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INDUCED TEXTURE IN A FERROFLUID : A
MÖSSBAUER STUDY
A. Meagher, S. Charles, S. Wells
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, SuppI6ment au no 12, Tome 49, dkcembre 1988
A. Meagher (I), S. W. Charles (2) and S. Wells (2)
(I) Laboratoriet for Teknisk Fysik, Danmarks Tekniskc Hojskole, Bygning 307, DK-28U0 Lyngby, Dartmark
(2) Adran Ffiseg, Coleg Prifysgol Gogledd Cymru, Bangor, GB-LL57 ZUW Gwynedd, Cymru, G.B.
Abstract. - Magnetic field induced texture in a 7
-
Fe203 ferrofluid is measured using Mossbauer spectroscopy. The amount of alignment saturates at 0.1 T and above at a relatively low value. We compare our results with those expected for a system of non-interacting particles with uniaxial anisotropy.Recently, building on the early work of Martinet [I], several authors 12-61 have investigated the orien- tational texture present in a frozen ferrofluid after it has been cooled in the presence of a magnetic field. Experimental techniques used included magnetization and susceptibility measurements. Here we wish to re- port our results on field induced texture as measured using 5 7 ~ e Mossbauer spectroscopy. This technique has been used previously to investigate relaxation phe- nomena in ferrofluids 17, 81 or as a fingerprint method for identifying the form of iron in a ferrofluid [9], but it has not, t o our knowledge, been applied to investi- gate texture in ferrofluids. It has, of course, been used to measure the texture in magnetic tape materials [lo, 111.
A ferrofluid os synthetic Fe301 particles in a diester carrier liquid (Reomol DioZ) was prepared using a phosphate ester surfactant. During the course of time the Fe304 particles tended to oxidize t o 7 -Fe203. We used old samples, consisting mainly of 7-Fe203 for the texture experiments. Electron microscopy showed that the particles are about 7 nm in diameter. Our sample was disc shaped. The 7-ray direction n was always nor- mal t o the plane of the sample, while both the external magnetic field applied during measurement, B,, and the texture inducing field, Bat were applied in the same direction in the sample plane. Tlie sample was cooled at a rate of about 10 K/min in Bat from room temper- ature to 77 K and measured at this latter temperature (T,) in B,,. The temperature at which the particles freeze (Tf) is about 240 K. For the Mossbauer mea- surements a source of "CO (Rh) at room temperature was used. Experimentally we measure the degree of texture by obtaining the intensity ratio between lines 2 f 5 and lines 1
+
6 in the Mossbauer spectrum. This ratio is given by,where
x
is the angle between the 7-ray direction n and the magnetic field direction at the iron nuclei in the sample. For collinear ferrimagnets such as7
-
Fez03 the magnetic field direction at the nuclei is (anti)parallel to the particle moment direction. Asx
varies between 0 and 90 degrees A25/A16 will vary between 0 and 413.Figure 1 shows A25/A16 as a function of the mag- nitude of the texture inducing field Bat. Data points are presented for two values of the field applied dur- ing measurement (B,)
,
zero and 13 mT (also applied perpendicular to the 7-ray direction). Despite some scatter in the data points, it is clear that A25/A16 ini- tially increases and reaches a plateau for Bat>
0.1 T. The plateau level depends strongly on the value ofB,,,
being 0.85 for B, = 0, and 1.22 for B, =13 mT. We observe no difference in the plateau level between B,, = 13 mT and Barn = 0.675 T , i.e. the plateau does not reach the theoretically expected value of 4/3. This means that all the spins are not aligned perpendicular t o n, perhaps due to pinning of the sur- face spins 1121. Recently Bacri et aI. 1131 have found that 50-100 diameter particles of y
-
Fez03 in a fer- rofluid have a saturation magnetization 24 % less than for the bulk material. In our case, we only need 20 % random spins (giving Az5/Ars = 213) to lower the ave- rage value of A25lAls from the theoretical maximum of 413 to the observed 1.22.In order to understand whether these results are compatible with a model of non-interacting particles we simulate the results expected for such a model and compare with the above results.
We assume that the ferrofluid may be modelled as a
Fig. 1. - A25/A16 as a function of Bat in Tesla. The upper curve corresponds to B, = 13 mT while the lower curve is for B,, = 0.
C8 - 1846 JOURNAL DE PHYSIQUE
system of identical non-interacting single domain par- ticles with uniaxial anisotropy and a lognormal dis- tribution [14] of particle sizes, with u = 0.35 as is typically found for such materials. The orientational- dependent energy E of a single particle in an externally applied magnetic field Ba is given by
where K is the magnetic anisotropy constant, V the volume and p the magnetic moment of the particle. e, u, and b are three unit vectors in the direction of, re- spectively, the particle easy axis, the particle magnetic moment, and the applied field. At thermal equilibrium we have probabilities P given by
P (e, u) = exp (- E/kT)
/
exp (- E/kT).
The measured parameter in our experiment A25/Als depends on C O S ~ ~ ( = ( n . ~ ) ~ for simple ferrimagnets).
A program has been written to numerically calculate Az5/Al6 using the above model. TO numerically simu- late the averaging over the surface of a sphere we use the 50 points and appropriate weighting factors given by McLaren [15]: our routine is adapted from that given by Stroud [16]. We assume that e and u are initially distributed over these 50 directions according t o the Boltzmann distribution, but that the easy axes freeze as the temperature is lowered through Tf. If we assume that K V and p do not change with tempera- ture, then there are three independent variables in the calculation. These areThe calculated values of Az5/A16 from the program are given a weighting of 80 % and added t o a value of A25/A16 = 213 with a weighting of 20 % (represent- ing the pinned spins) before being compared with the experimental results.
It has proved impossible to reproduce all the results of figure 1 within the limitations of the above model.
-
Consider the lower curve measured in zero field, so pBam/kTm = 0. The two remaining variables then control the height of, and speed of approach to, the plateau. KV/kT, = 10.5 gives the correct plateau value while pB/kTf = 5 describes the point where A25/A16 has risen halfway from its texture-free value to the plateau. These values correspond t o reasonable values of K V and p for N 10 nm y
-
Fez03 particles.However the upper curve of figure 1, obtained with B, = 13 mT cannot be reproduced using the same values of KV/kTm and pBat/kTf no matter what value is chosen for pB,/lcT,.
One probable reason for the failure of the simple model is the occurrence of field induced particle chain- ing, an effect observed by Goldberg et al. [17] for
Bat = 0.2 T. Hartmann and Mende [4] suggest that fields greater than 0.13 T would be needed to produce field induced agglomeration in their ferrofluid. Thus it is quite plausible that the plateau regions in figure 1 correspond t o chains of particles. Nevertheless there is an increase in A25/A16 with Bat at low values of B,, (less, say, than the 50 mT up to which Reed and Fendler 1181 have found no evidence for field induced chaining). We consider this as evidence for the field induced orientational texture of single particles in a ferrofluid.
Acknowledgements
We thank S. Morup and J. van Wonterghem for a useful collaboration.
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[6] Chantrell, R. W., Ayoub, N. Y. and Popplewell, J., J. Magn. Magn. Mater. 53 (1985) 199. [7] Winkler, H., Heinrich, H.-J. and Gerdau, E., J.
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[lo]
Pfannes, H. D. and Gonser, U., Appl. Phys. 1(1973) 93.
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