Thickness dependence of dynamic and static magnetic properties of pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ films on SrTiO$_3$(001)

We present a comprehensive study of the thickness dependence of static and magneto-dynamic magnetic properties of La$_{0.7}$Sr$_{0.3}$MnO$_3$. Epitaxial pulsed laser deposited La$_{0.7}$Sr$_{0.3}$MnO$_3$ / SrTiO$_3$(001) thin films in the range from 3 unit cells (uc) to 40 uc (1.2 - 16 nm) have been investigated through ferromagnetic resonance spectroscopy (FMR) and SQUID magnetometry at variable temperature. Magnetodynamically, three different thickness, $d$, regimes are identified: 20 uc $\lesssim d$ uc where the system is bulk like, a transition region 8 uc $\le d \lesssim 20$ uc where the FMR line width and position depend on thickness and $d=6$ uc which displays significantly altered magnetodynamic properties, while still displaying bulk magnetization. Magnetization and FMR measurements are consistent with a nonmagnetic volume corresponding to $\sim$ 4 uc. We observe a reduction of Curie temperature ($T_C$) with decreasing thickness, which is coherent with a mean field model description. The reduced ordering temperature also accounts for the thickness dependence of the magnetic anisotropy constants and resonance fields. The damping of the system is strongly thickness dependent, and is for thin films dominated by thickness dependent anisotropies, yielding both a strong 2-magnon scattering close to $T_c$ and a low temperature broadening. For the bulk like samples a large part of the broadening can be linked to spread in magnetic anisotropies attributed to crystal imperfections/domain boundaries of the bulk like film.