Effects of spin density wave quantization on the electrical transport in epitaxial Cr thin films

We present measurements of the electrical resistivity, $\rho$, in epitaxial Cr films of different thicknesses grown on MgO (100) substrates, as a function of temperature, $T$. The $\rho(T)$ curves display hysteretic behavior in certain temperature range, which is film thickness dependent. The hysteresis are related to the confinement of quantized incommensurate spin density waves (ISDW) in the film thickness. Our important finding is to experimentally show that the temperature $T_{mid}$ where the ISDW changes from $N$ to $N$\,+\,1 nodes {\it decreases} as the film thickness {\it increases}. Identifying $T_{mid}$ with a first order transition between ISDW states with $N$ and $N$\,+\,1 nodes, and using a Landau approach to the free energy of the ISDW together with Monte Carlo simulations, we show that the system at high temperatures explores all available modes for the ISDW, freezing out in one particular mode at a transition temperature that indeed decreases with film thickness, $L$. The detailed dependence of $T_{mid}(L)$ seems to depend rather strongly on the boundary conditions at the Cr film interfaces.