Experimental investigation of Superspin glass dynamics

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 lEtat 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?

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
?-Fe2O3 nanoparticles

• ?-Fe2O3 nanoparticles dispersed in H2O1
• Citrate molecules adsorbed onto particle surface
  to prevent aggregation
• Mean diameter 8.5 nm
• Lognormal distribution of particle size (s
  0.25)
• Volume fractions (F) ranging from 0.01 ?35
• Dipole-dipole interaction energies varying from
  ltlt 1 K to 45 K

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 ? peak with frequency as expected
  for both superparamagnets and spin glasses
• We can apply Arrhenius Law
• t t0 exp (Ea/kBTpeak)
• For dilute sample (F 1 ) t0 10-9 s
• For concentrated sample (F 35 ) t0
  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)
8
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

9
Temperature Cycling

T1 60 K 0.6 Tg
t2 t0 eB/(T1-?T), teff t0 eB/T1 If B is
constant with T (simple thermal slowing down) ?
teff/t2 (t2/t0)-?T/T1 With t0 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)
10
Thermoremnant Magnetisation (TRM)

• In an atomic spin glass curves scale t/tw µ
• Horizontal spacing of relaxation curves much less
  than seen for atomic spin glasses (µ ltlt1?)
• but tinflection tw (indicating µ 1) as in
  spin glasses

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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 ? ltEagt ltJgt
• Only smallest particles will have Ea ltlt ltJgt (as
  in an atomic spin glass)
• Larger particles with Ea ltJgt may relax
  independently of interparticle interactions
• ? correct M/MFC by subtracting B ln(t/t0) term
  to account for superparamagnetic-like relaxation
  of larger particles

• Scaling of the relaxation curves can be achieved
  after subtracting B ln(t/t0) term
• Scaling parameters are comparable to those found
  for atomic spin glasses

?/twµ tw1-µ (1t/tw)1-µ -1/1-µ t/twµ
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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 t
  arising from particle volume distribution ? leads
  to slow dynamics which can evolve during tw

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)
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Zero Field Cooled Relaxation

• Observe a positive relaxation of the ZFC
  magnetisation
• Adding a B ln(t/t0) 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

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Conclusions

• Concentrated dispersion of ?-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/t0), 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