Many dense magnetic nanoparticle systems exhibit slow dynamics which is qualitatively indistinguishable from that observed in atomic spin glasses and its origin is attributed to dipole interactions among particle moments (or superspins). However, even in dilute nanoparticle systems where the dipole interactions are vanishingly small, slow dynamics is observed and is attributed solely to a broad distribution of relaxation times which in turn comes from that of the anisotropy energy barriers. To clarify characteristic differences between the two types of slow dynamics, we study a simple model of a non-interacting nanoparticle system (a superparamagnet) analytically as well as ferritin (a superparamagnet) and a dense Fe-N nanoparticle system (a superspin glass) experimentally. It is found that superparamagnets in fact show aging (a waiting time dependence) of the thermoremanent-magnetization as well as various memory effects. We also find some dynamical phenomena peculiar only to superspin glasses such as the flatness of the field-cooled magnetization below the critical temperature and memory effects in the zero-field-cooled magnetization. These dynamical phenomena are qualitatively reproduced by the random energy model, and are well interpreted by the so-called droplet theory in the field of the spin-glass study.

Jönsson, Yoshino, and Nordblad Reply: In their Comment to our work [1], Berthier and Bouchaud [2] report results of temperature shifts T in a numerical simulation of a four-dimensional Edwards-Anderson Ising spin-glass model using the same thermal protocol as in [1]. Their scaling analysis yields an apparently similar result to ours.In our experiments the data are limited to a narrow temperature region jTj < 0:02 T g . The expected saturation of L eff to the overlap length L T [3] is not observed for these small values of jTj. In this Reply, we instead point out that our experimental results can be understood in terms of temperature chaos as partial rejuvenation in a weakly perturbed regime.Within the droplet theory [3], it is assumed that there are dangerously irrelevant droplets whose free-energy gaps F L are arbitrarily small. The gap can be smaller than dF with probability 0dF=L=L 0 , wherẽ 0 > 0. Consequently, a perturbation which amounts to a small free-energy gain of order UL=L 0 can induce a droplet excitation with a probability pL=L U 0L=L U . Here L U L 0 U= ÿ1= is the overlap length with the chaos exponent ÿ . In the case of T shifts, U k B jTj and d s =2, where d s is the surface fractal dimension of the droplets. Importantly, the probability pL=L U is nonzero in the weakly perturbed regime L < L U and increases with L if > 0 smoothly connecting to the strongly perturbedSupposing that L T > L T i t w , all length scales smaller than the domain size L T i t w belong to the weakly perturbed regime. A finite region of size L within a domain can then become out of equilibrium with the probability pL=L T . This reflects the breaking up of domains into smaller ones, yielding a broad distribution of domain sizes up to the maximum L max L T i t w . Then a simple scaling argument gives that the effective domain size surrounding an arbitrary point of the system on average reaches L eff L T FL max =L T with Fx x ÿ cx 1 . Here the second term in Fx, with c being a positive constant, yields a correction term, which is the first order of 0U= to the no-chaos limit of L eff . Higher order terms can be neglected for small enough jTj. It can be seen in Fig. 1 that the ansatz fits our data for jTj & 0:4 K.In the simulations of Berthier-Bouchaud [2], length scales L & 5 are probed while L T * 20. In [5] the spatial correlation function is found to decay to 0 only after L T i t w , being consistent with L max L T i t w . Then the rejuvenation found in [2] can be understood as partial rejuvenation due to the temperature chaos effect in a weakly perturbed regime. We note that emergence of the temperature chaos effect has been confirmed in the same model as in [2] with modest system sizes [6]. Indeed, we have found that the ansatz proposed above also fits the result of Berthier-Bouchaud [2] very well with c 0:15 and 1. However, the largest T shifts used in [2] involve temperatures in the range 0:8-0:9T g , within which numerical (but not experimental) length/ time scales are dominated by critical fluctuations as shown by Fig...

Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetisation. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetisations on re-heating, it is found that the measured curves effectively disclose non-equilibrium spin glass characteristics such as ageing and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this "simple" dc-method is discussed, as well as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure

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Effects of dipole-dipole interactions on the magnetic relaxation have been investigated for three Fe-C nanoparticle samples with volume concentrations of 0.06, 5 and 17 vol%. While both the 5 and 17 vol% samples exhibit collective behaviour due to dipolar interactions, only the 17 vol% sample displays critical behaviour close to its transition temperature. The behaviour of the 5 vol% sample can be attributed to a mixture of collective and single-particle dynamics.