Effect of strain on the orbital and magnetic ordering of manganite thin films and their interface with an insulator

We study the effect of uniform uniaxial strain on the ground-state electronic configuration of a thin-film manganite. Our model Hamiltonian includes the double exchange, the Jahn-Teller electron-lattice coupling, and the antiferromagnetic superexchange. The strain arises due to the lattice mismatch between an insulating substrate and a manganite, which produces a tetragonal distortion. This is included in the model via a modification of the hopping amplitude and the introduction of an energy splitting between the Mn $e_g$ levels. We analyze the bulk properties of half-doped manganites and the electronic reconstruction at the interface between a ferromagnetic and metallic manganite and the insulating substrate. The strain drives an orbital selection modifying the electronic properties and the magnetic ordering of manganites and their interfaces.

Figure 1

Illustration of the possible spin and orbital order configurations for half-doped manganites. FM labels a three-dimensional ferromagnet, while the other three ($A$, $C$, and CE) are different antiferromagnetic orderings. The FM configuration is orbital disordered (represented here by isotropic spherical orbitals). The $A$-type, with FM planes coupled antiferromagnetically, favors the occupancy of the $x^2$-$y^2$ orbitals. The $C$ type, with FM lines in the $z$ direction coupled antiferromagnetically, favors the occupancy of the $3z^2$-$r^2$ orbitals. The CE-type ordering consists of FM zigzag chains coupled antiferromagnetically (only the $\mathit{xy}$ plane is shown here) and is associated with a peculiar orbital ordering (alternating $3x^2$-$r^2$, $3y^2$-$r^2$, and more isotropic orbitals) and checkerboard charge ordering.

Figure 2

Bulk phase diagram $\lambda$ vs $J_{\mathrm{AF}}$ for half-doped manganites. FM, $A$, $C$, and CE label the different magnetic and orbital orders considered (see Fig. 1). (a) Without strain. (b) With compressive strain $e_{\mathit{xy}}=-2\%$. (c) With tensile strain $e_{\mathit{xy}}=2\%$. The splitting between the $e_g$ levels is $\delta =50e_{\mathit{xy}}t$ [namely, $\left|\delta \right|=t$ in (b) and (c)].

Figure 3

Bulk phase diagrams $J_{\mathrm{AF}}$ vs $e_{\mathit{xy}}$ for $\lambda =1t$ with $\delta =0$ (a) and $\delta =100e_{\mathit{xy}}t$ (b).

Figure 4

Two-dimensional ($\mathit{xz}$ plane) projection of the considered heterostructure. The circles represent the Mn sites while the squares are the $A$ sites (La, Sr, Ca, etc.) shifted by $(1,1,1)\frac{a}{2}$ with respect to the Mn. $a$ is the lattice parameter. Full squares represent the $A_{0.7}^{3+}{A}_{0.3}^{\text{'}2+}{\text{O}}^{2-}$ plane, with a charge density of $+0.7$ per $A$ atom. Empty squares correspond to the Sr${}^{2+}$O${}^{2-}$ planes where the charge density is zero. Periodic boundary conditions are applied in all three directions.

Figure 5

Average charge per plane for the three possible configurations considered at a manganite-insulator interface for $\lambda =1$, $\alpha =1$, and $e_{\mathit{xy}}=0$. The straight lines in black represent the positive background charge. (a) FM: all ferromagnetic planes, (b) 1CE: all ferromagnetic planes except for a single CE plane at each manganite-insulator interface (layers $l=2,11$), and (c) 2CE: two CE planes at each manganite insulator interface (layers $l=2,3,10,11$).

Figure 6

Phase diagram $\alpha$ vs $J_{\mathrm{AF}}$ for the manganite-insulator interface with $\lambda =1$. FM stands for all FM Mn planes, 1CE stands for a configuration with a single CE layer at the manganite surface, and 2CE stands for two CE layers at the manganite surface. The lines represent the boundaries between the different ground-state configurations: The black lines (squares) correspond to the results with $e_{\mathit{xy}}=0$, the red lines (stars) are for compressive strain $e_{\mathit{xy}}=-2\%$, and the blue lines (circles) for tensile strain $e_{\mathit{xy}}=2\%$. $\delta =50e_{\mathit{xy}}t$ is assumed.

Figure 7

Phase diagram $\lambda$ vs $J_{\mathrm{AF}}$ for the manganite-insulator interface with $\alpha =1$. The labels are the same as in Fig. 6. $\delta =50e_{\mathit{xy}}t$ is assumed.

Figure 8

Phase diagrams $J_{\mathrm{AF}}$ vs $e_{\mathit{xy}}$ for the manganite-insulator interface with $\lambda =1$ and $\alpha =1$. The strain-induced $e_g$ level splitting is $\delta =0$ in (a) and $\delta =100e_{\mathit{xy}}t$ in (b).