HAL Id: jpa-00229097
https://hal.archives-ouvertes.fr/jpa-00229097
Submitted on 1 Jan 1988
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
SUSCEPTIBILITY PEAKS IN A FINE PARTICLE
SYSTEM
M. El-Hilo, K. O’Grady, J. Popplewell, R. Chantrell, N. Ayoub
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, dkcembre 1988
SUSCEPTIBILITY PEAKS IN A FINE PARTICLE SYSTEM
M. El-Hilo (I), K. 07Grady (I), J. Popplewell (I), R. W. Chantrell (') and N. Ayoub (3.)
( I ) Department of Physics, U.N.C. W., Bangor, Gwynedd, LL57 BUW, G.B.
( 2 ) School of Physics, Lancs. Polytechnic, Preston, P R I ZTQ, G.B.
(3) Department of Physics, Yarmouk University, Irbid, Jordan
Abstract. - From measurements of the peaks in the dc susceptibility with concentration, for a system of FesO4 particles,
we have obtained a simple power-law relationship between Tg (temperature at Xm,) and I, (the saturation magnetisation of the dispersion) i.e., Tg cc
C .
The change in Tg is shown to be driven by dipolar interactions between the particles.I n t r o d u c t i o n
The behaviour of a fine particle system in a small ap- plied field, as a function of temperature is well known [l-31. These previous reports do not include the effects of dipolar interactions between the particles, which are discussed for ac measurements by Dormann et al. [4]. This behaviour is important because it is directly anal- ogous t o the behaviour of certain spin-glass alloys [5]. Here we consider the behaviour of small particle sys- tems in dc fields.
In a solid matrix the magnetic moment of an isolated single-domain particle will align with the applied field
via the NBel process [6].
7-'
=
fo exp ( - K V / k T ) . (1) At low temperature the vast majority of the mo- ments are unable t o rotate over the anisotropy bar- riers during the time of measurement and are termed blocked. For a dc measurement this measurement time is taken to be 100 seconds giving K V5
25 IcT, forfo = 10' sec. [7].
In any system there will be a distribution of particle sizes giving rise t o a distribution of blocking tempera-
and solid below 200 K. From electron microscopy we determined the physical size and the form of the dis- tribution of the particle sizes. For the sample exam- ined a lognormal distribution was found with median diameter
D,
= 9.5 nm and u = 0.3. All magnetic measurements were made using a PAR 155 vibrating sample magnetometer fitted with and Oxford Instru- ments CFL200 flowing gas cryostat. The room temper- atur magnetisation measurements were used t o find the magnetic size following the method of Bradbury et al. [lo] which gives values corrected for the effects of dipolar interactions, D,, = 8.2 nm and a, = 0.37.Measurements of the peak in the dc susceptibility were made for nine different concentrations prepared by diluting the original sample. Measurements were
-
-made after the samples were frozen in zero field (ran- domly oriented anisotropy axes) and then warmed up in the presence of a small field
(H
= 22.8 0.1 Oe).
For each sampleTg
was determined from the maxi- mum in the initial susceptibility curve with an error(F
2 K). All the values of T, were found to lie within a range (95 K --+ 140 K) which is well below the freezing point of the colloid ( N 200 K).
ture TB a t which KV
5
25 ~ T B . As the temperature and discussion is raised the initial susceptibility X i increases due t othe increase in the fraction particles for T
>
T~ Figure 1 shows plots of the susceptibility versus tem- thermalag,tat.on reduces the value ofX, following the
perature for four of the concentrations examined. Fig- Langevin function giving rise t o a peak a t a tempera-ture Tg. This peak is broader and more rounded than that expected for isolated monodispersed particles.
Fine particle systems are known to follow Curie- Weiss behaviour due t o the dipolar interactions in the ensemble [8]. The interactions in a solid dispertion in general produce apparent negative ordering tempera- ture
ON
which arises due t o progressive (un) blocking of particle moments and the dipolar coupling. E x p e r i m e n t a lA fine particle dispersion containing magnetite par-
ticles has been prepared by precipitation of the parti- cles from a mixed solution of ferric and ferrous salts[9], The dispersion was liquid a t room temperature Fig. 1. - The variation of Xi with temperature.
C8
-
1836 JOURNAL DE PHYSIQUEure 2 shows the values of T g from frigure 1 and the other samples plotted on logarithmic axes. These data clearly show the power law dependence of Tg on the saturation magnetisation (I,) which gives T, cc
17,
where m = 0.171 0.005.
2.1L LOGTTg)
LOG (IS)
1.90
00 0 3 0.6 0.9 1 2 Fig. 2.
-
Log (I,) versus Log ( T g ) .The origin of the increase in Tg with particle concen- tration lies in the naure of dipolar interactions in the dispersion. In the absence of interactions the suscepti- bility would be given by a simple Curie law integrated over the particle size distribution, up to the critical diameter
D,.
With dipolar coupling between the mo- ments Curie-Weiss behaviour is anticipated givingwhere I: is the saturation magnetisation for the bulk material.
In order to account for the increase in T,, 6' has to be negative ( 0 ~ ) implying antiferromagnetic coupling be- tween the particle moments. Figure 3 shows the vari- ation of 1/X; with temperature giving a negative or- dering temperature which increases in magnitude with
Fig. 3. - The variation of
l/xi
with temperature.increasing concentration. It is interesting to note that the negative ordering temperature can be accounted for by progressive (un) blocking of the moments in the distribution but the increase in the value of
ON
with concentration can be only explained by the coupling of the moments.Another point of interest is the factors affecting the value of the parameter m. We believe that m is de- termined by the particle size in the sample whereby m decreases as the particle size increases. This may be indicative of the presence of small atomic clusters of iron in Au/Fe spin-glasses which gave a value of
m = 0.54
as
reported by Cannella and Mydosh [5].A full theoretical study relating to the effect of the dipolar interactions on the value of Tg will be presented in a separate publications 1111.
[ I ] Tari,
A.,
Popplewel, J. and Charles, S. W., J.Magn. Magn. Mater. 15-18 (1980) 1125. [2] Gittleman, J . I., Abelas, B. and Bozowski, S.,
Phys. Rev. B 9 (1974) 3891.
[3] Khater, A., F e d , J. and Meyer, P., J. Phys. G
20 (1987) 1857.
[4] Dormann, J . L., Bessais, L. and Fiorani, D., J.
Phys. C 21 (1988) 2015.
[5] Cannella, V . and Mydosh, J. A., Phys. Rev. B 6 (1972) 4220.
[6] NBel,
L.,
G. R . Acad.Sci.
228 (1949) 664. 171 Been, C. P. and Livingston,J. D.,
J. Appl. Phys.30 (1959) 1205.
[8] O'Grady, K., Bradbury, A., Charles, S. W., Me- near,
S., Popplewell, J., J. Magn. Magn. Mater.
31-34 (1983) 958.
[9] Khalafalla, S. E. and Reimers, G.
W.,
I E E ETrans. Magn. MAG-16 (1980) 178.
[ l o ] Bradbury, A., Menear, S., O'Grady, K. and Chantrell, R. W., IEEE Trans. Magn. MAG-20
(1984) 1846.
