Hyperfine Field in Nano Particles

5.5.1. Hyperfine Field in Nano Particles

The Mössbauer spectra taken at 4°K are shown in Figure 5.13 for all the samples except for the 600 sample. It is seen that at very low temperature, all the samples give rise to a magnetic hyperfine field at the 57 Fe nuclei. It is definitely remarkable to note that by doing sensitive experiments like Mössbauer spectroscopy (see the section 1.6.1 for theoretical details), which is based on the details of the nucleus of the Fe ions/atoms even within a very narrow particle size range of nano particles, two different behaviour are manifested by the same nano particles within the same glass matrix at different tempera- tures of measurements, i.e. due to relaxation mechanism of magnetization or spin flip-flops. The lower the temperature, the slower is the relaxation, and we are able to ‘arrest’ or ‘detect’ the same nano particles in two different forms, i.e. super-paramagnetic and ferrimagnetic. While it shows the useful- ness of doing sensitive experiments like Mössbauer at different temperatures, it also indicates a remark- able behaviour of the magnetic nano particles.

It is seen from Figure 5.13 that the HFS lines of the magnetic spectrum are very broad and shallow for the blank glass. They become sharper from the 650 to the 900 sample. A computer curve fitting is carried out for each spectrum, except for the blak glass wherein the error is too high, by assuming the ‘superposition’ of a magnetic spectrum, a central doublet and an additional doublet due to

Fe 2+ ions. The experimental magnetic spectrum is fitted (i.e. the solid lines of Figure 5.13) by assuming two overlapping of two six-line HFS spectra and by taking only the ‘four external lines’ into account. The hyperfine field for the last four samples is found to be around 510 KG, as for the Fe 3+ ions in the tetrahedral site (i.e. A - site) of the bulk magnetite [29].

The Mössbauer data at 4°K are consistent with the presence of magnetite in all the samples, except in the blank glass and 600 samples. They confirm the results of XRD and TEM measurements, as described in the section 5.3.1. The areas under the concerned peaks are kept in the ratio 3 : 2 : 1 : 1 : 2 : 3. The relative concentrations of various species are also shown in Table 5.1. The largest proportion of magnetite is found to be present in the 700 sample. The values of the %Fe 2+ given by the experiments at 4°K agrees with those obtained from room temperature measurement within experimental error. By lowering the temperature does not significantly alter the values of the Mössbauer parameters of these ions.

Table 5.1. The Mössbauer Data for Nano Particles of Magnetite

Heat-Treatment 300°K

4°K 4°K Temperature

%Fe 2+ %Superpara %Ferri As-annealed

%Fe 2+

%Superpara

%Ferri

NANO MATERIALS

BLANK GLASS

0 5.145 VELOCITY mm/s

Figure 5.13 : The Mossbauer spectra at 4°K.

The magnetite present in the samples gives a ‘magnetically split’ spectra at 4°K. The magnetic splitting completerly collapses at room temperature, except for the 800 and 900 samples, due to the faster flip-flops or faster relaxation above the so-called blocking temperature, which is a typical behav- iour of small nano particles of magnetite. Below the Curie temperature of the bulk magnetite (i.e. 851°K)

197 and above the so-called blocking temperature, the thermal energy or thermal vibrations of the magnetite

MECHANICAL PROPERTIES

lattice can cause ‘many reversals’ of the direction of the magnetization in each nano particle during the time of measurement (i.e. spin flipping). An assembly of such nano particles is in a super-paramagnetic state. However, below the so-called blocking temperature, the direction of magnetization is ‘frozen-in’. The value of the blocking temperature depends on the particle size of the nano particles. Each sample contains a ‘distribution’ of particle sizes of the nano crystals of magnetite. At a given temperature, in one sample, it is then possible to find out a mixture of super-paramagnetic and ferrimagnetic particles, which is clearly evident in the 800 and 900 samples at room temperature (see Figure 5.11).

In several studies of various small particles of magnetite in the nano range, it is reported that the magnetic hyperfine splitting field below the blocking temperature is smaller than that found in larger crystals [30-32]. The Mössbauer data of the 800 and 900 samples clearly confirm this particular obser- vation. The values of the ‘hyperfine field’ are found to be 410 KG and 450 KG respectively for these two samples. In the bulk magnetite, McNab et al found a value of 486 KG [29]. This interesting obser- vation could be due to an “intrinsic size effect” [32] of the small nano particles of magnetite, or in other words, due to a “collective magnetic excitation” mechanism proposed by Morup and Topsoe [31]..

It has already been said above that the small “nano” particle has a ‘single domain’ structure. The thermal energy or thermal vibration at the temperature of the experiment can be sufficient to equilibrate the magnetization in a time span which is “short” compared to that of the experiment, i.e. a super- paramagnetic state with a continuous spin flipping or faster relaxation that are difficult to be blocked above the so-called blocking temperature. In an assembly of single domain nano particles, below their Curie temperature, the frequency “f ”, at which the gross particle magnetic moment ‘flips’ amongst the easy direction of magnetization, is much greater than the larmour precession frequency (i.e. ν L ) of the

Mössbauer nucleus 57 Fe. Since this precesion time (i.e. 1/ν L ) is about 10 –8 sec, very small particles with

a size less than 10 nm are required so that the ‘anisotropy’ energy per particle KV ≈ k B T. This criterion must be satisfied, since the anisotropy energy ‘governs’ the frequency of the ‘spin flipping’, i.e. relaxa- tion, of the magnetization vector, when H ext = 0. The relaxation time is written as follows :

(5.8) where, τ = 1/f is the time for the magnetic moment to flip through 180° , the particle frequency factor

τ =τ 0 exp(KV/ k B T)

(τ 0 ) is usually 10 –10 – 10 –9 sec, K is the anisotropy constant, V is the volume of the nano particle, and k B T is the thermal energy.

In large volume particles, i.e. bulk magnetite, KV is very large, and consequently τ >> 1/ν L . Hencece, a six-line HFS pattern is observed, when the Mössbauer experiment is performed, e.g. for the 650 sample at 4°K. On the other hand, when τ << 1/ν L , the nucleus can precess at a set frequency only

for a small part of a period before H hf can changes the direction. The “net result” of many such changes or “spin flips” in the direction of H hf is no ‘precession’ at all, i.e. H hf = 0, and consequently a central doublet is observed corresponding to super-paramagnetic Fe ions in the nano-crystalline magnetite phase,

e.g. for the 650 sample at room temperature (compare Figures 5.11 and 5.13) [9]. For the 900 sample, there is a distribution of sizes of the nano partcle, which gives rise to a

‘superimposed’ spectra. For example, for some nano particles τ >>1/ν L giving rise to six-line HFS pattern, and for some nano particles τ << 1/ν L giving rise to the central doublet, which is superimposed on the HFS pattern. The computer fitting work is done based on these premises, which also minimizes the error in the least square fitting procedure in the Lorentzian analysis..

As noted above, the value of H hf in small nano particles of magnetite is smaller than the bulk magnetite. It is known that when the particles are small, then there are significant number of ‘spins’ on

NANO MATERIALS

the surface of the nano particles. It can be argued that the surface ions have smaller hyperfine field than that of the ions in the interior of the nano particles giving rise to smaller average H hf due to the surface effect [32, 33]. Here, it is quite pertinent to consider the model proposed by Morup and Topsoe [31], which states that the lower value of H hf results from ‘fluctuations’ of magnetization direction around the energy minimum corresponding to an ‘easy’ direction of magnetization, e.g. <1 1 1> direction of magnetite. Morup and Topsoe could fit their experimental results of the Mössbauer spectra for small particles of magnetite without taking any ‘surface effect’ into account [31].

In this model, for k B T/KV << 1, the hyperfine field for a particle of volume V at a temperature T can be given by the relation :

H hf (V, T) = H hf (∞, T)[1 – (k B T/2KV)]

(5.9) There is an important implication of equation (5.9), i.e. at T ≈ 0°K, H hf will be simply independ-

ent of the particle size. In order to test this model, the Mössbauer experiment should be made at very low temperature (say, at 4°K) with the samples having different particle sizes, like in this present case from

4.5 nm to 7.0 nm. As shown in Figure 5.13, from the Mossbauer spectra at 4°K for the 650, 700, 800 and 900 samples, a value of H hf is obtained as 510 KG, which is remarkably independent of particle size even within this narrow range of nano particles. McNab et al found a value of 511 KG for H hf at 4°K for pure magnetite with particle size less than 10 nm. Thus, this is the first experimental confirma- tion of ‘collective magnetic excitation’ or “magnon” model of Morup and Topsoe [31] for small nano particles of magnetite of varying sizes (4.5 nm to 7.0 nm) embedded in an inert/non-magnetic glassy or amorphous matrix. This has a tremendous implication for various applications in nano-magnetic de- vices.

The particle size of magnetite in the 900 sample is known from XRD as 7.0 nm. Thus, the anisotropy constant (K) could be calculated from equation (5.9), by taking the value of H hf from the 300°K spectra, i.e. 450 KG. The anisotropy constant (K) is found to be 0.98 × 10 6 erg/cm 3 . For the 800 sample, the value of K is found to be 0.77 × 10 6 erg/cm 3 , by taking the estimated particle size of 6.4 nm and the value of H hf as 410 KG . Therefore, the anisotropy constant could be considered to be of the order of ~ 10 6 er/cm 3 , which is very high for these small nano particles. McNab et al found a value of

8 × 10 4 erg/cm 3 in pure magnetite for particle size less than 10 nm, by taking a distribution of particle sizes [29].

From the Mössbauer spectra at 4°K, i.e. hyperfine splitting, of the Blank glass and 600 sample, a rough estimate of the hyperfine field was made. By taking the anisotropy to be around ~ 10 6 erg/cm 3 , an average particle size of the nano crystals of magnetite was evaluated for these samples, which were found to be 1.2 nm and 1.5 nm respectively. This shows that some sort of ‘short-range’ magnetic order- ing was already present in the as-annealed glass. The SANS study later confirmed this observation (see the section 5.7) [5]. Therefore, the so-called ‘blank glass’ is not really ‘blank’, it also contains very small nano crystallites of magnetite of size 1.2 nm. The 600 sample (which was heat-treated at 600°C,

that is below T g ) contains slightly higher sized nano particles of 1.5 nm, showing some interesting magnetic properties as discussed above.

In the present case, there is also a distribution of particle sizes, as determined from the magneti- zation data between 4°K and 800°K at H ext = 9.56 KG for the 900 sample through a ‘volume weighted particle size distribution’ formalism [18, 19], but the distribution is found to be quite narrow, as evident from Figure 5.10.

MECHANICAL PROPERTIES