# Metal-to-Insulator Transition in Ultrathin Manganite Heterostructures
## 4 Mechanism of the MIT
### Orbital Reconstruction  
In bulk LSMO, the orbital is degenerate, and the double exchange is isotropic, leading to 3D ferromagnetic (FM) ordering. However, either 3\(\mathrm{z^{2}}\)-\(\mathrm{r^{2}}\) or x\(\mathrm{^{2}}\)-\(\mathrm{y^{2}}\) orbital ordering will lead to strong anisotropic transfer integral, and thus C-type AFM or A-type antiferromagnetism (AFM) (see Figure 8), respectively. For epitaxial LSMO films, a common reason to favor orbital reconstruction is the tetragonal distortion due to strain imposed by substrates. As shown in Figure 8, compressive strain favors the elongation of the octahedra, while tensile strain will flatten the octahedra, thus leading to the preference of 3\(\mathrm{z^{2}}\)-\(\mathrm{r^{2}}\) or x\(\mathrm{^{2}}\)-\(\mathrm{y^{2}}\) orbital occupancy, respectively [58]. No matter whether it is tensile or compressive strain, the AFM ground state is stabilized with respect to the FM, therefore driving the system to be an AFM insulator. This is true for LSMO under large degrees of strain, e.g., on LSMO/LAO with large compressive strain [34], and LSMO/DyScO\({}_{3}\) (LSMO/DSO) with large tensile strain [59; 60]. Using polarization-dependent (in-plane \(\sigma\) and out-of-plane \(\pi\)) X-ray absorption (XAS), [PERSON] et al. revealed a 3\(\mathrm{z^{2}}\)-\(\mathrm{r^{2}}\) orbital ordering in LSMO/LAO [34]. On the other side, when LSMO is under large tensile strain, e.g., LSMO/DSO, the x\(\mathrm{^{2}}\)-\(\mathrm{y^{2}}\) orbital is more populated [59]. Accompanying the large orbital polarization, a very thick dead layer of about 10 nm is observed in LSMO/LAO and  
Figure 7: Proposed mechanisms for the origin of the dead layer in LSMO thin films. LSMO/DSO [34; 39; 59]. The metallic behavior in thick LSMO films on LAO or DSO starts to recover when the strain relaxes in thick films. When the strain is relatively small and other effects start to play a role, discrepancy arises. This occurs for the LSMO films grown on NdGaO\({}_{3}\) (NGO) and STO substrates, where the lattice mismatch is \(-0.5\%\) and \(0.6\%\), respectively. [PERSON] et al. [34] and [PERSON] et al. [37] found that the LSMO film on (001) SrTiO\({}_{3}\) substrate will end up with 3\({}^{2}\)-r\({}^{2}\) orbital ordering at the interface. This counters to the expectation from the tensile strain imposed on LSMO, which flattens the MnO\({}_{6}\) octahedra and should favor x\({}^{2}\)-y\({}^{2}\) orbital occupation. The unexpected 3\({}^{2}\)-r\({}^{2}\) orbital reconstruction has been proposed to be caused by interface or surface effects, which become prominent in ultrathin LSMO films. First-principle theoretical calculations indicates that the MnO\({}_{2}\)- and (La,Sr)O-terminated surfaces show strong tendencies to have 3\({}^{2}\)-r\({}^{2}\) and x\({}^{2}\)-y\({}^{2}\) orbital reconstructions, respectively [61]. The missing top apical oxygen for the MnO\({}_{2}\) termination surface will provide a repulsive potential, and an elongated Mn-O bond along the surface normal direction, downshifting the 3\({}^{2}\)-r\({}^{2}\) orbital. Regarding the (La,Sr)O termination, the 3\({}^{2}\)-r\({}^{2}\) orbital will upward-shift due to strengthened pd\(\alpha\) hybridization when the above MnO\({}_{2}\) layer is missing. This predicted effect of surface termination on orbital polarization has been confirmed experimentally by [PERSON] et al. [52]. In the case of LSMO interfacing empty 3\({}^{2}\)-r\({}^{2}\) material, the Mn 3\({}^{2}\)-r\({}^{2}\) orbital has a large overlap with the empty 3\({}^{2}\)-r\({}^{2}\) through bridging the oxygen at the interface, and it favors delocalization into the empty 3\({}^{2}\)-r\({}^{2}\) orbital. Such a mechanism will lower the Mn 3\({}^{2}\)-r\({}^{2}\) orbital, and therefore enhance 3\({}^{2}\)-r\({}^{2}\) orbital occupation at the interface. This has been proposed to explain 3\({}^{2}\)-r\({}^{2}\) orbital reconstruction in ultrathin LSMO on STO, and contributes to the origin of the dead layer [37; 62].