Figure 2: Correlation between magnetic and structural properties of the (LaMnO_3+δ)_N/(SrTiO₃)_N superlattices.

(a) The hysteresis loops measured at T=4 K along the in-plane direction. (b) The magnetization as a function of temperature measured after field cooling along the in-plane direction. The cooling field was 1,000 Oe and the magnetization was measured during warming up in a field of 100 Oe. (c) The saturation magnetization (M_s) and the FM transition temperature (T_c) as a function of the superlattice period N. M_s* and T_c* are the mean-field estimates without the presence of interfacial reconstructions. (d) The Mn K-edge threshold energy measured from XAFS and the derived Mn valence (see Methods section). (e) Half-order Bragg peak intensity for four representative samples (N=2, 6, 16 and LaMnO_3+δ film). Each point in the data corresponds to one certain half-order Bragg peak with assigned index X, whose HKL values can be found in Supplementary Table 1. Half-order peaks with their X index ranging from [0,12], [13,34] and [35,55] correspond to peaks with one of H,K,L half-integer, peaks with all three-half-integers, and peaks with two-half-integers, respectively. (f) Pseudocubic lattice constant along the c axis (c_p) as a function of superlattice periodicity N deduced from half-order Bragg peaks. The results for two types of half-order peaks, representing DR and DO phase, respectively, are generated by averaging all measured peaks. The error bars indicate statistical variance.