Slow Dynamics in Mesoscopic Magnets and in Random Magnets

1. Slow Dynamics in Mesoscopic Magnetsand 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

2. Random materials Metastable states Slow dynamics Mesoscopic materials Lower barriers Slow dynamics Introduction Well-clarified Bulky materials with periodic structures Permanently stable ground states Ultra-fast excitations Central objects of future researches Experimental understanding of slow dynamics Issue:

3. Example: Magnet Ordinary ferromagnets (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) Super-Spin-Glass? Too many models have been proposed. Experimental studies have been confused them.

4. diluted FeN magnetic fluid and magnetic core of ferritin In this talk, 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) 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. An Ordinary Ferromagnet Isolated Nanomagnets Canonical Spin-Glass Hystereses All of them show thermal hystereses. Can I distinguish them each other by comparing the field-dependence?

6. An Ordinary Ferromagnet Isolated Nanomagnets 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. Field-dependence Canonical Spin-Glass

7. Ferromagnet Isolated nanomagnets Isothermal aging Canonical Spin-Glass a kind of aging effects can be widely observed.

8. Note their time-dependences Finally Estimated value at the final convergence is just on the curve by the Curie law Extrapolation estimated by Nature of [MZFCMFC]Isolated nanomagnets Although a remarkable difference exists between MZFC and MFC, it is temporary behavior. The equilibrium phase is unique and superparamagnetic.

9. Universal curve independent of W : Isothermal susceptibility (W∞, ) Cole-Cole relationship Nature of [MZFCMFC]Canonical spin-glass Relaxation curves after various cooling histories (W=0) 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. Ferritin In contrast with canonical spin-glasses, we canobserve 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. Memory and Rejuvenationin the isolated nanomagnets Ag89Mn11 Mathieu et al. Phys. Rev. B 65 (2002) 092401.

11. In contrast with canonical spin-glasses, we canobserve 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.] Memory and Rejuvenationin the ordinary ferromagnets Jonason et al. Phys. Rev. Lett. 81 (1998) 3243.

12. As an example, We shall discuss the experimental results for a strongly interacted super-spin system from the viewpoint of these characteristics of the slow dynamics. Aging effects are widely observed. irreversible, rejuvenation, and effects Features ofSlow dynamics

13. (Co0.95Fe0.05)49 (Pd0.14Si0.27O0.59)51 10nm Sample Susceptibility Critical plots Above 285 K, Unhysteretic susceptibility with Curie-Weiss behavior Super-spins fluctuate with ferromagnetic correlations Around 285K, Critical slowing-down and divergences of susceptibilities A ferromagnetic-like phase transition We can presume the irreversible phase superferromagnetic. Strongly interacted super-spins Ex. CoFe-SiO2 nano-granular film

14. Magnetization on reheating after ZFC with and without the halt Difference of MZFC with the halt from the reference The susceptibility becomes relatively small only in the vicinity of the aging temperature. Strongly interacted super-spins Slow dynamics 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? 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

17. Appendix

18. Appendix

19. Appendix w = 0, h  hFC

20. Appendix

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.

22. Appendix  (3θ)/ψ ~ 3, θ/ψ ~ 1, θ ~ ψ~ 3/4. χEA·h = 1.01 A/m

23. Appendix  λ~ 3/2 Ｄh= 1.18 A/m

24. Appendix

25. Appendix

26. Appendix heating

27. Appendix

28. Appendix