Aging, rejuvenation and memory: the example of spin glasses

Transcription

1 Aging, rejuvenation and memory: the example of spin glasses F. Bert, J.-P. Bouchaud, V. Dupuis, J. Hammann, D. Hérisson, F. Ladieu, M. Ocio, D. Parker, E. Vincent Service de Physique de l Etat Condensé, CEA Saclay, France (CNRS URA 2464) Osaka University, Kawamura s group, Nov. 24 th 2006

2 1. Introduction 2. Slow dynamics and aging 3. Rejuvenation and memory

3 1. Introduction 2. Slow dynamics and aging 3. Rejuvenation and memory

4 SPIN GLASS: YPICAL BEHAVIOUR M/H (emu/cm 3 ) RM ZFC FC ZFC g para (~1/) (K) FC Field-Cooled magnetization ZFC Zero-Field Cooled magnetization RM hermo-remanent Magnetization CdCr 1.7 In 0.3 S 4 H=10G ZFC(t)+RM(t) = FC(t) Nordblad et al, JMMM 54, 185 (1986)

5 Superspin Glass Small enough ferromagnetic nanoparticle single domain magnetism << c : response of single nanoparticle ~ response of single spin a superspin Varying concentration of nanoparticles in a liquid dispersion changes dipoledipole interparticle interaction Dilute nanoparticle system Concentrated nanoparticle system superparamagnet (non-interacting superspins) Superspin glass (interacting superspins) o what extent do superspin glasses behave like atomic spin glasses? Parker et al, J. Appl. Phys. 97, 10A502 (2005)

6 Magnetization (a.u.) ZFC-FC curves of Co nanoparticles (Co x Ag 1-x, with varying concentration x) FC (a) (c) ZFC FC x = 9.6% ZFC χ -1 (arb.) χ -1 (arb.) x = 19.4% (K) (K) 0 = 47K (K) 0 = 79K from X.X. Zhang, Hong Kong US FC ZFC x (%) B 0 χ -1 (arb.) (b) x = 12.7% S K 47 K 0 = 54K (K) S K 54 K S K 79 K he increase of 0 indicates an enhancement of interactions

7 1. Introduction 2. Slow dynamics and aging 3. Rejuvenation and memory

8 Spin glasses: slow dynamics + aging 1. dc : hermo-remanent Magnetization (RM) 80 Uppsala, Sweden (Lundgren, Nordblad ) Saclay, France (Hammann, Ocio, Alba, Vincent ) g H 0 t w t w : waiting time t : observation time M = f ( t, t t w ) m = M/M FC 0,14 t w [min] CdCr 1.7 In 0.3 S , , ,14 0,11 0, ,12 0,10 0, ,10 0,09 0,08 0,07 0,06 m = M/M FC 0,09 0,08 0,07 0,06 1E-4 1E-3 0,01 0, t/t w = 12 K = 0.7 g 0, t [min] Non-stationary dynamics : (t, t w ) (dc) Scaling variable : ~ t / t w (dc)

9 80 Spin glasses: slow dynamics + aging 2. ac susceptibility Uppsala, Sweden (Lundgren, Nordblad ) Saclay, France (Hammann, Ocio, Alba, Vincent ) g χ''-χ''0 (10-4 emu/cm 3 ) Hz 4 Hz 0.8 Hz 0.4 Hz 0.08 Hz 0.04 Hz t w 6 H 0 ω t w (min) 0,24 χ = f (ω, t w ) = χ eq (ω) + (ω.t w ) -α (α 0.2) χ" - χ" 0 (ω) 0,20 0,16 0,12 ω (Hz) CdCr 1.7 In 0.3 S 4 =12K=0.7 g 0, Non-stationary dynamics : (t, t w ) (dc), (ω, t w ) (ac) Scaling variables : ~ t / t w (dc), ω t w (ac) ω.t w

10 Structural and polymer glasses (ac) Dielectric response of a supercooled liquid g E 0 t w ω glycerol at 178K g =190K (dc) Mechanical response of a polymer g t w PVC at 310K g =350K t glycerol Leheny et al. (1998) σ 0 PVC Struik (1978) ~ same scaling laws as in spin glasses : ωt, t / t w

11 3. Spin glasses: noise measurements determination of the autocorrelation C(t w,t)=<v(t w )v(t)> recordings SQUID signal (V) noise recordings time (s) Comparison of autocorrelation and response, fluctuation-dissipation relations in the aging regime Corrélation : C(t w,t)/c(t,t) Relaxation : σ(t w,t)/σ(t,t) ,6 0,4 0,3 0,1 0,0 Aging Relaxation 0,2 0,0 1E-5 1E-3 0,1 10 Aging Correlation 0,4 0,4 0,2 0,0 1E-5 1E-3 0,1 10 ζ ζ 0, τ=t-t w (s) 0-20µ -40µ -60µ 0,6 0,4 0,2 0,0 σ(t w,t) (V) C(t w,t) (V 2 )

12 FD relation graph («CuKu graph») EFF 4 G EFF 3 G EFF 1,5 G D. Hérisson and M. Ocio, Phys. Rev. Lett. 88, (2002) Eur. Phys. J. B 40, 283 (2004) χ/ χ FC ,9 G 0,6 G 0,8 G σ/χ FC C/C(t,t) clear 1/ regime, and crossover to aging regime 1/ eff vanishing t w -dependence in the extrapolation eff = f(c) not domain growth-like (1/ eff =0, horizontal lines) 1-step RSB type models: straight lines of slope 1/ eff - compatible Miguel Ocio ( ) D. Hérisson PhD thesis continuous RSB models (SK, mean-field spin glass): χ=1-σ=(1-c) 0,47 (dashed line)

13 1. Introduction 2. Slow dynamics and aging 3. Rejuvenation and memory

14 Aging, rejuvenation and memory: basic observation «Negative temperature cycling» of a spin-glass (1992) t 1 t 3 t g 2 - temps : rejuvenation, restart of the relaxation : memory, no effect of the time spent at - χ [a.u.] CdCr 1.7 In 0.3 S 4 g =16.7K = 12 K - = 10 K = 12 K time [min] In simulations: no rejuvenation and memory effects in the Ising spin glass? okyo (akayama group), Roma (Parisi group), Recently: rejuvenation and memory effects in the Heisenberg spin glass Berthier & Young (2005) Experiments on Ising and Heisenberg spin glasses: see PRL 92, (2004) (nature of the Heisenberg spin-glass phase? chiral glass à la Kawamura?)

15 Multiple rejuvenation and memory effects in a spin glass χ'' x 10 3 [emu/cm 3 ] 1,4 CdCr 1.7 In 0.3 S 4 1,2 1,0 0,8 0,6 0,4 0,2 0.1 Hz Refroidissement par paliers Réchauffement continu 0, : rejuvenation : memory [K] «memory dips» experiments: Uppsala / Saclay PRL 81, 3243 (1998) [K] K/s t [s] more details and references in cond-mat/ hierarchical organisation of the metastable states as a function of rejuvenation Hierarchical models (REM, GREM, traps): Bouchaud and Dean (1995) Sasaki and Nemoto (2000) Sasaki et al, EPJ B 29, 469 (2002) memory

16 Rejuvenation and memory effects in terms of spins? not simply domain growth-like χ'' x 10 3 [emu/cm 3 ] 1,4 CdCr 1.7 In 0.3 S 4 1,2 1,0 0,8 0,6 0,4 0,2 0.1 Hz Refroidissement par paliers Réchauffement continu 0, [K] : rejuvenation : memory [K] K/s t [s] Aging at fixed : growth of SG-order up to some coherence length L * Rejuvenation different equilibrium correlations at different s (chaos-like?) Memory L* n <<.. << L * 2 << L* 1 hierarchy of length scales net separation of L i s with temperature («-microscope» effect)

17 A microscopic mechanism for rejuvenation and memory? S.Miyashita and E.V., EPJ B 22, 203 (2001) 1) emperature dependent effective interactions (due to frustration) Example : J 2 >0 J 2 >0 J eff effective interaction between σ 1 and σ 2 varies with temperature rejuvenation

18 A microscopic mechanism for rejuvenation and memory? 2) Memory spots (due to inhomogeneity of interactions) Example: J 1 >> 3J 0 > 0 (b) (c) memory (a) barrier = 2J 1-6J 0 slow relaxation, frozen at low In a real spin glass : should occur naturally at various length/energy scales Is this necessary to memory? see Yoshino et al, EPJ B 20, 367 (2001) and entropy induced slowing down by anaka and Miyashita, Progr. heoret. Phys. Suppl. 157, 34 (2005)

19 g H 0 Spin glass : rejuvenation vs cooling rate effects ZFC procedure with stops (Uppsala 2001) χ x 10 3 [emu/cm 3 ] Au:Fe 8% FC ZFC [K] H = 50 Oe fast cooling (100mK/s) step cooling (t w i =3600s, i=1,6) slow cooling (4mK/s) aging combination of cooling rate effects -cumulative rejuvenation & memory effects -specific [ M step -M fast ] / M fast slow cooling step cooling Au:Fe 8% H = 50 Oe V. Dupuis, PhD thesis, Orsay 2002, and cond-mat/ [K]

20 MEMORY EFFEC IN NANOPARICLES γ-fe 2 O 3 nanoparticles, d~8.5nm, f v =35% V. Dupuis, D. Parker et al, AIP Conf. Proc. 832, 295 (2006)

21 MEMORY EFFECS IN A GELAINE GEL he spin glass dynamics of gelatine gels Alan Parker and Valéry Normand Research Division, Firmenich SA (Geneva, Switzerland) Elasticity measured during heating and cooling at 0.2K/min dashed line: continuous heating and cooling G' (Pa) 1.0x x x x x10 3 cond-mat/ solid line: with 2 stops (2h at 25 and 15 C) emperature (K) Bottom figure : difference plot G' (Pa) double memory reading in PMMA (dielectric measurement) emperature (K)

22 Conclusions Spin glasses : aging effects waiting time dependence of ac+dc susceptibility, and in noise similar to aging in structural and polymer glasses Effect on aging of thermal history: rejuvenation and memory phenomena (-specific) + cooling rate effects (-cumulative) Rejuvenation and memory : aging at different temperatures can take place at well-separated length scales hierarchy of embedded coherence length scales, selected by (microscope effect) Same scenario in other glassy systems? probably yes (R&M in nanoparticles, PMMA, gelatine ) more details and references in cond-mat/