Collinear spin-density-wave ordering in Fe/Cr multilayers and wedges

Several recent experiments have detected a spin-density wave (SDW) within the Cr spacer of Fe/Cr multilayers and wedges. We use two simple models to predict the behavior of a collinear SDW within an Fe/Cr/Fe trilayer. Both models combine assumed boundary conditions at the Fe-Cr interfaces with the free energy of the Cr spacer. Depending on the temperature and the number N of Cr monolayers, the SDW may be either commensurate (C) or incommensurate (I) with the bcc Cr lattice. Model I assumes that the Fe-Cr interface is perfect and that the Fe-Cr interaction is antiferromagnetic. Consequently, the I SDW antinodes lie near the Fe-Cr interfaces. With increasing temperature, the Cr spacer undergoes a series of transitions between I SDW phases with different numbers n of nodes. If the I SDW has n=m nodes at T=0, then n increases by one at each phase transition from m to m-1 to m-2 up to the C phase with n=0 above T_IC(N). For a fixed temperature, the magnetic coupling across the Cr spacer undergoes a phase slip whenever n changes by one. In the limit N^→∞, T_IC(N) is independent of the Fe-Cr coupling strength. We find that T_IC(∞) is always larger than the bulk Néel transition temperature and increases with the strain on the Cr spacer. These results explain the very high IC transition temperature of about 600 K extrapolated from measurements on Fe/Cr/Fe wedges. Model II assumes that the I SDW nodes lie precisely at the Fe-Cr interfaces. This condition may be enforced by the interfacial roughness of sputtered Fe/Cr multilayers. As a result, the C phase is never stable and the transition temperature T_N(N) takes on a seesaw pattern as n>∼2 increases with thickness. In agreement with measurements on both sputtered and epitaxially grown multilayers, model II predicts the I phase to be unstable above the bulk Néel temperature. Model II also predicts that the I SDW may undergo a single phase transition from n=m to m-1 before disappearing above T_N(N). This behavior has recently been confirmed by neutron-scattering measurements on CrMn/Cr multilayers. While model I very successfully predicts the behavior of Fe/Cr/Fe wedges, a refined version of model II describes some properties of sputtered Fe/Cr multilayers.