Slow Dynamics in Mesoscopic Magnets and in Random Magnets H. Mamiya National Institute for Materials Science Tsukuba 305-0047, Japan Collaboration M. Ohnuma, NIMS, Japan T. Furubayashi, NIMS, Japan I. Nakatani, NIMS, Japan S. Nimori, NIMS, Japan M. Sasaki, Tohoku University, Japan P. E. Jönsson, RIKEN, Japan H. Takayama, University of Tokyo, Japan Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The work are made in collaboration with Drs…and Profs.

Introduction Bulky materials with periodic structures Well-clarified Bulky materials with periodic structures Permanently stable ground states Ultra-fast excitations Mesoscopic materials Lower barriers Slow dynamics Random materials Metastable states Slow dynamics Central objects of future researches In the last century, bulky materials with periodic structures have been intensively studied. So, their well-clarified properties have been applied to various industries. For example, the data storage devices have been based on the permanency of the ground states, while ultra-fast excitations have been useful for central processing units. On the other hand, mesoscopic materials, as well as random materials, will be central objects of future researches, and both systems show slow dynamics due to its metastability or to the lowness of its barrier height. So, experimental understanding of slow dynamics will be important in these systems. Experimental understanding of slow dynamics Issue:

Example: Magnet Ordinary ferromagnets Canonical spin-glasses (usually with pinning centers) Ferromagnet with Wandering Axis? Random Ferromagnet? Reentrant Spin-Glass? Superferromagnet? Correlated superspin glasses? Speromagnet? Cluster-Glass? Canonical spin-glasses Isolated nanomagnets (ideal superparamagnets) An example is a group of magnetic materials. In addition to ordinary ferromagnets, ideal systems, canonical spin-glasses and isolated nanomagnets, have been intensively studied. However, actual materials are somewhat complicated and many models have been proposed. Because their behaviors are similar in appearance. experimental studies have been confused them. Super-Spin-Glass? Too many models have been proposed. Experimental studies have been confused them.

In this talk, pure Tb and Ni3Al foils, Cu0.97Mn0.03 wires (100m) We show experimental features of the slow dynamics in ordinary ferromagnets, in a canonical spin-glass, and in isolated nanomagnets, pure Tb and Ni3Al foils, Cu0.97Mn0.03 wires (100m) diluted FeN magnetic fluid and magnetic core of ferritin In this talk, I will first show experimental features of the slow dynamics in ordinary ferromagnets, pure terbium and nickel-three-aluminum foils, in a canonical spin-glass, copper-manganese wires and in isolated nanomagnets, diluted FeN magnetic fluid and magnetic core of ferritin from the point of view of irreversible, aging, rejuvenation, and memory effects. Time permitting, I will discuss strongly interacted super-spin systems using the knowledge of the clarified features. from the point of view of irreversible, aging, rejuvenation, and memory effects. Then, we will discuss strongly interacted super-spin systems using the knowledge of the feature,.

Hystereses All of them show thermal hystereses. Isolated Nanomagnets Canonical Spin-Glass An Ordinary Ferromagnet First, I will report the hysteresis. This viewgraph shows the temperature-dependence of the magnetization obtained for CuMn the alloy. As well-known, Spin-Glasses show a difference between the zero-field-cooled magnetization and the field-cooled magnetization below the glass temperature. However, both ordinary ferromagnets with pinning centers and magnetic fine particles show thermal hystereses. Can I distinguish them each other by comparing the field-dependence? All of them show thermal hystereses. Can I distinguish them each other by comparing the field-dependence?

Field-dependence An Ordinary Ferromagnet Isolated Nanomagnets Canonical Spin-Glass This viewgraph shows the thermal hystereses of CuMn alloy at various field. As well-known, the spin-glass temperature decreases with increasing magnetic field. However, we should note that in both ordinary ferromagnets and isolated nanomagnets, the irreversibility appears at lower temperature as magnetic field increases. Because their experimental appearances are almost the same, it is not easy to distinguish them each other. In all of the systems, the irreversibility appears at lower temperature as magnetic field increases. Because their experimental appearances are almost the same, It is not easy to distinguish them each other.

Canonical spin-glasses Ordinary ferromagnets Isothermal aging Isolated nanomagnets Ferromagnet Canonical Spin-Glass Next, I will discuss the isothermal relaxations. This viewgraph shows the MZFC of CuMn alloy after equilibration during various wait times. As well-known, in Spin-Glasses, the response of MZFC is delayed with the equilibration. However, such aging effects can be observed in ordinary ferromagnets. Moreover, TRM also shows aging effects even in isolated nanomagnets. Thus, a kind of aging effects can be widely observed. For this reason, we must clarify deeper underlying difference. ZFC or AC TRM Canonical spin-glasses Remarkable Ordinary ferromagnets Observable Isolated nanomagnets No a kind of aging effects can be widely observed.

Nature of [MZFC  MFC] Isolated nanomagnets Note their time-dependences Finally Estimated value at the final convergence is just on the curve by the Curie law Extrapolation estimated by Now, I will consider the nature of the difference between MZFC and MFC In the isolated nanomagnets system, as mentioned a little while ago, there is a a remarkable difference below 30 K. This viewgraph shows their time-dependences. We can find, the difference tends to disappear if the relaxation curves are extrapolated by using the barrier height distribution. And the estimated value of the final convergence is on the curve given by the Curie law. In short, it is temporary behavior. The equilibrium phase is unique and it is superparamagnetic. Although a remarkable difference exists between MZFC and MFC, it is temporary behavior. The equilibrium phase is unique and superparamagnetic.

Nature of [MZFC  MFC] Canonical spin-glass Cole-Cole relationship Universal curve independent of W : Isothermal susceptibility (W∞, ) Relaxation curves after various cooling histories (W=0) In contrast with the isolated nanomagnets, the nature of the difference between MZFC and MFC in SG is more interesting. This viewgraph shows relaxation curves after various cooling histories. Because they are plotted against the inverse of time, this point corresponds to eternity. We can find that the memories due to cooling histories disappear fast when no aging are performed. On the other hand, after sufficient equilibration, we can obtain an universal curve independent of tw. For example, this viewgraph shows such a curve on the Cole-Cole relationship. Note that while Kai’ is increased by 2% while the loss component is reduced by half. If the universal curve, that is the isothermal susceptibility, are plotted here, we can find that the difference between MZFC with sufficient equilibration and MFC survives for a long time, as predicted by SG theories. eternity While memories due to cooling histories disappear fast, the difference between MZFC (W∞, t) and MFC (W=0, t) survives for a long time, as predicted by SG theories.

Memory and Rejuvenation in the isolated nanomagnets Ferritin Ag89Mn11 Mathieu et al. Phys. Rev. B 65 (2002) 092401. In contrast with canonical spin-glasses, we can observe neither rejuvenation nor memory effects for MZFC. Only the memory effects were seen for MFC, because the population ratio of to can be changed during the halts only on cooling in a field. Finally, I will show the memory and rejuvenation effects. This viewgraph shows MZFC after cooling with and without halts. We can find that Spin-Glasses have both of the effects. This viewgraph shows the results for the isolated nanomagnets. In contrast with SG, we can observe neither rejuvenation nor memory effects for MZFC. Only the memory effects were seen for MFC, because the population ratio of UP to DOWN can be changed during the halts only on cooling in a field.

Memory and Rejuvenation in the ordinary ferromagnets Jonason et al. Phys. Rev. Lett. 81 (1998) 3243. This viewgraph shows Ac susceptibility after cooling with and without halts. We can confirm that Spin-Glasses have both of the memory and rejuvenation effects.. This viewgraph shows the results for the ordinary ferromagnets. In contrast with SG, we can observe only the rejuvenation effects. These results are consistent with the previous report for ferromagnetic thiospinel CdCr2S4. In contrast with canonical spin-glasses, we can observe only the rejuvenation effects for AC(). These results are consistent with the previous report for ferromagnetic thiospinel CdCr2S4. [ Vincent et al. Europhys. Lett.50 (2000) 674.]

Features of Slow dynamics Ordinary ferromagnets Canonical spin-glasses Isolated nanomagnets Hysteresis MZFC  MFC (To be temporary) (Semi-)permanent Temporary Aging Observable Remarkable Only TRM Rejuvenation None Memory Little Only MFC Aging effects are widely observed. irreversible, rejuvenation, and effects We shall discuss the experimental results for a strongly interacted super-spin system from the viewpoint of these characteristics of the slow dynamics. As an example, At this moment, let me summarize the features of slow dynamics. Although the experimental results are roughly similar each other. we can find some intrinsic difference. Especially, the memory and rejuvenation effects are useful in distinguishing these phases at a glance. As an example, I shall discuss the experimental results for a strongly interacted super-spin system from the viewpoint of these characteristics of the slow dynamics.

Strongly interacted super-spins Ex. CoFe-SiO2 nano-granular film Above 285 K, Unhysteretic susceptibility with Curie-Weiss behavior Super-spins fluctuate with ferromagnetic correlations Susceptibility Critical plots Around 285K, Critical slowing-down and divergences of susceptibilities A ferromagnetic-like phase transition 10nm (Co0.95Fe0.05)49 (Pd0.14Si0.27O0.59)51 Sample As a typical strongly interacted super-spins, I will examine a CoFe-SiO2 nano-granular film like this. This viewgraph shows its susceptibility. We can find unhysteretic susceptibility above 285 K. Its inverse in the inset shows the temperature dependence is given by the Curie-Weiss law. In other words, super-spins fluctuate with ferromagnetic correlations. Around 285K, critical slowing-down and divergences of susceptibilities are observed. These results indicate a ferromagnetic-like phase transition. On the basis of them, we can presume the irreversible phase below 285 K superferromagnetic. We can presume the irreversible phase superferromagnetic.

Strongly interacted super-spins Slow dynamics The susceptibility becomes relatively small only in the vicinity of the aging temperature. Difference of MZFC with the halt from the reference Magnetization on reheating after ZFC with and without the halt This viewgraph shows MZFC after cooling with and without halts. We can find that the susceptibility becomes relatively small only in the vicinity of the aging temperature. In other words, the irreversible phase below Tc has both the memory and rejuvenation effects. This phase has these characteristic of the slow dynamics of SG, although it is presumed to be superferromagnetic. The irreversible phase below Tc has both the memory and rejuvenation effects, although it is presumed to be superferromagnetic.

Conclusion As shown for an example of interacted super-spin systems, Ordinary ferromagnets Superferromagnet? Random Ferromagnet? Reentrant Spin-Glass? Ferromagnet with Wandering Axis? Correlated superspin glasses? As shown for an example of interacted super-spin systems, the characteristics of the slow dynamics can be a key to experimental understanding of the confused systems. Speromagnet? Cluster-Glass? Super-Spin-Glass? spin-glasses Superparamagnets The characteristics of the slow dynamics can be a key to experimental understanding of the confused systems

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix w = 0, h  hFC Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix MZFC(τw, τ) ≈ MZFC(τw→∞, τ) + MAG(τw, τ), (1) MZFC(τw→∞, τ) ≈ χEA·h –a0·[L(τ)]−θ, (2) MAG(τw, τ) ≈ a1·[L(τ)/L(τw)]3−θ, (3) MFC(τ) ≈ χFＣ (τ) ·h + Mex (4) χFＣ (τ) ·h ≈ χD·h –a2·[L(τ)]−θ, (5) Mex ≈ a3· [L(τ)]−λ, (6) ≈ χD·h – a2·[ln(τ/τc)]−1 + a3·[ln(τ/τc)]−4λ/3, where Mex comes from unknown memories during cooling. L(x) ~ [ln(x/τc)]1/ψ, τc ~ τ0·(1−T/Tg)−zυ. Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix  (3θ)/ψ ~ 3, θ/ψ ~ 1, θ ~ ψ~ 3/4.  χEA·h = 1.01 A/m  (3θ)/ψ ~ 3, θ/ψ ~ 1, θ ~ ψ~ 3/4. 　χEA·h = 1.01 A/m Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix  λ ~ 3/2  Ｄh = 1.18 A/m Thank you Mr. Chairman.  λ ~ 3/2 　Ｄh　= 1.18 A/m Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix heating Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are … heating

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …

Appendix Thank you Mr. Chairman. My name is MAMIYA from NIMS, japan. I am honored to be invited to give a talk here. Taking advantage of this opportunity, I would like to thank organizers. Title of my talk is … The co-workers are …