Phase separation in strained cation- and anion-deficient Nd$_{0.52}$Sr$_{0.48}$MnO$_3$ films

The magnetic and transport properties of anion- and cation-deficient Nd$_{0.52}$Sr$_{0.48}$MnO$_3$ films with different thicknesses, as well as of two films from this system grown on different SrTiO$_3$ and LaAlO$_3$ substrates, are studied. Below Curie temperature $T_{\mathrm{C}}$, the films with different thicknesses exhibit phase separation: they represent magnetic clusters (drops) embedded in a nonconducting paramagnetic (at $T>T_{\mathrm{N}}$, where $T_{\mathrm{N}}$ is the Néel temperature) or antiferromagnetic $(T<T_{\mathrm{N}})$ matrix. The temperature dependences of the resistivity of the films are well described in terms of the polaron mechanism of conduction. In external magnetic field $H$ = 0.01 T, the drops may reach 15 nm in size. They consist of magnetic polarons with a small radius (1–2 nm). The drops are shown to interact with each other in the films. Because of competition between drop-drop dipole interaction and the magnetic energy, the drops disintegrate into droplets with a size comparable to that of a magnetic polaron in a field of 1T. An explanation is given for the discrepancy between our results and the frequently observed growth of the drops with a rise in the external magnetic field. As the film gets thicker, the fraction of the ferromagnetic phase grows with thickness nonlinearly. In the film grown on SrTiO$_3$ (compressed by 0.9%), the characteristic Néel and Curie temperatures are lower than in the film grown on LaAlO$_3$. The diameters of ferromagnetic drops (both maximal at $H$ = 0.01 T and minimal at $H$ = 1 T) turn out to be roughly the same as in the films with different thicknesses.