Low temperature dynamics of magnetic nanoparticles

Transcription

1 Low temperature dynamics of magnetic nanoparticles J.-P. Bouchaud, V. Dupuis, J. Hammann, M. Ocio, R. Sappey and E. Vincent Service de Physique de l Etat Condensé CEA IRAMIS / SPEC (CNRS URA 2464) CEA Saclay (France) Spin Physics and Nanomagnetism, 6th birthday of E. Chudnovsky New-York, March 29

2 1. Low-temperature dynamics: thermal or quantum? 2. Super-spin glass state

3 1. Low-temperature dynamics: thermal or quantum? 2. Super-spin glass state

4 The beginning of the story The starting point of my first adventure with Eugene

5 There were other adventures with Eugene

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7 South Manhattan in 1998, seen from the Tampico driven by captain Eugene

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9 Dynamics of super-spins Small enough ferromagnetic nanoparticle single domain T<<T Curie : response of single nanoparticle ~ response of single macro-spin a superspin Easy axis anisotropy barrier U~K.V T<<KV blocking of magnetization QTM H KV Chudnovsky, PRL 6, 661 (1988)

10 Thermal activation, Quantum tunneling θ m Flipping time τ of the nanoparticle magnetic moment: H easy axis U 3-1nm τ = τ exp * kbt ( T ) U ~ K // V T * (T) effective temperature for the dynamics: T * (T) quantum T cr K K // M s T cr thermal E.M. Chudnovsky & L. Gunther, PRL 6 (1988) 661 T cr T

11 Observation of macroscopic quantum tunneling of magnetization in nanoparticles? 1. In nanoparticle assemblies: many difficulties related to particle size distribution (to be discussed in this talk) 2. In individual nanoparticles : many difficulties also but nice results

12 Magnetic viscosity measurements H=6 Oe, T>T b Field-cool down to T <T b H= at t= s U=KV M - M arb (1-6 emu) mk 5 mk 1 K Given P(U)m i (U), t M ( t, T ) = P( U ) mi ( U )exp du * τ ( U, T ( T )) Magnetic viscosity: M ( t, T ) S( T ) = k * BT P( U c ) mi ( U c ) ln t nature distribution time (s) with U c t = k BT * ln τ

13 S(T) S(T) Low-T anomalies observed in many magnetic systems : quantum origin? M ( t, T ) S ( T ) = k * BT P ( U c ) m i ( U c ) ln t nature distribution

14 Eugene Chudnovsky in Barcelona, actively participating in the experiments on macroscopic Quantum Tunneling

15 A new method: the Residual Memory Ratio (RMR) M (1-3 e.m.u.) Relaxation with a heating cycle T = 3 K x.t (x = 1.3) M Temperature Thermal if Quantum We define: log [ time ( s ) ] RMR( x) Sappey et al, Europhys. Lett. 37, 639 (1997) S( T, x) S( T ) T ( K ) RMR 1..5 Calculated RMR (x) ( i ) U U +5 U - 5 T * ( K ) ( i i ) T ( K ) T =.5 K T cr = 1 K x thermal quantum 2 1 ( i i ) ( i ) 1 2 RMR is sensitive to T * (T) while being extremely insensitive to other poorly known quantities.

16 γ-fe 2 O 3 d~7nm, σ d =.3 x v =.43%, in silica estimated T cr ~.1 K Maghemite nanoparticles S = d M / d ln(t) ( a.u. ) S ( a. u. ) T ( K ) RMR K.1 K.5 K 1. K 2. K 3. K T ( K ) x Sappey et al, EPL 37, 639 (1997) and JMMM 221, 87 (2) Clear anomalies below.5k Intermediate between pure quantum and thermal Distribution of crossover temperatures

17 CoFe 2 O 4 d ~ 5.7 nm, σ d =.2 x v =2.3%, in water estimated T cr ~5K Cobalt ferrite nanoparticles S (1-6 emu / decade ) T ( K ) Sappey et al, JMMM 221, 87 (2) RMR K 1 K 1 K 6 mk 1 mk 15 mk 2 mk 5 mk Clear QTM-like for T<15mK (flat RMR) But at T~3-1K RMR does not go to zero: more complex behaviour than simple model (defects? surface effects?) X

18 Eugene Chudnovsky in Barcelona, discussing with the experimentalists

19 1. Low-temperature dynamics: thermal or quantum? 2. Super-spin glass state

20 Ineracting Co nanoparticles in Ag matrix: superspin glass state (Co x Ag 1-x, metal matrix RKKY interactions) X.X. Zhang group, Phys. Rev. B75, (27) Magnetization (a.u.) FC ZFC (a) x = 9.6% χ -1 (arb.) (c).4.3 FC.2 ZFC x = 19.4% χ -1 (arb.) T (K) T = 47K T (K) T (K) T = 79K FC ZFC χ -1 (arb.) (b) x = 12.7% S1 T = 54K 1 2 T (K) S2 S3 With increasing concentration x : increasing 9.6 interparticle 12.7 interactions, 19.4 x (%) seen as: - increase 3 K 44 K 84 K T B of T B and T, - flattening of FC curve 47 K 54 K 79 K Tsuperspin glass state

21 Spin glass: aging, rejuvenation and memory effects χ'' x 1 3 [emu/cm 3 ] 1,4 CdCr 1.7 In.3 S 4 1,2 1,,8,6,4,2.1 Hz Refroidissement par paliers Réchauffement continu, T [K] «memory dips» experiments: Uppsala / Saclay PRL 81, 3243 (1998) Bouchaud et al, Phys. Rev. B 65, (21) See details and references in e.g. cond-mat/63583 T [K] K/s t [s] χ -relaxation: aging T : rejuvenation T : memory

22 Temperature (K) Memory effect in a superspin glass γ-fe 2 O 3 nanoparticles in water d=8.5nm 1x1 4 2x1 4 3x1 4 4x1 4 5x1 4 6x1 4 time (s) Φ=35% χ" (emu/cm 3 ) χ"-χ" ref χ" cooling χ" heating Temperature (K) no visible rejuvenation but clear memory effect.5. Reference cooling with stop at 6K reheating V. Dupuis et al, AIP Conf. Proc. 832, 295 (26) Temperature (K)

23 Memory effect in Co nanoparticles Co 2 Ag 8 granular film M (emu) M (emu) 4.x x x x1-4 8.x1-5 9.x1-6 6.x1-6 3.x1-6. S3 Ref. aged at 57 K for 6 hrs M/M = 2.8% T (K) aging at T w.7 T B for 6 hrs M/M 2.8% J. Du et al, Phys. Rev. B 75, (27) (X.X. Zhang group, HKUST)

24 Concentrated Fe 3 N nanoparticle system Clear T-specific memory effect, although not so well-marked as in atomic SG s Time scales are different: SG τ 1-12 s SSG τ 1-9 s or much longer Longer τ shorter accessible time scale t exp /τ bridge the time gap between real and numerical spin glasses see Wandersman et al, EPL 84, 3711 (28)

25 Conclusions Despite the problem of size distribution, strong deviations from thermal activation have been identified in assemblies of magnetic nanoparticles (RMR method) macroscopic Quantum Tunneling of Magnetization Concentrated suspensions of (interacting) magnetic nanoparticles may behave as a superspin glass Memory effects are seen like in spin glasses Will bridge the gap between spin-glass simulations and experiments Happy birthday Eugene!