Spin Glass Physics – from archetypal dilute alloys to super ferromagnets

1. Spin Glass Physics – from archetypal dilute alloys to super ferromagnets Per Nordblad Uppsala University

2. Outline • Spin Glass • Equilbrium properties • Non-equilibrium characteristics • Universality of frustration-disorder Carl von Linné (1707-1778)

3. Distribution of interaction strength H = - ½∑JijSiSj Jij= J ferro -J antiferro ±J spin glass Gaussian distribution: Zero mean: spin glass Positive mean: re-entrant ferro Negative mean: re-entrant antiferro Order Disorder Frustration

4. Phase diagram FexMn1-xTiO3

5. Equilibrium transition - Tg Fe0.5Mn0.5TiO3 Ag (11at%Mn)

6. Critical slowing down z ≈ 10 τ0~ 10-13 s Tg=20.9 K

7. AT-line – In-field transition?

8. Non-equilibrium - Ageing

9. Rejuvenation – memory - chaos

10. Length scales – domain growth

11. Nano particles • Superparamagnetism and blocking • Size distributions • Single particle relaxation • Collective dynamics • Concentration • Interaction • Matrices

12. Fe(C) particles Properties: d = 5.3±0.3 nm c = 0.06, 5 and 17% K = 0.9 105 J/m3 Ms = 1.0 106 A/m M.F. Hansen et al. J. Phys.: Condens. Mater. 14, 4901 (2002) Ac-susceptibility: 125 and 1000 Hz

13. Arrhenius contra collective dynamics 0=10-10 s Tc=40 K

14. Ac-suceptibility of Fe(C) • Pictures f = 0.017 – 170 Hz f = 0.01 - 9100 Hz

15. Critical slowing down! The slowing down of the relaxation times with decreasing temperature can for the two dense samples be described by critical slowing down. The dilute sample follows an Arrhenius law. Parameters for the critical slowing down: 17%: z 10, Tg 50 K, 0  2 10-8 s 5%: z 11, Tg 35 K, 0  2 10-5 s

16. Dense ferrofluids • Narrow size distribution • Frozen fluid • ’Arrhenius’ particles • Dipolar interaction • Disorder and frustration • Critical slowing down • Non-equilibrium dynamics – ageing and memory phenomena • Superspin glass

17. Tuning the interaction - DMIM • No trace of oxidation • fcc crystal structure • Good control of the average diameter between 0.7 and 6 nm

18. Control of particle size and anisotropy

19. Phase diagrams • Pictures

20. Enhanced interction strength in metallic matrices Ac-susceptibility of an FeWAg mechanically alloyed system. J.A. de Toro et al. Phys. Rev. B 69, 224407 (2004) 0.1-1000 Hz Tg=19.7 K zν=10.2 τ0=10-10 s

21. Magnetic perovskites Example: La0.5Sr0.5CoO3

22. Spin Glass Physics • Hamiltonian • Interactions • Disorder and frustration • Phase diagram • Non-equilibrium in ferro- and spin glass phases • Experimental observable • MC experiments – several observables • Time scales and systems

23. THANK YOU! • Some references: • M.F. Hansen et al., J. Phys.: Cond. Mat. 14, 4901 (2002) • K. Gunnarsson et al., Phys. Rev. Lett. 61, 754 (1988) • D.N.H. Nam et al., Phys Rev. B 59, 4189 (1999) • J.A. de Toro et al., Phys. Rev. B 69, 224407 (2004) • W. Kleemann et al., Phys. Rev. B 63, 134423 (2001) • F. Luis et al., Phys. Rev. Lett. 88, 217205 (2002) • P.E. Jönsson et al., Phys. Rev. B 70, 174402 (2004) • D. Petit et al., Phys. Rev. Lett. 88, 207206 (2002) • T. Jonsson et al., Phys. Rev. Lett. 75, 4138 (1995) • J. Mattsson et al., Phys. Rev. Lett. 74, 4305 (1995)

25. Thermal procedure in aging experiments on glassy systems. Memory, Ag(Mn) Glassy behavior – aging and memory

26. ZFC Magnetization after different wait times Aging in a Cu(Mn) spin glass Relaxation rate P. Granberg et al. Phys. Rev. B 38, 7097 (1988)

27. Aging in Fe(C) Fe(C) 5%

28. ZFC Magnetisation Memory continued

29. Ag(Mn) Heisenberg Fe0.5Mn0.5TiO3 ISING Memory

30. Memory in Fe(C)

31. Memory in the FeAgW mechanically alloyed system

32. r preparation of the ferrofluid, a mixture of 4.25 g of Sarkosyl-O (n-oleoyl sarcosine), 20 ml ofFe(CO)5, and 50 ml ofDecalin (decahydronaphthalene) was placed in a reaction vessel. The chemicals were all of high purity quality. Special care was taken with Fe(CO)5 which is a poisonous liquid at room temperature. The Fe(CO)5 evolves carbon monoxide when exposed to heat or light. The chemical reactions were therefore carded out in a fume cupboard. A continuous flow of argon was passed through the apparatus during the reaction to remove carbon monoxide. The liquid was heated under vigorous stirring. After a heating time of about 105 rain, refux conditions occurred at a temperature of about 390 K. At intervals of about 50-100 rain the vessel was rapidly cooled, and 1-ml samples were removed by use of a syringe, whereafier the vessel was heated again. As the reaction proceeded, the temperature increased to about 460 K due to the change in the boiling point of the liquid. The liquid was stirred and refluxed for about 8-9 h including the time needed for removal of samples. Eight samples were collected and Fabrication J.V Von Wonthergem et al. J.Colloid Interface Sci. 12, 558 (1988)

33. Maghemite system • Mechanically alloyed FeAgW system • Discontinuous Co or Co(Fe) layers Some nanoparticle systems with wider particle distribution

34. Memory and aging in Co(Fe) DMIM S. Sahoo et al. Phys. Rev. B 67, 214422 (2003)

35. A Maghemite system T. Jonsson et al PRL 75 4183 (1995)

36. Aging in the maghemite particle system