Strain-induced tuning of the electronic Coulomb interaction in $3d$ transition metal oxide perovskites

Epitaxial strain offers an effective route to tune the physical parameters in transition metal oxides. So far, most studies have focused on the effects of strain on the bandwidths and crystal field splitting, but recent experimental and theoretical works have shown that also the effective Coulomb interaction changes upon structural modifications. This effect is expected to be of paramount importance in current material engineering studies based on epitaxy-based material synthesization. Here, we perform constrained random phase approximation calculations for prototypical oxides with a different occupation of the $d$ shell, ${\mathrm{LaTiO}}_3$ ($d^1$), ${\mathrm{LaVO}}_3$ ($d^2$), and ${\mathrm{LaCrO}}_3$ ($d^3$), and systematically study the evolution of the effective Coulomb interactions (Hubbard $U$ and Hund's $J$) when applying epitaxial strain. Surprisingly, we find that the response upon strain is strongly dependent on the material. For ${\mathrm{LaTiO}}_3$, the interaction parameters are determined by the degree of localization of the orbitals, and grow with increasing tensile strain. In contrast, ${\mathrm{LaCrO}}_3$ shows the opposite trend: the interaction parameters shrink upon tensile strain. This is caused by the enhanced screening due to the larger electron filling. ${\mathrm{LaVO}}_3$ shows an intermediate behavior.

Figure 1

(a)–(c): Nonmagnetic band structures of LTO, LVO, and LCO together with their Wannier-projected bands. Ab initio bands and Wannier-projected bands are denoted with thin (red) and thick (blue) lines, respectively. Fermi level has been aligned to zero. (d)–(f): Partial density of states (DOS) for three systems at their 0% strain cases. $e_g$ and $t_{2g}$ orbitals (blue and red) of TM ions are separated by the octahedral symmetry, and O-$p$ orbitals are located well below the Fermi level. The energy separation between $t_{2g}$ and $p$ orbitals is decreasing from LTO to LCO.

Figure 2

Evolution of the cRPA Hubbard parameters ($U,U^{\mathrm{bare}}$, and $U^{\mathrm{bare}}/U$, within the $t_{2g}$/$t_{2g}$ model) and the spread of the Wannier function are shown in red solid lines with filled circles. Average GFO tilting $\alpha$ (blue dotted line with filled squares) is also shown. Experimental values [48, 49, 50] were employed along the series LTO, LVO, and LCO for the structurally distorted bulk phases. Results for LVO and LCO in the LTO structures are shown with red dashed lines with open circles.

Figure 3

Effective interactions $U$ and $J$ [(a)–(c)] and $U^{\mathrm{bare}}$ and $J^{\mathrm{bare}}$ [(d)–(f)] for LTO, LVO, and LCO employing both the $t_{2g}/t_{2g}$ (red) and $t_{2g}/t_{2g}\text{−}p$ (blue) setup as a function of epitaxial substrate strain. The $U$ and $J$ values of LCO obtained by using the LTO structures are shown with dashed lines in (c). (g)–(i) Spread of the Wannier functions and (j)–(l) $U/U^{\mathrm{bare}}$.

Figure 4

Bandwidth of $t_{2g}$ orbitals [(a)–(c)], center of mass $E$ of the O-$p$ bands with respect to the Fermi level [(d)–(f)], and $U/W$ ratio LTO, LVO, and LCO as a function of epitaxial strain [(g)–(i)].

Figure 5

Orbital-resolved DOS for LTO, LVO, and LCO as a function of epitaxial strain. Shaded (yellow) region denotes the width of $t_{2g}$ orbitals, which is defined as bandwidth, $W$.

Figure 6

(a) The schematic diagram showing IP and OP bond angles and bond lengths. Evolution of (b) ${\alpha }_{\mathrm{IP}}$, (c) ${\alpha }_{\mathrm{OP}}$, (d) $d_{\mathrm{IP}}$, and (e) $d_{\mathrm{OP}}$ upon epitaxial strain.