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

Abstract

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 $m\ensuremath{-}1$ to $m\ensuremath{-}2$ up to the C phase with $n=0$ above ${T}_{\mathrm{IC}}(N).$ For a fixed temperature, the magnetic coupling across the Cr spacer undergoes a phase slip whenever n changes by one. In the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ ${T}_{\mathrm{IC}}(N)$ is independent of the Fe-Cr coupling strength. We find that ${T}_{\mathrm{IC}}(\ensuremath{\infty})$ is always larger than the bulk N\'eel transition temperature and increases with the strain on the Cr spacer. These results explain the very high $\mathrm{IC}$ 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 ${T}_{\mathrm{N}}(N)$ 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 N\'eel temperature. Model II also predicts that the I SDW may undergo a single phase transition from $n=m$ to $m\ensuremath{-}1$ before disappearing above ${T}_{\mathrm{N}}(N).$ 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.