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The extended principle of superposition has been a touchstone of spin glass dynamics for almost thirty years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields $H$ up to 10 Oe at the reduced temperature $T_\mathrm{r}=T/T_\mathrm{g} = 0.95$, where $T_\mathrm{g}$ is the spin glass condensation temperature. For $H > 10$ Oe, they observe a departure from linear response which they ascribe to the development of non-linear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin glass correlation length, $\xi(t,t_\mathrm{w};H)$. Here, $t$ is the time after $H$ changes, and $t_\mathrm{w}$ is the time from the quench for $T>T_\mathrm{g}$ to the working temperature $T$ until $H$ changes. We connect the growth of $\xi(t,t_\mathrm{w};H)$ to the barrier heights $\Delta(t_\mathrm{w})$ that set the dynamics. The effect of $H$ on the magnitude of $\Delta(t_\mathrm{w})$ is responsible for affecting differently the two dynamical protocols associated with turning $H$ off (TRM, or thermoremanent magnetization) or on (ZFC, or zero field-cooled magnetization). In this paper, we display the difference between the zero-field cooled $\xi_{\text {ZFC}}(t,t_\mathrm{w};H)$ and the thermoremanent magnetization $\xi_{\text {TRM}}(t,t_\mathrm{w};H)$ correlation lengths as $H$ increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group., Comment: 23 pages and 18 figures

The growth of the spin-glass correlation length has been measured as a function of the waiting time $t_{\mathrm{w}}$ on a single crystal of CuMn (6 at.\%), reaching values $\xi\sim 150$ nm, larger than any other glassy correlation-length measured to date. We find an aging rate $\mathrm{d}\ln\,t_{\mathrm{w}}/\mathrm{d}\ln\,\xi$ larger than found in previous measurements, which evinces a dynamic slowing-down as $\xi$ 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., Comment: Version accepted in PRB (see https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.094202)

We report the effect of varying cobalt thickness on the temperature-dependent time decay of the electrical resistance of Co/Sb multilayer samples. We find that for a given temperature, a five fold change in the Co thickness produces a 100 fold change in the characteristic decay time of the resistance. We find that the characteristic decay time, as a function of temperature, follows an Arrhenius law. During deposition, the Co evolves single domain magnetic nanoparticles, on the Sb, in either a Volmer-Weber or Stranski-Krastanov growth mode. This metastable state is then encased in 2.5 nm of Sb producing an embedded nanoparticle system. Scanning Tunneling Microscopy (STM) measurements taken before sample aging (annealing at a given temperature for enough time to complete the resistance decay) and after aging show that these nanoparticles undergo morphological transformations during aging. These transformations lead to well defined time dependent decays in both the magnetization and the electrical resistance, making this material an excellent candidate for an electronic time-temperature sensor., Comment: 9 pages, 10 figures

Using a series of fast cooling protocols we have probed aging effects in the spin glass state as a function of temperature. Analyzing the logarithmic decay found at very long time scales within a simple phenomenological barrier model, leads to the extraction of the fluctuation time scale of the system at a particular temperature. This is the smallest dynamical time-scale, defining a lower-cut off in a hierarchical description of the dynamics. We find that this fluctuation time scale, which is approximately equal to atomic spin fluctuation time scales near the transition temperature, follows ageneralized Arrhenius law. We discuss the hypothesisthat, upon cooling to a measuring temperature within the spin glass state, there is a range of dynamically in-equivalent configurations in which the system can be trapped, and check within a numerical barrier model simulation, that this leads to sub-aging behavior in scaling aged TRM decay curves, as recently discussed theoretically, see arXiv:0902.3556 ., Comment: 10 pages, 4 figures

A novel method for analyzing the intermittent behavior of linear response data in aging systems is presented and applied to spin-glass thermoremanent magnetization (TRM) (Rodriguez et al. Phys. Rev. Lett. 91, 037203, 2003). The probability density function (PDF) of magnetic fluctuations is shown to have an asymmetric exponential tail, demonstrating that the demagnetization process is carried by intermittent, significant, spin rearrangements or \emph{quakes}. These quakes are most pronounced shortly after the field removal, $t/t_w \approx 1$ and in the non-equilibrium aging regime $t/t_w >>1$. For a broad temperature range, we study the dependence of the TRM decay rate on $t$, the time since the initial quench and on $t_w$, the time at which the magnetic field is cut. The $t$ and $t_w$ dependence of the rate is extracted numerically from the data and described analytically using the assumption that the linear response is subordinated to the intermittent process which spasmodically release the initial imbalances created by the quench., Comment: 8 pages, 9 figures. The paper has been expanded and restructured, the figures have been enlarged and improved. Final version, to appear in Phy. Rev. B

It is currently believed that the decay of the thermoremanent magnetization in spin glasses is composed of two terms; The "stationary" term which does not depend on the sample history and dominates the short time decay ($<1s$) and a long time aging term which depends on the samples history. The sample history includes both the thermal history and the time spent in a magnetic field (waiting time) before that field is removed. We report finding a third component of the decay at times much larger than the waiting time. This decay is independent of the waiting time, but part of the same mechanism that produces aging. We explain this decay in terms of the initial state distribution that is developed during the cooling process. This explanation is tested by performing Iso-thermoremanent magnetization decay measurements. Follow up calculations using the Spin Glass phase space barrier model suggest that the long time decay is logarithmic and that the maximum aging time is approximately three thousand years, in this sample, at a measuring temperature of .83 $T_{g}$., Comment: 5 pages, 4 figures

The recent demonstration that nanoparticles associated with various biological molecules and pharmacological agents can be administered systemically to humans, without toxicity from the particles, has opened a new era in the targeting of such particles to specific tissues in the body for the imaging and therapy of disease. The majority of particles used for this purpose contain iron and are detected in the body by magnetic resonance imaging. We believe a superconducting quantum interference device (SQUID) could provide quantitative and spatial information relevant to localization of superparamagnetic nanoparticles directed to a specific cell target in vivo. We envision a scanning system consisting of a DC induction field, a transport device, and an array of planar first order gradiometer coils coupled to DC SQUID amplifiers. We performed a set of computer simulations using experimentally determined values for concentrations of paramagnetic particles achievable in specific tissues of the mouse in vivo and concentrations of particles linked to monoclonal antibodies specific to antigens of two human cancer cell lines in vitro. An instrument to target distance of 10 centimeters was selected so that for an average adult scanning both the anterior and posterior surfaces could provide coverage of most of the body. The simulations demonstrate the feasibility of SQUID magnetometry for monitoring achievable concentrations of superparamagnetic particles in vivo and raise the possibility of using this approach to detect and localize collections of abnormal cells targeted by such particles., Comment: 29 pages, 11 figures,19 references

The discovery of memory effects in the magnetization decays of spin glasses in 1983 began a large effort to determine the exact nature of the decay. While qualitative arguments have suggested that the decay functions should scale as $t_{w}$, the only time scale in the system, this type of scaling has not yet been observed. In this letter we report strong evidence for the scaling of the TRM magnetization decays as a function of $t_{w}$. By varying the rate and the profile that the sample is cooled through its transition temperature to the measuring temperature, we find that the cooling plays a major role in determining scaling. As the effective cooling time decreases, $\frac {t}{t_{w}}$scaling improves and for $t_{c}^{eff}<20s$ we find almost perfect $\frac{t}{t_{w}}$ scaling. We also find that subtraction of a stationary term from the magnetization decay has a small effect on the scaling but changes the form of the magnetization decay and improves overlap between curves produced with different $t_{w}$., Comment: 4 pages, 3 figures