Spin glass behaviour in interacting magnetic nanoparticles

D. Parker, F. Ladieu, D. L’Hôte, S. Nakamae, J.-P. Bouchaud and E. Vincent Service de Physique de l’Etat Condensé (SPEC) CEA Saclay (France) E. Wandersman, V. Dupuis, E. Dubois, R. Perzynski Laboratoire des Liquides Ioniques et Interfaces Chargées Université Pierre et Marie Curie – Paris (France)

Spin glass, superspin glass: introduction

What is a spin glass ? Theory : random bonds

= - Jij Si.Sj

{Jij} gaussian, or ±J

a disordered and frustrated magnetic system "Real" spin glasses : random dilution of magnetic ions Jij example: metallic alloys, Cu:Mn 3% RKKY interactions same generic behaviour in all samples (Tc≠0 in 3d, slow dynamics, aging...)

→ « model » disordered systems

rij

SPIN GLASS: HISTORY-DEPENDENT BEHAVIOUR 0.08

3

M/H (emu/cm )

FC

para (~1/T)

0.06 0.04 TRM

Tg

ZFC

0.02

CdCr1.7In0.3S4 H=10G

ZFC 0.00 0

5

10

15

20

25

30

T (K)

FC ≡ Field-Cooled magnetization ZFC ≡ Zero-Field Cooled magnetization TRM ≡ Thermo-Remanent Magnetization

35

40

Super-spins, superspin glass • Small enough ferromagnetic nanoparticle

single domain

• T

close to 1

0.12 1000 1000

100

1000

time (s)

10000

100000

10000

tinflection

?

0.018 0.20

0.016 0.015 0.16

0.014

M/M FC

-d(M/MFC)/d(logt)

0.017

0.013 0.012 0.011

µ = 0.4

0.12

0.010 100

1000

10000

100000

time (s)

*(or

more precisely /tw = tw1- [(1+t/tw)1- -1]/[1-µ]

1

t/tw )

10

100 µ

λ/tw

1000

Accounting for relaxation of independant particles • Distribution of particle size → distribution of anisotropy energies Ea = KV • Small particles have Ea