Strong coupling of Jahn-Teller distortion to oxygen-octahedron rotation and functional properties in epitaxially strained orthorhombic LaMnO${}_3$

First-principles calculations reveal a large cooperative coupling of Jahn-Teller (JT) distortion to oxygen-octahedron rotations in perovskite LaMnO${}_3$. The combination of the two distortions is responsible for stabilizing the strongly orthorhombic $A$-AFM insulating ($I$) $ePbnm$ ground state relative to a metallic ferromagnetic (FM-$M$) phase. However, epitaxial strain due to coherent matching to a crystalline substrate can change the relative stability of the two states. In particular, coherent matching to a square-lattice substrate favors the less orthorhombic FM-$M$ phase, with the $A$-AFM phase stabilized at higher values of tensile epitaxial strain due to its larger volume per formula unit, resulting in a coupled magnetic and metal-insulator transition at a critical strain close to 1%. At the phase boundary, a very large magnetoresistance is expected. Tensile epitaxial strain enhances the JT distortion and opens the band gap in the $A$-AFM-$I$ $c$-$ePbnm$ phase, offering the opportunity for band-gap engineering. Compressive epitaxial strain induces a transition within the FM-$M$ phase from the $c$-$ePbnm$ orientation to the $ab$-$ePbnm$ orientation with a change in the direction of the magnetic easy axis relative to the substrate, yielding strain-controlled magnetization at the phase boundary. Similar behavior is expected in other JT active $Pbnm$ perovskites.

Figure 1

Definition of Jahn-Teller distortion amplitudes, $Q_2=\frac{1}{\sqrt{2}}$ ($X_1-X_4-Y_2+Y_5$) (left) and $Q_3=\frac{1}{\sqrt{6}}$ ($2Z_3-2Z_6-X_1+X_4-Y_2+Y_5$) (right).

Figure 2

Comparison of bulk AFM orthorhombic (left) and bulk FM tetragonal (right) structures. The structure and outline of the unit cell is viewed along the $c$ axis. AFD denotes an antiferrodistortive oxygen-octahedron rotation pattern. The spheres are oxygen atoms, the shading shows the oxygen octahedra, and the other atoms are omitted for clarity.

Figure 3

(a) Computed total energies for epitaxially constrained $Pbnm$ phases of LaMnO${}_3$ with different magnetic orderings as a function of epitaxial strain. The labels $c$-$ePbnm$ and $ab$-$ePbnm$ correspond to two different choices of matching plane to the substrate, as discussed in the text. Thick lines represent insulating character and dotted lines, metallic. Blue (filled) symbols represent $A$-AFM and red (empty) symbols represent FM ordering. The lowest energy phase at each strain is specified along the bottom of the plot, separated by vertical lines representing the phase boundaries; the subscripts give the direction of the magnetic easy axis. In (b) and (c), we show the magnetocrystalline anisotropy energies computed in various planes of FM $ab$-$ePbnm$ and FM $c$-$ePbnm$, respectively, as labeled on the figure; the zero of energy is chosen as the minimum energy obtained in each panel. In (d) and (e), of FM $ab$-$ePbnm$ and FM $c$-$ePbnm$ respectively, we show the lattice vectors relative to the substrate plane with the direction of the magnetic easy axis represented as a thick red arrow and labeled with the value of the angle it makes with the substrate plane.

Figure 4

Epitaxial strain dependence for $A$-AFM ordering (circles) and FM ordering (diamonds) of (a) the JT distortion amplitude; (b) rotation angles for $R$ and $M$ distortions; (c) the $c$ lattice parameter, and (d) the direct and indirect band gaps. Horizontal blue (red) lines represent values in the bulk $A$-AFM ground state (FM alternative state) for comparison. Arrows highlight the differences in properties between bulk and 0% strained phase. The symbol corresponding to the lowest-energy state at a given strain is filled and the symbols representing the higher-energy state at the same strain are open.

Figure 5

The dependencies of total energies on the amplitudes of oxygen-octahedron-rotation distortions $M$${}_3{}^{+}$[001] (circles) and $R$${}_4{}^{+}$[110] (diamond) of cubic LaMnO${}_3$ ($a_0=3.976$ Å) are shown for $A$-AFM ordering (left) and FM ordering (right). Open symbols represent pure rotations and filled symbols represent rotations in the presence of a nonzero Jahn-Teller distortion ($Q_3=0.926$ a.u.). For each curve, the zero of energy is taken at zero rotation. Thick lines represent insulating systems and dotted lines represent metallic systems. Total energies are set to zero when there are no oxygen-octahedron rotations.

Figure 6

The geometrical interpretation of how rotations lower the energy cost of the Jahn-Teller distortion is illustrated in the top half of the figure. In the bottom half, the dependencies of total energies on the amplitude of the Jahn-Teller distortions ($M$${}_2{}^{+}$[001]) for zero and two nonzero oxygen octahedron rotation distortions are shown for $A$-AFM ordering (left) and FM ordering (right). For each curve, the zero of energy is taken at zero Jahn-Teller distortion amplitude. As in Fig. 5, thick lines with filled circles represent insulating systems and dotted lines with blank circles represent metallic.