# Metal-to-Insulator Transition in Ultrathin Manganite Heterostructures
## 1 Introduction  
Thanks to the fast development of advanced thin film epitaxial techniques, such as pulsed laser deposition (PLD) and molecular beam epitaxy (MBE), artificial low-dimensional materials can be fabricated with thickness that is controlled precisely down to the atomic scale. This provides unprecedented opportunities to tailor complex oxides for new functionalities by material architecture with atomic precision [1; 2; 3]. By introducing strain [4; 5], interface [6; 7], broken symmetry [8; 9], and by reducing dimensionality [10], new matter states or novel functionalities have been realized in oxide heterostructures, which are fundamentally different from those exhibited by their corresponding bulk forms. Typical examples include the interface-induced multiferroism [11], the polar metal in geometrically designed nickelate heterostructures [12] and the polarized vortex in PbTiO\({}_{3}\)/SrTiO\({}_{3}\) superlattices [13], etc. It is widely believed that novel phenomena are driven by tailoring the intimate coupling between spin, charge, orbital, and lattice. Though the underline physics is still too complicated to fully understand in transition metal oxide heterostructures, thickness variation becomes a very common and simple approach to induce emergent physical properties. Particularly crucial is when the layers enter into the ultrathin region, where the thickness is only several unit cells (u.c.) or a few nanometers. Many phase transitions, such as the metal-to-insulator transition [14; 15; 16; 17; 18], ferromagnetism to anti/paramagnetism [16; 17; 18; 19], ferroelectricity to paraelectricity [20], have been found by reducing the thickness by even just one unit cell, in different kinds of ultrathin perovskite thin films. Besides the rich fundamental physics, understanding the mechanism of thickness-driven collective phase transitions is very important for the next-generation miniature electronic devices. Among these emergent phenomena, the metal-to-insulator transition (MIT) in manganites La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\) thin films is a highly focused topic. La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\) exhibits perovskite structure with corner-shared MnO\({}_{6}\) octahedra forming a 3-dimensional network (see Figure 1a). Depending on the doping level, La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\) has different crystalline symmetry and rich electronic groundstates, as shown in Figure 1b[21]. Near both end sides of the phase diagram (\(x<0.1\) & \(x>0.5\)), an antiferromagnetic insulating phase is found to be the ground state, while it is a ferromagnetic metal in between states (\(0.2<x<0.5\)). The most striking properties of La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\) are above room temperature (Curie temperature) and near 100% spin polarization in \(x=1/3\) La\({}_{2/3}\)Sr\({}_{1/3}\)MnO\({}_{3}\) (LSMO) [22; 23], which is also often written as the compound La\({}_{0.7}\)Sr\({}_{0.3}\)MnO\({}_{3}\). LSMO is the most itinerant electron material, with the highest Curie temperature (\(T_{\rm C}\)\(\sim\)369 K) among all of the known manganites [22]. These unique properties make LSMO an extremely interesting material for technological applications [24; 25]. Efforts to obtain high quality epitaxial LSMO films can be traced back to the 1990s, by magnetron sputtering deposition and PLD [26; 27; 28; 29; 30]. The PLD technique was the key technique for growing LSMO films, and bulk-like properties in LSMO thin films have been reproduced by PLD, allowing us to fabricate LSMO-based spintronics devices [27; 28; 29; 30]. Excellent device functionalities have been demonstrated in LSMO spintronics devices [24; 25; 29; 30]. Reducing the thickness of LSMO is crucial for the miniaturization of the device. However, it becomes very challenging to obtain high-quality ultrathin LSMO films, since the properties of LSMO are greatly deteriorated when the thickness is reduced down to a few unit cells [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. The LSMO films undergo a metal to insulator transition with reducing thickness.