1. 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

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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 ≈ 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)

8. Memory effects
Make a stop during the cooling for 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

9. Temperature Cycling t2 = τ0 eB/(T1-ΔT), teff = τ0 eB/T1Tg 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 (2001)

10. 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

11. 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

12. 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) (2005)
2 M Sasaki, P Jönsson, H Takayama, Nordblad P; Phys. Rev. Lett. 93, (2004)

13. 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

14. 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