1. Slow Dynamics in Mesoscopic Magnets and in Random Magnets
H. Mamiya
National Institute for Materials Science
Tsukuba , 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.

2. 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:

3. 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.

4. 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,.

5. 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?

6. 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.

7. 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.

8. 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.

9. 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.

10. Memory and Rejuvenation in the isolated nanomagnets
Ferritin
Ag89Mn11
Mathieu et al. Phys. Rev. B 65 (2002)
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.

11. 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.]

12. 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.

13. 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.

14. 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.

15. 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

16. 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 …

17. 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 …

18. 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 …

19. 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 …

20. 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 …

21. 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 …

22. 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 …

23. 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 …

24. 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 …

25. 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 …

26. 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

27. 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 …

28. 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 …