $e_g$ and $t_{2g}$ states are shown in separate panels. Additionally, the band center of each $d$ orbital is given by a dashed line.

Figure 7

Changes in occupation number of the five Co $3d$ (blue) and Ir $5d$ (yellow) orbitals in SCIO with respect to the occupation number in the end members SCO, SIO without SOC as a function of strain. Solid and empty symbols represent changes in occupation numbers for spin-up and spin-down states, respectively.

Figure 8

Changes in occupation number of the five Co $3d$ (blue) and Ir $5d$ (yellow) in SCIO with respect to the occupation number in the end members SCO, SIO, with SOC as a function of strain.

Figure 9

Spatial distribution of the unoccupied states integrated between the Fermi level and 6.0 eV without SOC (isosurface value is $0.06e^{-}$ ${\AA }^{-3}$) for (a) the end member ${\mathrm{SrCoO}}_3$ for G-AFM coupling and (b) the double perovskite SCIO at $a_{\mathrm{NGO}}$ as a representative example.

Figure 10

(a)–(c) Real and (d)–(f) imaginary part of the dielectric tensor within the I.P. (blue line), $G_0{W}_0$ (petrol line), and $G_0{W}_0+\mathrm{BSE}$ (red line) approximations for SCIO strained at (a), (d) $a_{\mathrm{NGO}}$, (b), (e) $a_{\mathrm{STO}}$, and (c), (f) $a_{\mathrm{GSO}}$. The in- and out-of-plane components are denoted by solid and dashed lines, respectively. (g)–(i) The absorption coefficient in comparison with that obtained from transmission measurements (black line). We note that in experiments for compressive strain a sample grown on an LSAT substrate was used instead of NGO; however, both have a similar (pseudocubic) lattice constant: $a_{\mathrm{LSAT}}=3.868\AA$ vs $a_{\mathrm{NGO}}=3.855\AA$, respectively [25].