The growth of the spin-glass correlation length has been measured as a function of the waiting time tw on a single crystal of CuMn (6 at.%), reaching values ξ ∼ 150 nm, larger than any other glassy correlation-length measured to date. We find an aging rate d ln tw/d ln ξ larger than found in previous measurements, which evinces a dynamic slowing-down as ξ grows. Our measured aging rate is compared with simulation results by the Janus collaboration. After critical effects are taken into account, we find excellent agreement with the Janus data.
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.
We investigate the quantum dynamics of number fluctuations inside an atomic condensate during coherent spin mixing among internal states of the ground state hyperfine manifold, by quantizing the semiclassical nonrigid pendulum model in terms of the conjugate variable pair: the relative phase and the atom number. Our result provides a theoretical basis that resolves the resolution limit, or the effective "shot-noise" level, for counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.
The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.
The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spinglass transition temperature T g . The spin-glass correlation length, ξ(t, t w ; T ), is analysed both in experiments and in simulations in terms of the waiting time t w after the spin glass has been cooled down to a stabilised measuring temperature T < T g and of the time t after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The nonlinear magnetic susceptibility is reported from experiment and simulations, using ξ(t, t w ; T ) as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, M ZFC (t, t w ; T ), is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line in D = 3 is discussed.
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