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The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green’s function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

Only a few four-coordinated Co 2+-complexes show single-molecule magnet (SMM) properties without an applied dc field. Common for those is a large magnetic anisotropy generated by the close proximity of the (Formula presented.) and (Formula presented.) orbitals. This type of magnetic anisotropy is strongly correlated with the extent of structural distortion from ideal tetrahedral towards linear coordination. Quantification of the governing magneto-structural correlations is hence crucial for the development of better SMMs. For this purpose, we synthesized and analyzed four significantly distorted tetrahedral cobalt complexes that exhibit extremely large magnetic anisotropies and slow relaxation of magnetization in zero field. The N−Co−N bite angles vary from 70.8 to 72.7°, and magnetic measurements show strong anisotropy with D-values in the range from (Formula presented.) 75 to (Formula presented.) 114 cm −1. Ab initio calculations supported the experimental results and highlighted a significant increase of D up to (Formula presented.) 141 cm −1, correlated with the reduction of the energy difference between the (Formula presented.) and (Formula presented.) orbitals. Based on these magneto-structural correlations and in contrast to the current assumption that the smaller bite angle is the better, we predict that with an ideal bite angle in the range from 76–78° in distorted Co(N 2R) 2 complexes, the energy difference between the two important d-orbitals is at a minimum and hence the magnetic anisotropy is maximized.

A mononuclear Co(II) complex of a Schiff base ligand derived from 5-Bromo-vanillin and 4-aminoantipyrine, that has a compressed tetragonal bipyramidal geometry and exhibiting field-induced slow magnetic relaxation, has been synthesized and characterized by single crystal X-ray diffraction, elemental analysis and molecular spectroscopy. In the crystal packing, a hydrogen-bonded dimer structural topology has been observed with two distinct metal centers having slightly different bond parameters. The complex has been further investigated for its magnetic nature on a SQUID magnetometer. The DC magnetic data confirm that the complex behaves as a typical S = 3/2 spin system with a sizable axial zero-field splitting parameter D/hc = 38 cm−1. The AC susceptibility data reveal that the relaxation time for the single-mode relaxation process is τ = 0.16(1) ms at T = 2.0 K and BDC = 0.12 T.

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal., 26 pages, 10 figures

The development of methyl transverse relaxation optimized spectroscopy has greatly facilitated the study of macromolecular assemblies by solution NMR spectroscopy. However, limited sample solubility and stability has hindered application of this technique to ongoing studies of complexes formed on membranes by the neuronal SNAREs that mediate neurotransmitter release and synaptotagmin-1, the Ca2+ sensor that triggers release. Since the 1H NMR signal of a tBu group attached to a large protein or complex can be observed with high sensitivity if the group retains high mobility, we have explored the use of this strategy to analyze presynaptic complexes involved in neurotransmitter release. For this purpose, we attached tBu groups at single cysteines of fragments of synaptotagmin-1, complexin-1 and the neuronal SNAREs by reaction with 5-(tert-butyldisulfaneyl)-2-nitrobenzoic acid (BDSNB), tBu iodoacetamide or tBu acrylate. The tBu resonances of the tagged proteins were generally sharp and intense, although tBu groups attached with BDSNB had a tendency to exhibit somewhat broader resonances that likely result because of the shorter linkage between the tBu and the tagged cysteine. Incorporation of the tagged proteins into complexes on nanodiscs led to severe broadening of the tBu resonances in some cases. However, sharp tBu resonances could readily be observed for some complexes of more than 200 kDa at low micromolar concentrations. Our results show that tagging of proteins with tBu groups provides a powerful approach to study large biomolecular assemblies of limited stability and/or solubility that may be applicable even at nanomolar concentrations., We thank Ad Bax for the suggestion of exploring the use tBu groups as probes for structural studies of the neurotransmitter release machinery, and Ad Bax, Lewis Kay and Charampalos Kalodimos for fruitful discussions on this subject. The Agilent DD2 console of the 800 MHz spectromenter used for the research presented here was purchased with a shared instrumentation grant from the NIH (S10OD018027 to JR). Rashmi Voleti was supported by a fellowship from the Howard Hughes Medical Institute. The preparation of BDSNB was performed at the NANBIOSIS –CIBER BBN Peptide Synthesis Unit (U3). This work was supported by grant I-1304 from the Welch Foundation (to JR) and by NIH Research Project Award R35 NS097333 (to JR).

We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions, well thermalized at temperature $T_{in}$. In large systems, the dynamics strictly agrees with the integration of the mean-field dynamical equations. In particular, we confirm the existence of an onset initial temperature, within the liquid phase, below which the energy of the inherent structures undoubtedly depends on $T_{in}$. This behavior is in contrast with that of pure models, where there is a 'threshold energy' that attracts all the initial configurations in the liquid. Our results strengthen the analogy between mean-field spin glass models and supercooled liquids., 15 pages, 8 figures

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached both with thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids., Comment: 10 pages, 6 figures

The Discrete Nonlinear Schr\"odinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019 Physical Review Letters 122 084102], it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is "forced" by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with L\'evy processes., Comment: 23 pages. Abstract and Introduction fully rewritten, also other minor changes

Generalized mode-coupling theory (GMCT) is a first-principles-based and systematically correctable framework to predict the complex relaxation dynamics of glass-forming materials. The formal theory amounts to a hierarchy of infinitely many coupled integro-differential equations, which may be approximated using a suitable finite-order closure relation. Although previous studies have suggested that finite-order GMCT leads to well-defined solutions, and that the hierarchy converges as the closure level increases, no rigorous and general result in this direction is known. Here we unambiguously establish the existence and uniqueness of solutions to generic, schematic GMCT hierarchies that are closed at arbitrary order. We consider two types of commonly invoked closure approximations, namely mean-field and exponential closures. We also distinguish explicitly between overdamped and underdamped glassy dynamics, corresponding to hierarchies of first-order and second-order integro-differential equations, respectively. We find that truncated GMCT hierarchies closed under an exponential closure conform to previously developed mathematical theories, such that the existence of a unique solution can be readily inferred. Self-consistent mean-field closures, however, of which the well-known standard-MCT closure approximation is a special case, warrant additional arguments for mathematical rigour. We demonstrate that the existence of a priori bounds on the solution is sufficient to also prove that unique solutions exist for such self-consistent hierarchies. To complete our analysis, we present simple arguments to show that these a priori bounds must exist, motivated by the physical interpretation of the GMCT solutions as density correlation functions. Overall, our work contributes to the theoretical justification of GMCT for studies of the glass transition, placing GMCT on a firmer mathematical footing., Comment: 7 pages Revised version that contains minor changes and, in Sec. V, a revised argument. The former Sec. VI was suppressed and replaced by a more stringent bound derived now in Sec. V

In this work we review the Co2 IIILn2 III family of compounds reported up to date that shows SMM features. The vast majority of them show a butterfly arrangement with LnIII ions placed at the body positions. The number of DyIII examples constitutes the majority, probably because of the intrinsic properties of this lanthanide ion regarding SMMs characteristics. Butterfly complexes have a SAP geometry around LnIII ions with a variety of distortion degrees. However, when looking at the key Ueff parameter trend through this family of complexes, it becomes clear that a pure geometrical consideration is not enough to explain it. Ab initio based calculations provide evidence of highly anisotropic mJ ground states for complexes where LnIII = DyIII, pointing to exclusively mJ = 15/2 ground Kramers doublets. These calculations also agree with the thermally activated relaxation involving the first excited state and, in some examples where multiple relaxation pathways are observed, higher excited states. A few examples prove that Raman and/or direct mechanisms cannot be discarded a priori. Only two examples of isostructural LnIII families of the same Co2 IIILn2 III complex can be found. Fil: Funes, Víctor Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Inorgánica, Analítica y Química Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentina Fil: Alborés, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Inorgánica, Analítica y Química Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentina

Herein we report a dinuclear [(μ-mbpymNO)- {(tmh)3Dy}2] (1) single-molecule magnet (SMM) showing two nonequivalent DyIII centers, which was rationally prepared from the reaction of Dy(tmh)3 moieties (tmh = 2,2,6,6-tetramethyl-3,5- heptanedionate) and the asymmetric bis-bidentate bridging ligand 4-methylbipyrimidine (mbpymNO). Depending on whether the DyIII ions coordinate to the N^O or N^N bidentate donor sets, the DyIII sites present a NO7 (D2d geometry) or N2O6 (D4d) coordination sphere. As a consequence, two different thermally activated magnetic relaxation processes are observed with anisotropy barriers of 47.8 and 54.7 K. Ab initio calculations confirm the existence of two different relaxation phenomena and allow one to assign the 47.8 and 54.7 K energy barriers to the Dy(N2O6) and Dy(NO7) sites, respectively. Two mononuclear complexes, [Dy(tta)3(mbpymNO)] (2) and [Dy(tmh)3(phenNO)] (3), have also been prepared for comparative purposes. In both cases, the DyIII center shows a NO7 coordination sphere and SMM behavior is observed with Ueff values of 71.5 K (2) and 120.7 K (3). In all three cases, ab initio calculations indicate that relaxation of the magnetization takes place mainly via the first excited-state Kramers doublet through Orbach, Raman, and thermally assisted quantum-tunnelling mechanisms. Pulse magnetization measurements reveal that the dinuclear and mononuclear complexes exhibit hysteresis loops with double- and single-step structures, respectively, thus supporting their SMM behavior.

Four complexes containing Dy-III and Pr-III ions and their Ln(III)-Zn-II analogs have been synthesized in order to study the influence that a diamagnetic Zn-II ion has on the electronic structure and hence, the magnetic properties of the Dy-III and Pr-III single ions. Single-crystal X-ray diffraction revealed the molecular structures as [Dy-III(HL)(2)(NO3)(3)] (1), [Pr-III(HL)(2)(NO3)(3)] (2), [(ZnDyIII)-Dy-II(L)(2)(CH3CO2)(NO3)(2)] (3) and [(Zn2PrIII)-Pr-II(L)(2)(CH3CO2)(4)(NO3)] (4) (where HL=2-methoxy-6-[(E)-phenyliminomethyl]phenol). The dc and ac magnetic data were collected for all four complexes. Compounds 1 and 3 display frequency dependent out-of-phase susceptibility signals ((M)), which is a characteristic signature for a single-molecule magnet (SMM). Although 1 and 3 are chemically similar, a fivefold increase in the anisotropic barrier (U-eff) is observed experimentally for 3 (83cm(-1)), compared to 1 (16cm(-1)). To rationalize the larger anisotropic barrier (1 vs. 3), detailed ab initio calculations were performed. Although the ground state Kramer's doublet in both 1 and 3 are axial in nature (g(zz)=19.443 for 1 and 18.82 for 3), a significant difference in the energy gap (U-eff) between the ground and first excited Kramer's doublet is calculated. This energy gap is governed by the electrostatic repulsion between the Dy-III ion and the additional charge density found for the phenoxo bridging ligand in 3. This extra charge density was found to be a consequence of the presence of the diamagnetic Zn-II ion present in the complex. To explore the influence of diamagnetic ions on the magnetic properties further, previously reported and structurally related Zn-Dy-III complexes were analyzed. These structurally analogous complexes unambiguously suggest that the electrostatic repulsion is found to be maximal when the Zn-O-Dy-O dihedral angle is small, which is an ideal condition to maximize the anisotropic barrier in Dy-III complexes.

The electrocapillarity and zero-frequency differential capacitance, Cd, have been studied using pendant drop method, at the Hg interface of an ionic liquid (IL), 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide, [C2mim+][TFSA−], and have been compared with those of [C2mim+]BF 4 − , an IL with the common cation and a different anion, to focus on the anion dependence of zero-frequency Cd. The Hg interface of [C2mim+][TFSA−], the IL of the larger anion in the present study, exhibits greater zero-frequency Cd than that of [C2mim+]BF 4 − , the IL of the smaller anion. This behavior contradicts a simple expectation in which larger ion leads to smaller Cd. This apparent contradiction is explained by proximity of the charged moiety of TFSA− to the electrode surface compared with that of BF 4 − . The potential dependence of zero-frequency Cd for the two ILs both exhibits one-hump camel shape around the potential of zero charge (Epzc), which has been predicted to be specific behavior of the electrical double layer of ILs by theory and simulation. The humps are located at potentials more negative than Epzc. From a mean-field lattice-gas theory for the EDL in ILs, this negative shift can be interpreted that the charged moiety for C2mim+ is more easily condensed in the EDL than those for BF 4 − and TFSA−.

We introduce a kinetically constrained spin model with a local softness parameter, such that spin flips can violate the kinetic constraint with an (annealed) site-dependent rate. We show that adding MC swap moves to this model can dramatically accelerate structural relaxation. We discuss the connection of this observation with the fact that swap moves are also able to accelerate relaxation in structural glasses. We analyse the rates of relaxation in the model. We also show that the extent of dynamical heterogeneity is strongly suppressed by the swap moves., Comment: 20 pages, accepted version

We study the evolution of the maximum energy $E_\max(t)$ reached between time $0$ and time $t$ in the dynamics of simple models with glassy energy landscapes, in instant quenches from infinite temperature to a target temperature $T$. Through a detailed description of the activated dynamics, we are able to describe the evolution of $E_\max(t)$ from short times, through the aging regime, until after equilibrium is reached, thus providing a detailed description of the long-time dynamics. Finally, we compare our findings with numerical simulations of the $p$-spin glass and show how the maximum energy record can be used to identify the threshold energy in this model., 22 pages, 5 figures; revised presentation

Molecular materials, and in particular those based on Lanthanides, have been extensively studied for their use in data storage, spintronics and quantum computing, as they promise high anisotropic systems and magnetic bistability of the discrete entity. Actually, in Athe last twenty-five years a plethora of compounds have been reported, thus showing slow of their magnetic relaxation and the characteristic magnetic hysteresis at low temperature. Moreover, some of the last investigations have reach blocking temperatures (temperature for which the system shows superparamagnetic behavior) at the liquid nitrogen level, hence facilitating the applicability of devices based on these molecules. However, the slow relaxation is commonly accompanied by quantum phenomena, favoring a fasten relaxation. The quantum effects open the possibility to different magnetic objects, but only if the operating mechanisms are well known. Dipolar interactions, with the neighboring molecules, and hyperfine interactions, with the metal ion, are known to be some of the reasons why this fast relaxations occurs. With the aim of acquiring a better understanding of the quantum events, and the contribution of the different interactions, different systems have been chosen to be studied in this work. Thus, the synthesis and magnetic characterization of magnetically diluted (suppression of dipolar interactions) and isotopic enrichment (tuning of the hyperfine interactions) of the different systems have been performed in order to find a general direction for the optimization of the slow relaxation process., Les matériaux moléculaires, et plus précisément ceux à base d’ions lanthanides, ont été largement étudiés pour leur utilisation dans différentes applications, dont le stockage de l’information ou l’ordinateur quantique. Cet intérêt s’explique du fait que des systèmes contenant des ions lanthanides donnent lieu à une large anisotropie et une bistabilité magnétiques d‘origine purement moléculaire. Durant les vingt-cinq dernières années, beaucoup d’articles ont été publiés dans lesquels les composés à base de ces ions montraient une relaxation lente de leur aimantation et une hystérèse magnétique à basse température. Récemment, des recherches ont menées à l’obtention de systèmes moléculaires présentant des températures de blocage (température maximale à laquelle le système se comporte comme à superparamagnétique) proche de l’azote liquide ce qui facilite le transfert dans des dispositifs basés sur ces systèmes.Cependant, cette relaxation lente de l’aimantation est souvent accompagnée des phénomènes quantiques, donnant lieu à d’autres relaxations beaucoup plus rapides. Les phénomènes quantiques peuvent donner lieu à de nouvelles applications mais à condition de bien comprendre leurs mécanismes d’action. Les interactions dipolaires et les hyperfines, les premiers provenant des molécules voisines et la deuxième de l’interaction spin-noyau dans le métal, sont connus pour participer à l’origine de ces phénomènes. Quelques systèmes ont été choisis durant ce travail de thèse dans le but de mieux comprendre les évènements quantiques et la contribution des différentes interactions. Ceci a mené à la synthèse et aux caractérisations magnétiques de différents systèmes magnétiquement dilués (étude des interactions dipolaires) et isotopiquement enrichis (étude des interactions hyperfines), afin de mettre en évidence une tendance générale pour l’optimisation des processus de relaxation lente.

Colloidal suspensions have long been studied as a model for atomic and molecular systems, due to the ability to fluorescently label and individually track each particle, yielding particle-resolved structural information. This allows various local order parameters to be probed that are otherwise inaccessible for a comparable molecular system. For phase transitions such as crystallisation, appropriate order parameters which emphasise 6-fold symmetry are a natural choice, but for vitrification the choice of order parameter is less clear cut. Previous work has highlighted the importance of icosahedral local structure as the glass transition is approached. However, counting icosahedra or related motifs is not a continuous order parameter in the same way as, for example, the bond-orientational order parameters $Q_{6}$ and $W_6$. In this work we investigate the suitability of using pentagonal bipyramid membership, a structure which can be assembled into larger, five-fold symmetric structures, as a finer order parameter to investigate the glass transition. We explore various structural and dynamic properties and show that this new approach produces many of the same findings as simple icosahedral membership, but we also find that large instantaneous displacements are often correlated with significant changes in pentagonal bipyramid membership, and unlike the population of defective icosahedra, the pentagonal bypyramid membership and spindle number do not saturate for any measured volume fraction, but continues to increase., Comment: accepted by JStat Mech: Theory and Experiment 2019

Controlling quantum tunneling of magnetization (QTM) is a persistent challenge in lanthanide-based single-molecule magnets. As the exchange interaction is one of the key factors in controlling the QTM, we targeted lanthanide complexes with an increased number of radicals around the lanthanide ion. On the basis of our targeted approach, a family of pseudo-octahedral lanthanide/transition-metal complexes were isolated with the general molecular formula of [M(L-center dot(-))(3)] (M = Gd (1), Dy (2), Er (3), Y (4)) using the redox-active iminopyridyl (L-center dot(-)) ligand exclusively, which possess the highest ratio of radicals to lanthanide reported for discrete metal complexes. Direct current magnetic susceptibility studies suggest that dominant antiferromagnetic interactions exist between the radical and lanthanide ions in all of the complexes, which is strongly corroborated by magnetic data fitting using a Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian (-2J Hamiltonian). A good agreement between the fit and the experimental magnetic data obtained using g = 2, J(rad-rad) = -111.9 cm(-1) for 4 and g = 1.99, J(rad-rad) = -111.9 cm(-1), J(Gd-rad) = -1.85 cm(-1) for 1. Complex 2 shows frequency-dependent slow magnetization relaxation dynamics in the absence of an external magnetic field, while 3 shows field-induced frequency-dependent X-M" signals. An ideal octahedral geometry around the lanthanide ion is predicted to be unsuitable for the design of a single-molecule magnet (SMM); nevertheless, complex 2 exhibits slow relaxation of magnetization with a record high anisotropy barrier for a six-coordinate Dy(III) complex. A rationale for this unusual behavior is detailed and reveals the strength of the synthetic methodology developed.

We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses by means of the study of correlations between different chaos indicators computed in the static and the correlation times of the Parallel Tempering dynamics. The sample-distribution of the characteristic time for the Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size scaling., Comment: New appendix added. Version to appear in JSTAT

The present report deals with the syntheses, crystal structures, dc/ac magnetic properties and DFT/ab initio CASSCF calculations of two isomorphous bis((1):(2):(2)-acetate)GdIII2/DyIII2 compounds of the formula [LnIII2L(2)(acetate)(4)(MeOH)(2)] (1, Ln = Gd; 2, Ln = Dy), where HL is (E)-N-(3-ethoxysalicylidene)acetohydrazide. The two lanthanide(iii) centres in each compound are symmetry-related owing to the presence of an inversion centre. Both compounds exhibit intramolecular ferromagnetic exchange interactions. The DyIII2 analogue is a single-molecule magnet (SMM) with U-eff = 52.8 cm(-1) and (0) = 1.52 x 10(-6) s. DFT calculations for 1 and ab initio calculations for 2 also reveal ferromagnetic interactions. Ab initio calculations of the SMM behaviour of 2 and two other reported and structurally related compounds reveal the importance of the weak exchange interaction present between the two Dy-III ions, and a relaxation mechanism has been developed to take into account the magnetic exchange interaction and to rationalize the observed difference in the U-eff values.

Ab initio CASSCF calculations have been undertaken to probe the origin of magnetic anisotropy in two structurally related {(DyN8)-N-III} SIMs {[Dy(tmtaa)(2)](-) and [K(DME)(2)][Dy(tmtaa)(2)]; 1 and 2, respectively}. Our calculations reveal that complex 1 possesses a larger barrier for reorientation of magnetization (U-cal) than does 2. This is essentially due to the intrusion of K+ ions, which distort the geometry and the donor abilities of the ligands in complex 2, compared with 1. Moreover, the ligand field around Dy-III was found to stabilize |m(J)> = |+/- 13/2> as the ground state, with stronger mixing by other |m(J)> levels. This corresponds to the observation of large g(xx) and g(yy) values at the ground state, leading to an efficient QTM process and very fast relaxation. The computed ground-state |m(J)> levels and the estimated g tensors for both complexes are in agreement with experimental results obtained from magnetic and EPR spectroscopic studies. In addition, we have developed various magneto-structural correlations for complexes 1 and 2, in order to understand how small structural distortions are likely to influence the magnetic anisotropy. These correlations offer clues to enhancing the barrier height for magnetization reversal in {(DyN8)-N-III} complexes.

Chiral bipyrimidine-bridged dinuclear LnIII complexes of general formula [(μ-bipym){((+)-tfacam)3Ln}2] and [(μ-bipym){((-)-tfacam)3Ln}2], have been prepared from the assembly of Ln(AcO)3·nH2O (LnIII = Dy, Gd), (+)/(−)-3-(trifluoroacetyl)camphor enantiopure ligands ((+)/(-)-Htfacam) and bipyrimidine (bipym). The structure and chirality of these complexes have been supported by single-crystal X-Ray diffraction and circular dichroism. The study of the magnetic properties of the GdIII complexes revealed a very weak antiferromagnetic interaction between the GdIII ions through the bipyrimidine bridging ligand. Ab initio CASSCF calculations indicated that the ground Kramers doublet (KD) of both DyIII centers is almost purely axial with the anisotropy axis located close to the two tfacam−ligands at opposite sides of each DyIIIatom, which create an axial crystal field. In keeping with this, ac dynamic measurements indicated slow relaxation of the magnetization at zero field with Ueff = 55.1 K, a pre-exponential factor of τo = 2.17·10−6 s and τQTM = 8 μs. When an optimal dc field of 0.1 T is applied, QTM is quenched and Ueff increases to 75.9 K with τo = 6.16 × 10−7 s. The DyN2O8 coordination spheres and SMM properties of [(μ-bipym){((+)-tfacam)3Ln}2] and their achiral [(Dy(b-diketonate)3)2(μ-bpym)]analogous have been compared and a magneto-structural correlation has been established, which has been supported by theoretical calculations., ID-O, JH, and EC are grateful to Ministerio de Economía y Competitividad (MINECO) for Project CTQ2014-56312-P, the Junta de Andalucía (FQM-195 and the Project of excellence P11-FQM-7756) and the University of Granada. A part of this work has been made at HFLSM, IMR, Tohoku University. IDO also acknowledges support by COLABS. GR would like to thank SERB (EMR/2014/000247) for financial support. SDthanks UGC for Senior Research Fellowship. AC thanks the Marie Curie COFUND Action from the European Commission for co-financing his postdoctoral fellowship.

We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second., 26 pages, 12 figures. Version accepted for publication in JSTAT

In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In this invited contribution, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. We also discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers, atoms trapped in optical cavities., Invited contribution to a special issue on the occasion of Abdus Salam's 90th birthday; v2: Refs. added

Four isostructural (Ni2Ln2(CH3CO2)3(HL)4(H2O)2) 3 + (Ln 3+ =Dy (1), Tb (2), Ho (3 )o r Lu (4)) complexes and a di- nuclear (NiGd(HL)2(NO3)3 )( 5) complex are reported (where HL = 2-methoxy-6-((E)-2'-hydroxymethyl-phenyliminometh- yl)-phenolate). For compounds 1-3 and 5, the Ni 2 + ions are ferromagnetically coupled to the respective lanthanide ions. The ferromagnetic coupling in 1 suppresses the quantum tunnelling of magnetisation (QTM), resulting in a rare zero dc field Ni-Dy single-molecule magnet, with an anisotropy barrier Ueff of 19 K. Following the remarkable observation of single-molecule magnet (SMM) behaviour within a (Mn12OAc) cluster, numerous transition-metal SMM complexes have subsequently been re- ported. (1) The interest stems from the many potential applica- tions, such as storage of digital information, molecular qubits, and spin valves. (2) The two parameters that govern the effec

Four low-coordinate SIMs have been studied to probe their relaxation dynamics using ab initio calculations. Our calculations reveal that both the symmetry and the equatorial ligand field play a key role in controlling the barrier heights in three-coordinate [Ln(III)(NSiMe3)(3)] complexes (Ln = Dy/Er). This study reveals an unprecedented blockade of magnetization up to three excited states for the Er(III) complex.

We establish the coordination potential of the Schiff base ligand (2-methoxy-6-[(E)-2'-hydroxymethyl-phenyliminomethyl]-phenolate (H2L)) via the isolation of various M(II)-Ln(III) complexes (where M(II) = Ni or Zn and Ln(III) = La or Pr or Gd). Single crystals of these five complexes were isolated and their solid state structures were determined by single crystal X-ray diffraction. Structural determination revealed molecular formulae of [NiGd(HL)(2)(NO3)(3)] (1), [NiPr(HL)(2)(NO3)(3)] (2) and [Ni2La(HL)(4)(NO3)](NO3)(2) (3), [Zn2Gd(HL)(4)(NO3)](NO3)(2) (4), and [Zn2Pr(HL)(4)(NO3)](NO3)(2) (5). Complexes 1 and 2 were found to be neutral heterometallic dinuclear compounds, whereas 3-5 were found to be linear heterometallic tri-nuclear cationic complexes. Direct current (dc) magnetic susceptibility and magnetization measurements conclusively revealed that complexes 1 and 4 possess a spin ground state of S = 9/2 and 7/2 respectively. Empirically calculated Delta T-chi M derived from the variable temperature susceptibility data for all complexes undoubtedly indicates that the Ni(II) ion is coupled ferromagnetically with the Gd(III) ion, and anti-ferromagnetically with the Pr(III) ion in 1 and 2 respectively. The extent of the exchange interaction for 1 was estimated by fitting the magnetic susceptibility data using the parameters (g = 2.028, S = 9/2, J = 1.31 cm(-1) and zJ = +0.007), supporting the phenomenon observed in an empirical approach. Similarly using a HDVV Hamiltonian, the magnetic data of 3 and 4 were fitted, yielding parameters g = 2.177, D = 3.133 cm(-1), J = -0.978 cm(-1), (for 3) and g = 1.985, D = 0.508 cm(-1) (for 4). The maximum change in magnetic entropy (-Delta S-m) estimated from the isothermal magnetization data for 1 was found to be 5.7 J kg(-1) K-1 (Delta B = 7 Tesla) at 7.0 K, which is larger than the -Delta S-m value extracted from 4 of 3.5 J kg(-1) K-1 (Delta B = 7 Tesla) at 15.8 K, revealing the importance of the exchange interaction in increasing the overall ground state of a molecule for better MCE efficiency.

We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different properties at short or long distances. Specifically, on lengthscales larger than the typical domains' size the topology is that of critical random percolation, similarly to what observed in clean systems or models with different kinds of quenched disorder. On smaller lengthscales a dilution dependent fractal dimension emerges. The Hausdorff dimension increases with increasing dilution $d$ up to the value $4/3$ expected at the bond percolation threshold $d=1/2$. We discuss how such different geometries develop on different lengthscales during the phase-ordering process and how their simultaneous presence determines the scaling properties of observable quantities., Comment: 15 pages, 9 figures

A family of mononuclear tetrahedral cobalt(II) thiourea complexes, [Co(L-1)(4)](NO3)(2) (1) and [Co(L-x)(4)](ClO4)(2) where x = 2 (2), 3 (3), 4 (4) (where L-1 = thiourea, L-2 = 1,3-dibutylthiourea, L-3 = 1,3-phenylethylthiourea, and L-4 = 1,1,3,3-tetramethylthiourea), has been synthesized using a rationally designed synthetic approach, with the aim of stabilizing an Ising-type magnetic anisotropy (-D). On the basis of direct-current, alternating-current, and hysteresis magnetic measurements and theoretical calculations, we have identified the factors that govern the sign and magnitude of D and ultimately the ability to design a single-ion magnet for a tetrahedral cobalt(II) ion. To better understand the magnetization relaxation dynamics, particularly for complexes 1 and 2, dilution experiments were performed using their diamagnetic analogues, which are characterized by single-crystal X-ray diffraction with the general molecular formulas of [Zn(L-1)(4)](NO3)(2) (5) and [Zn(L-2)(4)]-(ClO4)(2) (6). Interestingly, intermolecular interactions are shown to play a role in quenching the quantum tunneling of magnetization in zero field, as evidenced in the hysteresis loop of 1. Complex 2 exhibits the largest U-eff value of 62 cm(1) and reveals open hysteresis loops below 4 K. Furthermore, the influence of the hyperfine interaction on the magnetization relaxation dynamics is witnessed in the hysteresis loops, allowing us to determine the electron/nuclear spin S(Co) = 3/2/I(Co) = 7/2 hyperfine coupling constant of 550 MHz, a method ideally suited to determine the hyperfine coupling constant of highly anisotropic metal ions stabilized with large D value, which are otherwise hard to determine by conventional methods such as electron paramagnetic resonance.

The first supramolecular cage formed by three benzo-15-crown-5 macrocycles encapsulating a [Dy(OH2)(8)](3+) guest cation is reported, with the Dy(III) centre exhibiting local pseudo square antiprismatic D-4d symmetry. The anisotropy barrier extracted from ac susceptibility studies, emission spectroscopy and ab initio calculations reveals that the second excited state Kramers doublet plays a key role in the magnetization dynamics due to the Ising character and near coparallel nature of the ground and first excited Kramers doublets.

We investigate the relaxation dynamics of magnetic vortex lines in type-II superconductors following rapid changes of the external driving current by means of an elastic line model simulated with Langevin molecular dynamics. A system of flux vortices in a sample with randomly distributed point-like defects is subjected to an external current of appropriate strength for a sufficient period of time so as to be in a moving non-equilibrium steady state. The current is then instantaneously lowered to a value that pertains to either the moving or pinned regime. The ensuing relaxation of the flux lines is studied via one-time observables such as their mean velocity and radius of gyration. We have in addition measured the two-time flux line height autocorrelation function to investigate dynamical scaling and aging behavior in the system, which in particular emerge after quenches into the glassy pinned state., 16 pages, 5 figures

The monometallic pseudo-octahedral complex, [Co(H2O)2(CH3COO)2(C5H5N)2], is shown to exhibit slow magnetic relaxation under an applied field of 1500 Oe. The compound is examined bya combination of experimental and computational techniques in order to elucidate the nature of its electronic structure and slow magnetic relaxation. We demonstrate that any sensible model of the electronic structure must include a proper treatment of the first-order orbital angular momentum,and we find that the slow magnetic relaxation can be well described by a two-phonon Raman process dominating at high temperature, with a temperature independent quantum tunnelling pathway being most efficient at low temperature.

The reaction of hydrated nickel(II) salts (chloride or nitrate) and hydrated lanthanide nitrate salts with the Schiff base ligand 2-methoxy-6-[(E)-phenyliminomethyl] phenol (HL) in methanol resulted in the isolation of three isostructural linear heterometallic trinuclear complexes and a heterometallic tetranuclear complex. The molecular structures of these complexes were determined via single crystal X-ray diffraction revealing molecular structures of formulae [Ni2La(L-)(6)](NO3)(0.55)(OH)(0.45) (1), [Ni2Pr(L-)(6)]-(NO3)(0.48)(OH)(0.52) (2), [Ni2Tb(L-)(6)](NO3)(0.5)(Cl)(0.5) (3) and [Ni2Dy2(L-)(2)(o-vanillin)(2)(CO3)(2)(NO3)(2)(MeOH)(2)] (4). Structural analysis for 1-3 reveals that the lanthanide ion is sandwiched between two Ni(II) ions and the Ni center dot center dot center dot Ln center dot center dot center dot Ni metallic core displays a linear arrangement, with an average angle Ni center dot center dot center dot Ln center dot center dot center dot Ni bond angle of 179.7 degrees. Analysis of 4 reveals the metal ions are arranged such that two Ni-Dy subunits are bridged by two carbonate ligands via the Dy sites. Direct current magnetic susceptibility measurements for complexes 1-4 reveal that the Ni(II) ions are coupled ferromagnetically with the Tb(III) (3) and Dy(III) (4) ions, and antiferromagnetically with the Pr(III) ion (2). For complex 1 a long range intramolecular ferromagnetic interaction is witnessed between the Ni(II) ions (Ni center dot center dot center dot Ni = 6.873(9) angstrom) via a closed shell La(III) ion. The magnetic data of 1 were fitted using the HDVV Hamiltonian revealing the following parameters; J = +0.46 cm(-1), g = 2.245, D = +4.91 cm(-1). Alternating current magnetic susceptibility measurements performed on complexes 2-4 revealed that 3 and 4 displayed frequency dependent chi(M)'' signals (H-ac = 3.5 Oe and H-dc = 0 Oe) which is a characteristic signature of a single-molecule magnet behaviour.

Glasses prepared by physical vapour deposition have been shown to be remarkably more stable than those prepared by standard cooling protocols, with properties that appear to be similar to systems aged for extremely long times. When subjected to a rapid rise in temperature, ultrastable glasses anneal towards the liquid in a qualitatively different manner than ordinary glasses, with the seeming competition of different timescales and lengthscales. We numerically reproduce the phenomenology of ultrastable glass annealing with a kinetically constrained model, a three dimensional East model with soft constraints, in a setting where the bulk is in an ultrastable configuration and a free surface is permanently excited. Annealing towards the liquid state is given by the competition between the ballistic propagation of a front from the free surface and a much slower nucleation-like relaxation in the bulk. The crossover between these mechanisms also explains the change in behaviour with film thickness seen experimentally., Comment: 8 pages, 3 figures

International audience; This chapter provides an introduction to several important and interesting facets of out-of-equilibrium dynamics. If in the past hard condensed matter and classical statistical physics remained rather separate research fields, the focus now on several kinds of out-of-equilibrium dynamics is bringing them closer together. In this chapter, the stress is upon the common concepts, with the aim of showing that there is much to gain in considering out-of-equilibrium dynamics as a research field in itself. This chapter by no means self-contained. Rather, each section is a door toward a vast research area. The most striking, useful, or important concepts and tools are presented, often in an informal and introductory way, with the hope that this will stimulate the interest of readers who will then turn to the cited specialized reviews and books to fully satisfy their curiosity and acquire more complete knowledge of the subject.

© 2016 The Royal Society of Chemistry. We investigate the magnetic dilution effect on the relaxation mechanisms and the estimation of the energy barrier in a photo-luminescent Dy(III)/Y(III) based Single-Ion Magnet (SIM). The photo-luminescent spectroscopy permits the careful determination of the Orbach barrier, which is in a good agreement with the ab initio calculations. This barrier does not change upon magnetic dilution. The magnetic properties investigations highlight that the determination of the energy barrier is affected by magnetic dilution due to the changes in Quantum Tunnelling of the Magnetization (QTM). ispartof: RSC Advances vol:6 issue:110 pages:108810-108818 status: published

Ab initio CASSCF + RASSI-SO + SINGLE_ANISO and DFT based NBO and QTAIM investigations were carried out on a series of trigonal prismatic M(Bc(Me))(3) (M = Tb(1), Dy(2), Ho(3), Er(4), [Bc(Me)](-)= dihydrobis(methylimidazolyl)borate) and M(Bp(Me))(3) (M = Tb(1a), Dy(2a), Ho(3a), Er(4a) [Bp(Me)](-)= dihydrobis(methypyrazolyl)borate) complexes to ascertain the anisotropic variations of these two ligand field environments and the influence of Lanthanide-ligand bonding on the magnetic anisotropy. Among all the complexes studied, only 1 and 2 show large U-cal (computed energy barrier for magnetization reorientation) values of 256.4 and 268.5 cm(-1), respectively and this is in accordance with experiment. Experimentally only frequency dependent chi" tails are observed for complex 1a and our calculation predicts a large U(cal)of 229.4 cm(-1) for this molecule. Besides these, none of the complexes (3, 4, 2a, 3a and 4a) computed to possess large energy barrier and this is affirmed by the experiments. These observed differences in the magnetic properties are correlated to the Ln-Ligand bonding. Our calculations transpire comparatively improved Single-Ion Magnet (SIM) behaviour for carbene analogues due to the more axially compressed trigonal prismatic ligand environment. Furthermore, our detailed Mulliken charge, spin density, NBO and Wiberg bond analysis implied stronger Ln(...)H-BH agostic interaction for pyrazole analogues. Further, QTAIM analysis reveals the physical nature of coordination, covalent, and fine details of the agostic interactions in all the eight complexes studied. Quite interestingly, for the first time, using the Laplacian density, we are able to quantify the prolate and oblate nature of the electron clouds in lanthanides and this is expected to have a far reaching outcome beyond the examples studied.

Three new Dy complexes have been prepared according to a complex-as-ligand strategy. Structural determinations indicate that the central Dy ion is surrounded by two LZn units (L(2-) is the di-deprotonated form of the N2 O2 compartmental N,N'-2,2-dimethylpropylenedi(3-methoxysalicylideneiminato) Schiff base. The Dy ions are nonacoordinate to eight oxygen atoms from the two L ligands and to a water molecule. The Zn ions are pentacoordinate in all cases, linked to the N2 O2 atoms from L, and the apical position of the Zn coordination sphere is occupied by a water molecule or bromide or chloride ions. These resulting complexes, formulated (LZnX)-Dy-(LZnX), are tricationic with X=H2 O and monocationic with X=Br or Cl. They behave as field-free single-molecule magnets (SMMs) with effective energy barriers (Ueff ) for the reversal of the magnetization of 96.9(6) K with τ0 =2.4×10(-7) s, 146.8(5) K with τ0 =9.2×10(-8) s, and 146.1(10) K with τ0 =9.9×10(-8) s for compounds with ZnOH2 , ZnBr, and ZnCl motifs, respectively. The Cole-Cole plots exhibit semicircular shapes with α parameters in the range of 0.19 to 0.29, which suggests multiple relaxation processes. Under a dc applied magnetic field of 1000 Oe, the quantum tunneling of magnetization (QTM) is partly or fully suppressed and the energy barriers increase to Ueff =128.6(5) K and τ0 =1.8×10(-8) s for 1, Ueff =214.7 K and τ0 =9.8×10(-9) s for 2, and Ueff =202.4 K and τ0 =1.5×10(-8) s for 3. The two pairs of largely negatively charged phenoxido oxygen atoms with short DyO bonds are positioned at opposite sides of the Dy(3+) ion, which thus creates a strong crystal field that stabilizes the axial MJ =±15/2 doublet as the ground Kramers doublet. Although the compound with the ZnOH2 motifs possesses the larger negative charges on the phenolate oxygen atoms, as confirmed by using DFT calculations, it exhibits the larger distortions of the DyO9 coordination polyhedron from ideal geometries and a smaller Ueff value. Ab initio calculations support the easy-axis anisotropy of the ground Kramers doublet and predict zero-field SMM behavior through Orbach and TA-QTM relaxations via the first excited Kramers doublet, which leads to large energy barriers. In accordance with the experimental results, ab initio calculations have also shown that, compared with water, the peripheral halide ligands coordinated to the Zn(2+) ions increase the barrier height when the distortions of the DyO9 have a negative effect. All the complexes exhibit metal-centered luminescence after excitation into the UV π-π* absorption band of ligand L(2-) at λ=335 nm, which results in the appearance of the characteristic Dy(III) ((4) F9/2 →(6) HJ/2 ; J=15/2, 13/2) emission bands in the visible region.

Two mononuclear Dy-III crown ether complexes [Dy(15C5)(H2O)(4)](ClO4)(3)center dot(15C5)center dot H2O (1) and [Dy(12C4)(H2O)(5)](ClO4)(3)center dot H2O (2) have been prepared and characterized. X-ray diffraction studies show that both compounds crystallize as half sandwich type structures with muffin and pseudo-capped square antiprismatic geometries respectively. Despite the comparable local environments of the Dy-III ions they display remarkably different dynamic magnetic properties with only 1 displaying SMM properties in zero field. The solid state emission spectra for both 1 and 2 display sharp bands associated with f-f transitions. From the fine structure of the F-4(9/2) -> H-6(15/2) band, the Stark splitting of the H-6(15/2) ground state permitted the energy difference between the ground and first excited state to be determined. For 1 this value (Delta E = 58.0 +/- 3.0 cm(-1) ) is in excellent agreement with ab initio calculations and the experimentally observed SMM behaviour. For 2, the photoluminescence data and theoretical calculations support a less well isolated ground state (Delta E = 30 +/- 3.0 cm(-1)) in which a rapid relaxation process affords no SMM behaviour in zero-field.

Two lanthanide(III) phosphonates [Ln(notpH(4))(H2O)]ClO4 center dot 3H(2)O [Ln = Dy(1), Ho(2)] in which the lanthanide ion has a pseudo-D-5h symmetry have been reported. Both show layer structures where the neighbouring lanthanide atoms are connected by a pair of O-P-O bridges. Magnetic studies reveal that field-induced slow relaxation can be observed in both cases. Complex 1 is of particular interest because it shows not only field-tunable dual relaxation processes originating from the single ion anisotropy as well as the spin collective effect, but also simultaneous emissions from the metal ion, the ligand and the radiative energy transfer from the ligand to metal. The emission of Dy-III can be correlated to the magnetic data.

We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities higher than that corresponding to the mode-coupling transition. The structural analysis reveals the emergence of icosahedral locally favoured structures, previously only found in trace quantities. We present a new approach to probe the shape of dynamically heterogeneous regions, which is insensitive to particle packing effects that can hamper such analysis. Our results indicate that the shape of the dynamically heterogeneous regions changes only weakly and moreover hint that the often-used four-point correlation length may exhibit a growth in excess of that which our method identifies. The growth of the size of the dynamically heterogeneous regions appears instead to be in line with the one of structural and dynamic propensity correlations., Comment: under review at J. Stat Mech: Theory and Experiment

We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip dynamics near zero temperature, we construct via real-space renormalization the full hierarchy of relaxation times of the master equation for any given realization of the random couplings. We then analyze the probability distribution of dynamical barriers as a function of the spatial scale. This real-space renormalization procedure represents a simple explicit example of the droplet scaling theory, where the convergence towards local equilibrium on larger and larger scales is governed by a strong hierarchy of activated dynamical processes, with valleys within valleys., v2=final version

Complex systems having metastable elements often demonstrate nearly log-time relaxations and a kind of aging: repeated stimuli weaken the system's relaxational response. Granular matter is known to exhibit a wealth of such behaviors, for which the role of thermal fluctuations is usually ignored. However, we demonstrate that the latter can pronouncedly affect contacting mesoscopic-scale asperities and be macroscopically observed via appropriate acoustic effects. We also propose a mechanism comprising slow relaxations and aging as intrinsic properties of a wide class of systems with metastable states., Comment: 5 pages, 4 figures

Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a “power law” distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the “slow relaxation” (SR) process and “super slow relaxation” (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into “power”, “exponential”, and “stretched exponential” type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.

SMMs are often based on transition-metal clusters, but significant attention has recently focused on complexes of single and multiple lanthanoid ions, because the crystal-field splitting of the lowest Russell–Saunders multiplet engenders large magnetic anisotropies. [5–11] These anisotropies are responsible for high relaxation barriers and therefore slow magnetic relaxation. However, well isolated high-spin ground states are difficult to achieve within polynuclear lanthanoid SMMs because the valence 4f orbitals have limited radial extension and are usually energetically incompatible with ligand orbitals. These inherent 4f orbital properties give predominantly ionic interactions and results in weak magnetic exchange coupling with neighboring spin centers, with very few exceptions. [7, 12] In principle, actinoids, and in particular uranium, possess properties that render these ions ideal candidates from which to construct SMMs. This is because, compared to the lanthanoids, uranium exhibits enhanced crystal field splitting, [13, 14] as well as increased covalency, the latter enabling significant spin couplings in polynuclear systems, [15] and therefore both stronger magnetic exchange and anisotropies can be envisaged. This premise was realized recently with reports of several closely related single-ion pyrazolylborate uranium(III) complexes which were shown to display SMM behavior. [14, 16–20] In addition, two neptunium complexes were shown to display slow relaxation of the magnetization. [15, 21] The fact that all uranium(III) SMMs reported to date are closely related to each other raises the question as to how sensitive SMM behavior in trivalent uranium is to the composition of the coordination sphere and its symmetry. SMM behavior in all published examples is much more pronounced in an external field than in zero field, which suggests that quantum tunneling of the magnetization plays a significant role in shortening the relaxation times. However, in principle, low-symmetry crystal field components cannot induce tunneling of the magnetization, because uranium(III) is a Kramers half-integer angular momentum ion. Also the nuclear spin I = 0o f 238 U cannot induce tunneling of the

International audience; Different experimental techniques, such as kinetic studies of ligand binding and fluorescence correlation spectroscopy, have revealed that the diffusive, internal dynamics of proteins exhibits autosimilarity on the time scale from microseconds to hours. Computer simulations have demonstrated that this type of dynamics is already established on the much shorter nanosecond time scale, which is also covered by quasielastic neutron scattering experiments. The autorsimilarity of protein dynamics is reflected in long-time memory effects in the underlying diffusion processes, which lead to a non-exponential decay of the observed time correlation functions. Fractional Brownian dynamics is an empirical model which is able to capture the essential aspects of internal protein dynamics. Here we give a brief introduction into the theory and show how the model can be used to interpret neutron scattering experiments and molecular dynamics simulation of proteins in solution under hydrostatic pressure.

We investigated the spin dynamics of Zn(II)-doped “single-chain magnet” (SCM) Co(hfac)2NITPhOMe (in short CoPhOMe) by means of 1H NMR measurements. CoPhOMe was the first magnetic chain that showed a slowly relaxing magnetization (commonly called spins’ or magnetization “slowing down” mechanism), which follows the predictions of the Glauber model: the electronic spin freezing sets in before any transition to long-range magnetic order. The slowing down of the magnetization is also evidenced in the Zn-doped samples, which present chains that reach an average length of some tenth of spins for the highest doping, together with growing finite-size effects as the doping concentration is increased. The nuclear spin–lattice relaxation rate T1-1(T) at different applied magnetic fields, displayed a high-temperature peak and a low-temperature shoulder that become lower and shifts toward higher temperatures with increasing the field. This behaviour is qualitatively in agreement with the recent AC susceptibility data that revealed the Glauber dynamics and finite-size effects, like the collective reversal of the spins of each chain segment.

International audience; This paper presents a study of the influence of non-denaturing hydrostatic pressure on the relaxation dynamics of lysozyme in solution, which combines molecular dynamics simulations and quasielastic neutron scattering experiments. We compare results obtained at ambient pressure and at 3 kbar. Experiments have been performed at pD 4.6 and at a protein concentration of 60 mg/ml. For both pressures we checked the monodispersity of the protein solution by small angle neutron scattering. To interpret the simulation results and the experimental data, we adopt the fractional Ornstein–Uhlenbeck process as a model for the internal relaxation dynamics of the protein. On the experimental side, global protein motions are accounted for by the model of free translational diffusion, neglecting the much slower rotational diffusion. We find that the protein dynamics in the observed time window from about 1 to 100 ps is slowed down under pressure, while its fractal characteristics is preserved, and that the amplitudes of the motions are reduced by about 20%. The slowing down of the relaxation is reduced with increasing q-values, where more localized motions are seen.

Reaction of [FeIII(bipy)(CN)4]¯ with fully solvated MII cations [M = Co (1) and Mn (2)] produces the isostructural bis double zigzag chains [[FeIII(bipy)(CN)4]2MII(H2O)]·MeCN·1/2H2O; 1 exhibits intrachain ferromagnetic and interchain antiferromagnetic couplings, slow magnetic relaxation and hysteresis effects. Luminita Marilena, Toma, Luminita.Toma@uv.es ; Lescouezec, Alain Francois Rodri, Alain.Lescouezec@uv.es ; Lloret Pastor, Francisco, Francisco.Lloret@uv.es ; Julve Olcina, Miguel, Miguel.Julve@uv.es

A peculiar slow relaxation of low-temperature photoconductivity in semi-insulating GaAs is analysed. Time evolutions of free electron concentration, n, and free hole concentration, p, are determined from independently measured photoconductivity and current due to the thermoelectric effect. It is shown that during low-temperature illumination the p/n ratio at first rises significantly and then decreases back towards the initial, low value. The same behaviour is obtained from a study of time evolution of photo-Hall mobility measured independently. Results are analysed and explained in terms of different trapping rates of photogenerated free electrons and holes by deep traps (15 References)