## 1 Introduction  
Magnetic thin films and two-dimensional magnetic materials have attracted worldwide attention owing to the interesting physical phenomenon and various applications. For example, the spin current transport in a confined thin film implies the prospect to control the spin signal in the nano-scale. Several spintronic devices have been proposed or implemented, such as the magnetic tunnel junction [1; 2; 3], magnetic random access memory (MRAM) [4; 5; 6], and solid-state drive (SSD). To improve the efficiency of spin devices, magnetic materials or magnetic heterostructures, particularly magnetic thin films composed of transition metal oxide (TMO), have been proposed and caught many researcher's eyes. Thanks to the huge family of TMO, many heterostructures, such as LaAlO\({}_{3}\)/SrTiO\({}_{3}\)[7; 8], BaTiO\({}_{3}\)/La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\)[9; 10; 11], BiFeO\({}_{3}\)/La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\)[12] and so on, provide diverse, unusual properties for different kinds of applications.  
The 4\(d\) ferromagnetic metal SrRuO\({}_{3}\) (SRO) with Currie temperature \(T_{\rm C}\simeq 150\) K [13] has been studied in many heterostructures [14; 15; 16]. Unusual properties such as the half-metallicity [17; 18; 19; 20], itinerant ferromagnetism [21; 22] and non-Fermi liquid [23; 24] in SRO have been well documented. In particular, monolayer SRO sandwiched by SrTiO\({}_{3}\) (STO) is predicted as a two-dimensional half-metallic electron gas based on DFT calculations [25]. However, experiments show that the SRO thin film exhibits a metal-insulator transition below 4 unit cell (u.c.) [26; 27]. Several theoretical studies have tried to explain this metal-insulator transition. However, most of them provide only partially correct properties for SRO thin films, such as correct insulating behaviors for two and three layers only [28] or simply non-ferromagnetic phase [27]. One successful study combines density functional theory (DFT) with many body dynamical mean-field theory (DFT+DMFT), which can reproduce the metal-insulator transition in SRO thin film and the antiferromagnetic insulator property in SRO monolayer [29]. However, a successful route toward the desired ultrathin spin-polarized (SP) layer hosting the SP-2 DEG based on SRO is still lacking.  
In this paper, we study the electronic and magnetic properties of SRO through ab initio calculations using the LDA + \(U\) method. Based on the Heisenberg model, we simulate the Curie temperature of bulk SRO by the usual mean-field method, self-consistent Gaussian approximation (SCGA) [30] and Monte Carlo (MC) method [31]. We successfully reproduced the Curie temperature of bulk SRO from the intersite exchange parameters given by DFT + \(U\) calculations. Moreover, we show that, by taking the on-site energy of both Ru and Ti ions into consideration, the metal-insulator transition in single layer SRO associated with the transition from half-metallic ferromagnetism to insulating antiferromagnetism can be induced by tuning the lattice constant from the SRO to STO one. Therefore, the half-metallic phase of single layer SRO in SRO/STO superlattice can be achieved by manipulating the strain effect or applying an external lateral stress. Our work thus paves a new way toward the desired ultrathin SP-2 DEG based on SRO.