Finite-size effects in Cu-Mn spin glasses

Finite-size effects in the spin glass (SG) Cu-Mn have been studied using magnetron-sputtered multilayer systems (MS's) of the form Cu_1-x{Mn}ₓ$/Cu and ${Cu}_{1{{-}}x}Mnₓ/Si with x=0.04, 0.07, 0.14 (and some data for 0.21). The SG layers have widths W_Cu-Mn ranging from 10 000 to 20 {} and are separated and magnetically decoupled from each other by interlayers of either 300 {} of Cu or 70 {} of Si. The MS's continue to show SG peaks in the zero-field-cooled (ZFC) ``dc'' magnetic susceptibility {χ} down to W_Cu-Mn=20 {}. The quasistatic freezing temperature Tf (defined as the location of the peak in {χ}) begins to decrease from its bulk value, Tfᵇ, at W_Cu-Mn{}1000 {} and approaches zero for SG thicknesses 0{≤}W_Cu-Mn{≤}10 {} with Cu interlayers or 30 {}{≤}W_Cu-Mn{≤}35 {} with Si interlayers.A plot of the ratio Tf/Tfᵇ versus W_Cu-Mn yields a separate ``universal'' curve for each of the two interlayer materials, independent of x. Structural analyses of the MS's using large- and small-angle x-ray diffraction, energy-dispersive x-ray spectroscopy, selected area diffraction, electron microscopic imaging, and parallel resistivity measurements, confirm that the samples are layered and indicate that interface intermixing is modest in the Cu_1-x{Mn}ₓ$/Cu MS but more substantial in the ${Cu}_{1{{-}}x}Mnₓ/Si MS. This latter result suggests that the Cu_1-x{Mn}ₓ$/Cu MS's are closer to isolated, uncontaminated layers of Cu-Mn, and further analysis thus focuses primarily upon these MS's. Various effects that might mimic size-dependent behavior are first considered, and then the ``universal'' variation of Tf/Tfᵇ with W_Cu-Mn for the Cu_1-x{Mn}ₓ$/Cu MS is analyzed in terms of (1) static finite-size scaling and (2) the activated dynamics of the Fisher and Huse cluster-excitation model.Appropriate parameters are derived for each model. This investigation is believed to be the first to examine how the properties of a long-range Ruderman-Kittel-Kasuya-Yosida SG such as Cu-Mn change as the lower critical dimension is crossed.