Experimental investigation of Superspin glass dynamics Dinah Parker1, E. Dubois2, V. Dupuis3, F. Ladieu1, G. Mériguet2, R. Perzynski3 and E. Vincent1 1Service de Physique de l’Etat Condensé DSM/DRECAM, CEA-Saclay (CNRS URA 2464) 2Laboratoire des Liquides Ioniques et Interfaces Chargées,Université Pierre et Marie Curie 3Laboratoire des Milieux Désordonnés et Hétérogènes, Université Pierre et Marie Curie Work supported by EC program DYGLAGEMEM

Superspin Glasses Small magnetic nanoparticle→ single domain magnetism Response of single nanoparticle ~ response of single spin → a ‘superspin’ Varying concentration of nanoparticles in a liquid dispersion changes interparticle interaction To what extent do superspin glasses behave like atomic spin glasses? Dilute nanoparticle system superparamagnet (non-interacting superspins) Concentrated nanoparticle system Superspin glass (interacting superspins)

Summary of previous work on superspin glasses Experimental investigations of superspin glasses have revealed some similarities with atomic spin glasses including The behaviour of the AC and DC magnetisation vs. temperature Critical behaviour indicative of collective dynamics (derived from AC susceptibility measurements) Aging and memory effects Uppsala University, Sweden- P. Nordblad, P. Jönsson, P. Svedlindh, M. F. Hansen, T. Jonsson, J. García-Palacios National Research Institute for Metals, Tsukuba, Japan- H. Mamiya, I. Nakatani, T. Furubayashi University of Tokyo, Japan- H. Takayama, M Sasaki, P. Jönsson University of Versailles/University of Pierre and Marie Curie, France and Institute of Materials Chemistry, Italy- J. L. Dormann, E. Tronc, M. Noguès, D. Fiorani

γ-Fe2O3 nanoparticles γ-Fe2O3 nanoparticles dispersed in H2O1 Citrate molecules adsorbed onto particle surface to prevent aggregation Mean diameter ~ 8.5 nm Lognormal distribution of particle size (σ ≈ 0.25) Volume fractions (Φ) ranging from 0.01 % →35 % Dipole-dipole interaction energies varying from << 1 K to ~ 45 K g-Fe2O3 1F. Gazeau, J. C. Bacri, F. Gendron, R. Perzynski, Yu. L. Raikher, V. I. Stepanov and E. Dubois, J. Magn Magn. Mat. 186 (1998) 175

DC Magnetisation vs. Temperature Measurements Dilute sample shows increase in FC magnetisation below TB→ indicative of superparamagnetic-like behaviour In concentrated sample FC curve is flattened below Tg → characteristic of atomic spin glass behaviour Increase in transition temperature seen in concentrated sample

Field Effects High fields give a flattening of the ZFC peak and a decrease in Tg, also seen in atomic spin glasses Observe a decrease in M/H with increasing H Tpeak remains constant up to ~ 5 Oe, much lower than for an atomic spin glass Typical superspin ~ 104 spins → enhanced Zeeman coupling w.r.t. atomic spin glasses

AC Susceptibility vs. Temperature Measurements See shift in χ’ peak with frequency as expected for both superparamagnets and spin glasses We can apply Arrhenius Law: τ = τ0 exp (Ea/kBTpeak) For dilute sample (Φ = 1 %) τ0 ≈ 10-9 s For concentrated sample (Φ = 35 %) τ0 ≈ 10-19 s → unphysically small as found for atomic spin glasses Suggests collective behaviour driven by interparticle interactions Previous studies have confirmed existence of a critical slowing down reminiscent of spin glass behaviour1 1 M F Hansen, P Jönsson, P Nordblad and P Svedlindh, J. Phys.:Condensed matter, 14, 4901 (2002)

Memory effects Make a stop during the cooling for 20000 s at 60 K (≈ 0.6 Tg) See relaxation of the AC susceptibility On reheating at constant rate the susceptibility follows the cooling curve Memory effect Multiple memory dips can be made

Temperature Cycling t2 = τ0 eB/(T1-ΔT), teff = τ0 eB/T1 Tg t1 T t t2 t3 ΔT T1 T2 T1 = 60 K = 0.6 Tg t2 = τ0 eB/(T1-ΔT), teff = τ0 eB/T1 If B is constant with T (simple thermal slowing down) → teff/t2 = (t2/τ0)-ΔT/T1 With τ0= 10-9s, data is inconsistent with calculation Similar to Heisenberg-like spin glasses1 1 V. Dupuis, E. Vincent, J-P Bouchaud, J. Hammann, A. Ito, H. A. Katori; Phys. Rev. B 64 174204 (2001)

Thermoremnant Magnetisation (TRM) t tw Tm T H tw = waiting time t = measuring time TRM protocol TM= 0.7 Tg (71 K) H = 0.5 Gauss Φ = 35 % In an atomic spin glass curves scale ~ t/tw μ Horizontal spacing of relaxation curves much less than seen for atomic spin glasses (μ <<1?) but tinflection ≈ tw (indicating μ ~ 1) as in spin glasses

Scaling of the TRM curves Distribution of particle size leads to distribution of anisotropy energies (Ea = KV) Average anisotropy energy of the same order as average dipole-dipole interaction → <Ea> ~ <J> Only smallest particles will have Ea << <J> (as in an atomic spin glass) Larger particles with Ea ≥ <J> may relax independently of interparticle interactions → correct M/MFC by subtracting –B ln(t/τ0) term to account for superparamagnetic-like relaxation of larger particles Scaling of the relaxation curves can be achieved after subtracting –B ln(t/τ0) term Scaling parameters are comparable to those found for atomic spin glasses *λ/twμ = tw1-μ [(1+t/tw)1-μ -1]/[1-µ] ≈ t/twμ

Do these TRM results conclude spin glass physics? No! Aging observed in TRM experiments can be attributed to superparamagnetic behaviour. 1,2 Simulations of non-interacting nanoparticle systems have shown aging and memory effects1 Aging observed due to the wide distribution of τ arising from particle volume distribution → leads to slow dynamics which can evolve during tw Not the case for the ZFC relaxation procedure as system is in ‘effective equilibrium’ during tw Only aging in TRM and ZFC experiments can indicate spin glass physics g t tw Tm T H tw = waiting time t = measuring time TRM protocol g t tw Tm T H tw = waiting time t = measuring time ZFC protocol 1 M. Sasaki, P.E. Jönsson, H. Takayama and H.Mamiya, Phys. Rev. B 71 (10) 104405 (2005) 2 M Sasaki, P Jönsson, H Takayama, Nordblad P; Phys. Rev. Lett. 93, 139701 (2004)

Zero Field Cooled Relaxation Observe a positive relaxation of the ZFC magnetisation Adding a –B ln(t/τ0) term enables scaling of the relaxation curves ZFC relaxation curves can be roughly scaled with parameters similar to those for the TRM procedure Indicates collective dynamics, not simply a relaxation of the superparamagnetic state

Conclusions Concentrated dispersion of γ-Fe2O3 nanoparticles shows many similarities with atomic spin glasses - characteristic M vs T behaviour - memory effects in AC susceptibility - T-shift relaxation behaviour similar to Heisenberg spin-glass Aging is seen in both TRM and ZFC relaxation experiments We propose a new term, –B ln(t/τ0), to account for superparamagnetic relaxation in the superspin glass relaxation curves Scaling of the relaxation curves gives parameters comparable with those found for atomic spin glasses