Magnetism of ${\left({\mathrm{LaCoO}}_3\right)}_n+{\left({\mathrm{LaTiO}}_3\right)}_n$ superlattices ($n=1,2$)

 ${\mathrm{LaCoO}}_3$ provides a poignant example of a transition metal oxide where the cobalt cations display multiple spin states and spin transitions and which continues to garner substantial attention. In this work, we describe first principles studies, based on $\mathrm{DFT}+U$ theory, of superlattices containing ${\mathrm{LaCoO}}_3$, specifically ${\left({\mathrm{LaCoO}}_3\right)}_n+{\left({\mathrm{LaTiO}}_3\right)}_n$ for $n=1,2$. The superlattices show strong electron transfer from Ti to Co resulting in ${\mathrm{Co}}^{2+}$, significant structural distortions and a robust orbital polarization of the ${\mathrm{Co}}^{2+}$. We predict high-spin ${\mathrm{Co}}^{2+}$ and a checkerboard (G-type) antiferromagnetic ground state. We provide a detailed analysis of the magnetic interactions and phases in the superlattices. We predict that ferromagnetic order on the ${\mathrm{Co}}^{2+}$ can be stabilized by hole doping (e.g., replacing La by Sr), which is rather unusual for ${\mathrm{Co}}^{2+}$ cations.

Figure 1

Atomic-scale structures of ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ and ${\left({\mathrm{LaCoO}}_3\right)}_2+{\left({\mathrm{LaTiO}}_3\right)}_2$ superlattices. (a) Top view and (b) side view of the ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ superlattice. (c) Side view of the ${\left({\mathrm{LaCoO}}_3\right)}_2+{\left({\mathrm{LaTiO}}_3\right)}_2$ superlatttice.

Figure 2

Total (black) and projected (colors) density of states (DOS) of the ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ superlattice onto the $3d$ orbitals of one Co atom. The Co atoms have high-spin states and AFM spin alignment, $U_{Co}=3\mathrm{eV}$ and $U_{Ti}=3\mathrm{eV}$ with $\mathrm{GGA}+U$ are used, and the in-plane lattice parameter is $a=3.784$ Å. Positive and negative DOS describe spin-up and spin-down electronic states, respectively.

Figure 3

Atomic structure of the ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ superlattice with $a^0{a}^0{a}^0$ octahderal tilt and schematic picture of the local electric field. Distances between the La plane and the ${\mathrm{TiO}}_2$ or ${\mathrm{CoO}}_2$ plane as as well as the shift between La and O in the same plane (prior to displacement) are shown. The structure is obtained by using $U_{Co}=3\mathrm{eV}, U_{Ti}=2.5\mathrm{eV}, \mathrm{GGA}+U$, and an in-plane lattice parameter of $a=3.784$ Å.

Figure 4

Projected density of states of ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ for (a) high-spin and (c) low-spin FM states. (b) and (d) Schematics of the corresponding atomic-like energy levels. $U_{Co}=3\mathrm{eV}$ and $U_{Ti}=3\mathrm{eV}$ with $\mathrm{GGA}+U$ are used, and the in-plane lattice parameter is $a=3.784$ Å.

Figure 5

$U_{Co}$ dependence of the energies of different magnetic states of ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$ within $\mathrm{GGA}+U$, for different in-plane lattice parameters (a) 3.663 Å, (b) 3.784 Å, and (c) 3.905 Å. Energies of LS FM phase are set to zero.

Figure 6

Magnetic stabilities of electron- and hole-doped ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$ superlattices, with (a) $a=3.663$ Å, (b) $a=3.784$ Å, and (c) $a=3.905$ Å. The energy of the LS FM phase is set to zero.

Figure 7

Five possible HS/LS orderings and four possible magnetic orderings of the ${\left({\mathrm{LaCoO}}_3\right)}_2+{\left({\mathrm{LaTiO}}_3\right)}_2$ superlattice.

Figure 8

$U$ dependence of energies for different spin configurations of ${\left(\mathrm{LTO}\right)}_2+{\left(\mathrm{LCO}\right)}_2$ with different in-plane lattice parameters. Energy of LS FM is set to be zero.

Figure 9

$U_{Co}$ dependence of the total energies for AFM states of ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$ superlattices. (a) Total energies per Co of different magnetic configurations (the total energy of the LS state is chosen as the zero of energy). (b) Spectral decomposition of the $+U$ energy contribution (see text).

Figure 10

$U_{Co}$ dependence of energies for different magnetic states of ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$. (a) energies of HS FM and HS AFM, where the energy of HS FM is set to be zero. (c) $\mathrm{\Delta }{E}_{fill}\left[HS\right], \mathrm{\Delta }{E}_{ord}\left[HS\right]$, and $\mathrm{\Delta }{E}_{fill}\left[HS\right]+\mathrm{\Delta }{E}_{ord}\left[HS\right]$. (c) Energies of LS FM and LS AFM, where the energy of LS FM is set to be zero. (c) $\mathrm{\Delta }{E}_{fill}\left[LS\right], \mathrm{\Delta }{E}_{ord}\left[LS\right]$, and $\mathrm{\Delta }{E}_{fill}\left[LS\right]+\mathrm{\Delta }{E}_{ord}\left[LS\right]$. (e) Energies of HS/LS FM and HS/LS FIM, where the energy of HS/LS FM is set to be zero. (f) $\mathrm{\Delta }{E}_{fill}[HS/LS], \mathrm{\Delta }{E}_{ord}[HS/LS]$, and $\mathrm{\Delta }{E}_{fill}[HS/LS]+\mathrm{\Delta }{E}_{ord}[HS/LS]$.

Figure 11

Schematic molecular orbital view of Co $3d$ energy level diagrams and in-plane magnetic interactions between two neighboring HS ${\mathrm{Co}}^{2+}$ cations. (a) and (b) Two neighboring Co with FM alignment; (c) and (d) two neighboring Co with AFM alignment. Solid horizontal lines indicate energy levels; dashed lines indicate the effect of interactions; arrows indicate electron filling colored by orbital type. ${\mathrm{\Delta }}^{11}$ and ${\mathrm{\Delta }}^{12}$ are exchange splitting for FM and AFM configurations, respectively. $\mathrm{\Delta }E$ is the energy lowering due to the magnetic interactions.

Figure 12

Schematic diagram of the in-plane magnetic interaction between HS Co and LS Co.

Figure 13

Schematic diagram of the in-plane magnetic interaction between LS Co and LS Co.

Figure 14

Schematic magnetic interaction model between two neighboring LS Co for (a) and (b) FM spin order and (c) and (d) AFM spin order. Panel (c) shows the difference in on-site energy $\delta E$ and how the hopping between the two orbitals $t$ leads to an energetic lowering by $t^2/\delta E$ for the bonding state; numerical values are provided in Table 1.

Figure 15

$U_{Co}$ dependence of the energies of different magnetic states of ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$ for different in-plane lattice parameters [3.663 Å for (a) and (b), 3.784 Å for (c) and (d), and 3.905 Å for (e) and (f)] and two different exchange-correlation functionals [(a), (c), and (e) for $\mathrm{GGA}+U$ and (b), (d), and (f) for $\mathrm{LDA}+U$]. Energies of LS FM phase is set to zero. The energy of the FM phase is set to zero. Panels (a), (c), and (e) are the same as Fig. 5.

Figure 16

Schematic diagram of the in-plane magnetic interaction between two neighboring HS Co and HS Co for FM (a) and (b) and AFM (c) and (d) configurations in hole-doped ${\left(\mathrm{LTO}\right)}_1+{\left(\mathrm{LCO}\right)}_1$. Full electronic occupation of a state is indicated by an arrow of filled circle, while partial occupation or presence of holes is indicated by the half-filled circles.

Figure 17

$U$ dependence of energies for different spin configurations of ${\left(\mathrm{LTO}\right)}_2+{\left(\mathrm{LCO}\right)}_2$ with lattice parameter $a=3.784$. Energy of LS FM is set to be zero. (a) and (b) are same as Figs. 8 and 8.

Figure 18

Schematic diagram of the out-of-plane magnetic interaction between HS Co and HS Co.

Figure 19

Total energies of different magnetic states of bulk ${\mathrm{LaCoO}}_3$ within (a) $\mathrm{GGA}+U$ and (b) $\mathrm{LDA}+U$, and the band gap of bulk ${\mathrm{LaCoO}}_3$ within (c) $\mathrm{GGA}+U$ and (d) $\mathrm{LDA}+U$. Band gap of bulk CoO within (e) $\mathrm{GGA}+U$ and (f) $\mathrm{LDA}+U$. The total energies of the nonmagnetic insulating phase (NM) are set to zero.