Effect of confinement and octahedral rotations on the electronic, magnetic, and thermoelectric properties of correlated $\mathrm{Sr}X{\mathrm{O}}_3/{\mathrm{SrTiO}}_3\left(001\right)$ superlattices ($X=\mathrm{V}$, Cr, or Mn)

By using density functional theory calculations with an on-site Coulomb repulsion term combined with Boltzmann transport theory, we explore the effect of $t_{2g}$ orbital occupation on the electronic, magnetic, and thermoelectric properties of ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_n\left(001\right)$ superlattices with $n=1,3$ and $X=\mathrm{V}$, Cr, and Mn. In order to disentangle the effect of quantum confinement and octahedral rotations and to account for a wider temperature range, $P4/mmm$ (untilted) and $P{2}_1/c$ (tilted) phases are considered. We find that the ground-state superlattice geometries always display finite octahedral rotations, which drive an orbital reconstruction and a concomitant metal-to-insulator transition in confined ${\mathrm{SrVO}}_3$ and ${\mathrm{SrCrO}}_3$ single layers with ferro- and antiferromagnetic spin alignments, respectively. On the other hand, the confined ${\mathrm{SrMnO}}_3$ single layer exhibits electronic properties similar to bulk. We show that confinement enhances the thermoelectric properties, particularly for ${\mathrm{SrVO}}_3$ and ${\mathrm{SrCrO}}_3$ due to the emergent Mott phase. Large room-temperature Seebeck coefficients are obtained for the tilted superlattices, ranging from 500 to $600\mu \mathrm{V}/\mathrm{K}$ near the band edges. The estimated attainable power factors of $27.9\left(26.6\right)\mu \mathrm{W}{\mathrm{K}}^{-2}{\mathrm{cm}}^{-1}$ in plane for the ${\left({\mathrm{SrCrO}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ superlattice with $P4/mmm(P{2}_1/c)$ symmetry and $28.1\mu \mathrm{W}{\mathrm{K}}^{-2}{\mathrm{cm}}^{-1}$ cross plane for the ${\left({\mathrm{SrMnO}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ superlattice with $P{2}_1/c$ symmetry compare favorably with some of the best-performing oxide thermoelectrics. This demonstrates that the idea to use quantum confinement to enhance the thermoelectric response in correlated transition-metal oxide superlattices [Phys. Rev. Mater. 2, 055403 (2018)] can be applied to a broader class of materials combinations.

Figure 1

Side and top view of optimized ${\left(\mathrm{SrV}{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ SLs with $P4/mmm$ symmetry (untilted, top row) and with $P{2}_1/c$ symmetry where octahedral tilts and rotations are fully considered (bottom row).

Figure 2

Projected densities of states and corresponding spin densities of tetragonal ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ SLs ($P4/mmm$ symmetry) with $X=\mathrm{V}$, Cr, and Mn. Top row: Layer-, element-, and spin-resolved densities of states for the ${\mathrm{TiO}}_2$, SrO, and $X{\mathrm{O}}_2$ layers. Central row: Site-, orbital-, and spin-resolved densities of states for the two distinct $X$ sites. Bottom row: Spin densities (side and top views), integrated from $-6\mathrm{eV}$ to the Fermi energy (0 eV), together with the local magnetic moments at the two distinct $X$ sites. The spin density of the vanadate 1/3 SL is shown for comparison. Red and blue correspond to positive/negative spin densities.

Figure 3

Band structure and in- and cross-plane majority-spin transmission ${\mathcal{T}}_{\uparrow }\left(E\right)$ of tetragonal ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_n\left(001\right)$ SLs ($P4/mmm$ symmetry) with $n=1,3$ and (a) $X=\mathrm{V}$, (b) Cr, and (c) Mn. Red and blue bands correspond to spin-up and spin-down channels, respectively. For the ${\left({\mathrm{SrMnO}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ SL, additional band character plots (d) show the contributions of O $2p$ and Mn $3d$ orbitals in the confined ${\mathrm{MnO}}_2$ single layer.

Figure 4

Projected densities of states and corresponding spin densities of tilted ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ SLs ($P{2}_1/c$ symmetry) with $X=\mathrm{V}$, Cr, and Mn. Top row: Layer-, element-, and spin-resolved densities of states for the ${\mathrm{TiO}}_2$, SrO, and $X{\mathrm{O}}_2$ layers. Central row: Site-, orbital-, and spin-resolved densities of states for the two distinct $X$ sites. Bottom row: Spin densities (side and top views), integrated from $-6\mathrm{eV}$ to the Fermi energy (0 eV) together with the local magnetic moments at the two distinct $X$ sites. In contrast to the untilted SLs, clear orbital order without charge or bond disproportionation emerges for the tilted V- and Cr-based SLs due to the extended degrees of freedom, accompanied by a metal-to-insulator transition.

Figure 5

Band structure and in- and cross-plane majority-spin transmission ${\mathcal{T}}_{\uparrow }\left(E\right)$ of tilted ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_n\left(001\right)$ SLs ($P{2}_1/c$ symmetry) with $n=1,3$ and $X=\mathrm{V}$, Cr, and Mn. Red and blue bands correspond to spin-up and spin-down channels, respectively.

Figure 6

Thermoelectric properties of ${\left(\mathrm{Sr}X{\mathrm{O}}_3\right)}_1/{\left({\mathrm{SrTiO}}_3\right)}_1\left(001\right)$ SLs ($X=\mathrm{V}$, Cr, and Mn) with $P4/mmm$ symmetry (absence of octahedral rotations, left panels) and $P{2}_1/c$ symmetry (including octahedral rotations, right panels). Three different temperatures are displayed in each case: 200, 300, and 400 K for the $P4/mmm$ SLs and 100, 200, and 300 K for the $P{2}_1/c$ SLs, reflecting the different temperature range where the SLs are expected to be stable. From top to bottom, Seebeck coefficient $S$, electrical conductivity $\sigma /\tau$, power factor $\mathrm{PF}/\tau$, and electronic figure of merit ${ZT|}_{\mathrm{el}}$ are shown, where $\tau$ denotes the relaxation time. Orange, dark-green, and brown lines (red, green, and blue lines with points) correspond to cross-plane (in-plane) transport. The vertical dashed line at zero energy denotes the Fermi level (if metallic) or the VBM (if semiconducting); in the latter case, the second vertical dashed line indicates the conduction band minimum (CBM).