Glassy dynamics in CuMn thin-film multilayers

Abstract

Thin film multilayered spin glass CuMn/Cu structures display glassy dynamics. The freezing temperature, T f , was measured for forty layers of CuMn films of thickness L = 4.5, 9.0, and 20.0 nm, sandwiched between non-magnetic Cu layers of thickness ≈ 60 nm. The Kenning effect, T f ∝ ℓn L, is shown to follow from power law dynamics where the correlation length grows from nucleation as ξ(t, T ) = c1a0(t/τ0) c 2 (T /Tg ) , leading to [(T f /Tg)c2ℓn(tco/τ0)] + ℓnc1 = ℓn(L/a0). Here, Tg is the bulk spin glass temperature, c1 and c2 are constants determined from the spin glass dynamics, tco is the time for the correlation length to grow to the film thickness, τ0 is a characteristic exchange time ≈ /kBTg, and a0 is the average M n − M n separation. For t ≥ tco, the magnetization dynamics are simple activated, with a single activation energy ∆max(L)/kBTg = (1/c2)[ℓn(L/a0) − ℓnc1] that does not change with time. Values for all these parameters are found for the three values of L explored in these measurements. We find experimentally ∆max(L)/kB = 907 K, 1,246 K, and 1,650 K, respectively, for the three CuMn thin film multilayer thicknesses, to be consistent with power law dynamics. We perform a similar analysis based on the activated dynamics of the droplet model, and find a much larger spread for ∆max(L) than found experimentally.

Slowing down of spin glass correlation length growth: Simulations meet experiments

“…For a polycrystalline bulk thiospinel, Joh et al found at a reduced temperature of T /T c = 0.72, z c = 7.576. There is no way of knowing the crystallite size in these "bulk" measurements, but they were certainly larger than the thin film thicknesses of Zhai et al [7]. Zhai et al found, for CuMn 11.7 at.% thin films at reduced temperatures of T /T c = 0.43, 0.59, 0.78, z c = 9.62.…”

“…For x 1, z c grows with ξ, but it is T -independent [9]. Furthermore, a mild extrapolation from z c (ξ = 12 a 0 ) to z c (ξ = 38 a 0 ) [9] is compatible with the thin-film value z c = 9.62 [7] (the film width was ∼ 38 a 0 ). For x 1, the ξ-independent z c (T = T c ) = 6.69±0.06 [9] agrees with the CuMn result at T = 0.95T c , z c = 6.80 [8].…”

Effect of magnetic fields on spin glass dynamics

“…The introduction of a protocol different from conventional measurements of M ZFC (t, T ) is a consequence of the time dependence of the field cooled magnetization, M FC (t, T ), for mesoscale CuMn films. Whereas in bulk, M F C (t, T ) varies little, and if anything, slightly diminishes with increasing measurement time 23 , at mesoscale, it increases rather substantially with increasing measurement time 17 . We believe this is a consequence of glassy dynamics.…”

“…The sample preparation and experimental protocol will be described in Section III. The latter will be different from that used in our previous investigation 6,17 , because the field-cooled magnetization in CuMn thin films is time dependent, as noted in previous work 18 , complicating the extraction of the irreversible magnetization. The experimental results will be presented in Section IV, and their analysis in Section V. Section VI contains the summary and conclusions, and Section VII the acknowledgments.…”

“…As shown previously, irreversibility sets in below a freezing temperature, T f , for thin film spin glasses well below the bulk spin glass transition temperature T g . As shown in 17 , this is because of a largest barrier height ∆ max (L) in mesoscopic spin glasses. A finite experimental time scale, τ exp sets T f by the relationship,…”