MAGNETIZATION DATA OF NANO PARTICLES OF MAGNETITE

5.4. MAGNETIZATION DATA OF NANO PARTICLES OF MAGNETITE

In the section 5.2, adequate description has been given on the theoretical side of the magnetiza- tion in terms of ‘saturation magnetization’ (M S ) and ‘volume’ (V) of the super-paramagnetic particles of magnetite, which is an interesting 'entity' for a detailed study. It is interesting since such glass-ceramic material with ultra-fine particles of magnetite could be used as many ‘magnetic devices’, such as 'high- density magnetic storage of information’ in hard disc of the computers, where a new horizon is just unfolding (see later) for terabyte range. It has also applications in magnetic imaging, etc.

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The magnetization measurements are definitely useful. As pointed out earlier in the section - 5.2, these measurements have to be performed at different temperatures and also as a function of magnetic field. For the ‘blank glass’, 700 (5.5 nm) and 900 (7.0 nm) samples, the magnetization (M) measure- ments were carried out in a well-standardised “magnetic balance” as a function of a wide range of magnetic field (H) between 0 and 60 KiloGauss (KG) at different temperatures between liquid helium temperature (4°K) and 800°K.

In order to estimate the values of saturation magnetization (M S ), the measurements were carried out at only one temperature, i.e. ≈ 270°K, for all the six samples. For the ‘blank glass’ and 600 samples, M S increased ‘linearly’ with H, but for all the other four samples, M S increased ‘non-linearly’ with H and then saturated near H = 50 KG, at which the ‘spins’ were blocked. None of the samples showed any 'hysteresis loop' at 300°K.

First of all, the M S values (at ≈ 270°K) are plotted against the temperatures of heat-treatment of all the six samples in Figure 5.3. The time of heat-treatment was kept constant at 8 hours for each of these samples, which means that the particle size is unique in each sample, by assuming of course that there is no distribution of nano particles or, at least the distribution should be very narrow within each sample. This has the implication for processing nano-particles of magnetite within a glassy matrix, since the magnetic property is very sensitive to the particle size, even within this narrow range of nano-size as explained in the section 5.2.

3 /gm u

(em S M

0 Temperature (°C) 500

Figure 5.3 : Saturation magnetization (M S ) at 270°K against heat treatment temperature.

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183 It is seen from Figure 5.3 that M S values for the ‘blank glass’ and 600 samples are low and quite

negligible, since they mainly show paramagnetic behaviour with not so large values of magnetic mo- ments. Then, M S increases above about 625°C, which might indicate the nucleation of the magnetite phase, upto abot 670°C, and this increase is quite rapid between 625 - 670°C as seen from Figure 5.3. Then, there is a change of slope, and M S increases much less rapidly, which could be ascribed to a growth process of nano particles of magnetite.

Generally speaking, in most physical systems when one physical quantity (here, in this case, saturation magnetization), i.e. the independent variable shows a “distinct” change of slope in its behav- iour against one dependent variable, i.e., temperature in this case, it is common to conclude that there are “two” processes operative. Hence, in the interpretation of the magnetic data of Figure 5.3, it can be said that there is a ‘nucleation’ of nano-particles of magnetite between 625-670°C and there is a ‘growth’ process operating between 670 - 900°C. But, there are more interpretations in store, if we take a much closure look in these data.

Alhough M S shows almost a linear relation with increasing particle size in the temperature range (600 - 900°C), it is interesting to note that the increase of M S is much more pronounced between 600 - 700°C than that between 700 - 900°C. Between 700 - 900°C the particle size, and hence the particle volume increases, but there is a ‘slow’ increase of M S , which could be interpreted as due to the increase of the ‘ferrimagnetic phase’ thereby reducing the contribution of the ‘super-paramagnetic’ particles. As shown later in the section 5.5, this has also been revealed by the Mössbauer data at 300°K. Furthermore, this could be due to the increasing dilution of the surface Fe ions on the nano particles of magnetite by other non-magnetic cations, such as Ca 2+ , Mg 2+ , etc. and it is also revealed by the Mössbauer spectra at 4°K with H ext = 50 KG, wherein the ‘spins’ of the nano particles of magnetite seem to be blocked.

The rapid increase of M S between 600 - 700°C could be ascribed to a ‘cation re-distribution’ process taking place during the nucleation of the nano particles of magnetite. According to Neel [15], the magnetic moment of one molecule of magnetite is written as :

M β = (4 + 2γ)µ B (5.6) where, γ is the coefficient characterizing the ‘inverse spinel’ structure, and µ B the Bohr magneton. For

a particular ‘cation distribution’ other than ‘normal’, 0 < γ < 1. The increasing value of γ associated with the increasing number and volume of the nano particle of magnetite could account for the rapid increase of M S between 600 - 700°C.

Obviously, this increase would be associated with the increase of the ‘symmetry’ of the Fe ions. This has been revealed by the decrease of the ‘quadrupole splitting’ and the increase of ‘isomer shift’ in this heat-treatment temperature range (i.e. within this nano range of magnetite particles) as shown later in Figure 5.12. It is worth mentioning that M S at ≈ 300°K increases by about 70% in the case of pure bulk magnetite in the particle size range of 20 nm - 75 nm [16], whereas it increases by about 50% between 650 - 900°C, i.e. within the nano particles size range of 4.5 nm - 7.0 nm. This shows the ‘remarkable’ behaviour of ultra-fine nano particles of magnetite embedded within a glassy matrix.

5.4.1. Variation of Temperature and Magnetic Field

The magnetic data in emu/gm, measured at different temperatures (4, 77 and 300°K) as a func- tion of applied magnetic field (H ext ) upto 60 KG, for the ‘blank glass’, 700 and 900 samples are interest- ing, as shown in Figure 5.4. Due to the ability of the material containing nano particles of magnetite to “remember” an earlier magnetic field (i.e. remanance), each sample was subjected to a decreasing alter-

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nating field at 300°K before each experiment. Then, the evolution of the magnetization (M) was studied as a function of temperature upto 800°K with an applied magnetic field (H ext ) equal to 9.56 KG. These data are shown in Figure 5.5.

emu/g 4K

900 glass

77 K 300 K

emu/g 4K

700 glass 77 K

300 K

30 4K

emu/g

Blank glass

300 K

0 10 20 30 40 HIKGI

Figure 5.4 : Magnetization as a function of the magnetic field at different temperatures.

MAGNETIC PROPERTIES

185 In the analysis of all the experimental magnetization curves as a function of magnetic fied [M(H)

in Figure 5.4] and as a function of temperature [M(T) in Figure 5.5], the paramagnetic part of the contribution of the Fe 2+ ions, which are evaluated by the Lorentzian analysis of the Mössbauer data [6-7], is first deduced from each of the M(H) and M(T) values. It should be noted that this correction is necessary, and this is carried out with µ Fe2+ = 540 emu/gm of iron and N Fe2+ ≈ 3.2 × 10 –4 mole/gm of glass in this particular case.

8 Mlemu/gl M (T)/M (T = 0) 5 5

Fe O 3 4

0 200 400 600 800 T(K)

2 Blank glass

600 T(K) 800

Figure 5.5 : Magnetization as a function temperature (H = 9.56 KG).

5.4.2. Magnetic Characteristics of Blank Glass

From the room temperature Mössbasuer spectra of the ‘blank glass’ [6-7], it is found that this sample is simply ‘paramagnetic’. The magnetic moment is measured as a function of magnetic field [M(H)]. As shown in Figure 5.5, the experimental curve at T = 300°K can be described as follows :

(5.7) with µ′ = 440 emu/gm of iron and without any remanance and by assuming a N′ value corresponding to

M = (N′µ′ 2 H)/3k B T

80% of the Fe ions in a ‘paramagnetic’ state. At 4°K, from the remanance value (see Table 5.1), the ‘ferrimagnetic’ contribution is estimated by assuming a saturation magnetization value of 50 emu/gm for these nano particles of magnetite, as in the 700 sample. At this low temperature, the 'ferrimagnetic' contribution is evaluated to be nearly 5%.

From the M = f(T) experiment, i.e. Figure 5.5, the dotted line means that the ‘paramagnetic’ contribution of the Fe 2+ ions is already deducted. The values of χ –1 = H/M are plotted in Figure 5.6. In this analysis, the ‘ferrimagnetic’ contribution has been neglected in view of the small remanant

magnetization value at 4°K. It is seen that χ –1 is a simple linear function of T : with χ –1 = 3k B T/ N′µ′

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with µ′ = 390 emu/gm of iron. This value is somewhat lower than that estimated previously (i. e. 440 emu/gm of iron), but is of the same order of magnitude. The difference could be due to approximate evaluation of the Fe 2+ contribution.

X (kG emu .g) –1

T(K) 300

Figure 5.6 : The inverse magnetic susceptibility as a function of temperature for the blank glass.

5.4.3. Magnetic Characteristics of the 700 and 900 Samples

In Figure 5.4, only the behaviour for increasing H values is illustrated for 700 and 900 samples at different temperatures of measurement. It has been estimated that at 4°K, the remanant magnetization values for the 700 and 900 samples are very similar to half those of M 60KG -M Fe2+ , according to M R =½M S [12]. This indicates that at this temperature, all the nano particles of magnetite in these two samples are surely below their ‘blocking’ temperature, and hence they naturally behave as ‘ferrimagnetic’ particles.

For the 700 and 900 samples, from these data at this low temperature for different magnetic fields after deducting the contribution of Fe 2+ ions, the curves are drawn for M = f(1/H) in order to be able to extrapolate their values of magetic moment at H = ∞, which are :

For the 700 sample, M (T = 4°K, H = ∞) = 4.95 emu/gm of glass. For the 900 sample, M (T = 4°K, H = ∞) = 5.85 emu/gm of glass. Obviously, it was assumed that at T = 4°K and H = ∞, all the ‘spins’ are aligned along the

direction of the applied magnetic field. The proportion of magnetite in the ‘ferrimagnetic’ state at 4°K, without any applied magnetic field, is given by the ratio 2M R /M (T = 4°K, H = ∞). These data agree well with those evaluated from the Mössbauer data [6-7].

From the values of M (T = 4°K, H = ∞), the values of ‘saturation’ magnetization of the nano particles in the ‘ferrimagnetic’ state are estimated as :

For the 700 sample, M S (T = 4°K, H = ∞) = 50 emu/gm of magnetite [Particle Size = 5.5 nm] For the 900 sample, M S (T = 4°K, H = ∞) = 59 emu/gm of magnetite [Particle Size = 7.0 nm]

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187 These values are smaller than the magnetization value of the ‘bulk’ magnetite (i.e. ≈ 98 emu/gm

of magnetite). The difference between these values can be explained by the difference in particle size. As noted

above, in the 700 sample, the particles are smaller than that of the 900 sample. The canting of 'spins' at the surface of the nano particles is found to be more frequent in the 700 sample, so that the resulting magnetization is smaller than it would be if all the ‘spins’ were ‘aligned’ along the same direction (see the section 5.5.2). If this difference of M S is taken into account, the M = f(H) curves of the 700 and 900 samples at 4°K after the deduction of the Fe 2+ contribution ‘superpose’ quite well, as shown in Figure

5.7. In this analysis, the 15 to 20% contribution of magnetite that is not in a ‘ferrimagnetic’ state is not taken into account. It is observed that 90% of the ‘saturation’ magnetization is obtained, even if a magnetic field as small as 5 KG is applied.

At 77°K and at 300°K, the remanence values give the proportion of the ferromagnetic nano particles (see Table 5.1) by assuming a constant ‘saturation’ magnetization from 4 to 300°K. The contribution of the ‘super-paramagnetic’ nano particles can be evaluated at each value of magnetic fieldf : M Super = f(H), which is estimated by subtracting the contributions of Fe 2+ and ‘ferrimagnetic’ state from the experimental magnetic moments. The last one is calculated from the remanence value as : M R =½M S and by assuming a ‘ferrimanetic’ evolution as : M Ferri = f(H), which is similar to that found at 4°K (see Figure 5.7).

M(emu/g)

(a)

(b)

H(kG)

H(kG)

Figure 5.7 : Magnetization against magnetic field at 4°K (a) after deducting Fe 2+ contribution, (b) M value multiplied by the ratio M S 900 /M S 700 .

In Figure 5.8, the values of M due to ‘super-paramagnetic’contribution vs. H ext /T are plotted for both the 700 and 900 samples. The magnetization curves superpose well both at 77 and 300°K, and agree well with the Langevin function (the full lines). From the high field part of the curves, the ‘mean

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particle diameter’ and the saturation moments (M Super ) of the ‘super-paramagnetic’ nano particles were estimated as per the equation (5.4). The nano particles in the 700 sample are smaller than those in the 900 sample. The low field part of the curves is not used, because the precision is poorer in this region. This typical ‘super-paramagnetic’ behaviour confirms the earlier ‘hypothesis’ that 20% of the iron ions are in a ‘paramagnetic’ state (Fe 2+ ), some in ‘ferrimagnetic’ state and the balance iron ions are in a ‘super-paramagnetic’ state.

4 emu/g

700 glass

77 K 300 K

900 glass

77 K 300 K

( ) H –1

Gauss K

T Figure 5.8 : Superposition of the agnetization curves of the superparaagnetic particles

against H ext /T , both at 77°K and 300°K.

The M = f(T) curves for the 700 and 900 samples can be described by assuming that all the remaining 80% of the iron ions are in a ‘ferrimagnetic’ or a ‘super-paramagnetic’ state of magnetite. This means that :

N(V) Ferri + N(V) Super = Total Magnetic Volume = Constant

As the temperature increases, some ‘ferrimagnetic’ nano particles transform into ‘super-para- magnetic’ nano particles due to faster relaxation → the ‘spins’ in the same nano particles flip-flop too fast. Hence, we can write :

M=M S-Ferri [N(V)] Ferri +M S-Super [N(V)] Super [coth α – 1/α]

with

α =M S-Super V Super H ext /k B T.

Both M S-Super and M S-Ferri are supposed to be dependent on temperature in the same manner as ‘bulk’ Fe 3 O 4 [17], as shown in Figure 5.5, whose values have already been estimated earlier. For each temperature, it is possible to calculate the %ferrimagnetic fraction. This is shown in Figure - 5.9 for the 700 and 900 samples as a function of temperature (H = 9.56 KG). As the temperature increases, the

189 proportion of the ‘ferrimagnetic’ nano particles decreases. It is seen that all the nano particles are in a

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‘paramagnetic’ state at T > 800°K. This temperature is lower than the “Curie” temperature of the bulk magnetite (851°K).

600 T(K) 800

Figure 5.9 : The contribution of ferrimagnetic particles (% volume of magnetite) as a function of temperature (H = 9.56 KG).

The differentiation of the curves of Figure 5.9 results in the ‘volume weighted’ particle size distribution in the 700 and 900 samples [18-19], as shown in Figure 5.10. The temperature is propor- tional to to the volume of the particle. In the 700 sample, the particle size distribution is larger than that in the 900 sample, but the ‘mean value’ is smaller. Thus, there is a distinct change of magnetic behaviour between the 700 sample and the 900 sample, within such a narrow range of particle sizes between

5.5 nm and 7.0 nm, as found out by X-ray data in the section 5.3, or between 2.8 nm and 3.6 nm as found out by magnetization data.

In summary, the magnetization measurements on the basalt glass samples heat-treated at differ- ent temperatures show the evolution of crystallization and also the magnetic behaviour. The ‘blank glass’ has paramagnetic behaviour with M = 390 emu/gm of iron. The 700 and 900 samples contain 20% of paramagnetic Fe 2+ ions and 80% of nano particles of magnetite. The nano particles of magnetite behave like a super-paramagnetic or a ferrimagnetic material depending on the crystal size, even within the “nano range”. The mean particle diameter has been evaluated for the super-paramagnetic particles of these two samples as 2.8 nm to 3.6 nm. The saturation magnetization of the nano particles is smaller (28 to 52 emu/gm) than those of the bulk magnetite (~ 98 emu/gm). A volume particle size distribution has been calculated for the nano particles of super-paramagnetic magnetite [8].

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increasing volume of particles n

o ti

rac

f ic

agnet am

par per

su

600 T(K) 800

Figure 5.10 : Volume particle size distribution as a function of temperature (T is proportional to the volume of the particle).

5.4.4. Lattice Expansion in Ferrites with Nano Particles

The magnetic properties of bulk and nano particles of MnCr 2 O 4 spinel oxide show that it is a ferrimagnetic insulator showing paramagnetic (PM) to collinear ferrimagnetic (FM) transition below T C ≈ 45°K and collinear FM to non-collinear FM state below 18°K. The nano particle was prepared by employing the novel technique of mechanical milling. The measurement shows a few unusual magnet- ism in the nano particles in terms of a ‘lattice expansion’ with the decrease of particle size. A sharp magnetic transition at 18°K associated with the non-collinear spin structure is not seen in the nano- particles [20], but the non-collinearity of spin is shown in case of nano particles of magnetite, as de- scribed in the section 5.5.2 [6]. The decrease of magnetization in the nano particles is interpreted by the

“core-shell” model, and it is attributed to the increasing disorder effect. However, the increase of T C , and systematic increase of Bloch exponent with decreasing particle size, seem to be unusual, which is highlight by a ‘lattice expansion’ of the nano particles [20].

Generally speaking, the decrease of particle size results in a decrease of ‘lattice parameter’ in nano materials. This is true in case of a wide class of nano materials, synthesized by various procedures as noted above. There are several explanations for the ‘lattice expansion’ in nano materials, such as change in oxygen coordination number with the cations and change of valence state of cations [21], and

191 contribution of ‘excess volume’ of grain boundary spins [22]. There are some arguements that the ‘lat-

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tice expansion’ in mechanically milled samples may be related to the mechanical strain induced effect, rather than intrinsic properties of the sample [22], which is not well justified, since the 'lattice expansion' has been observed in both mechanical milled nano particles as well as in those prepared by the chemical route. Some details of the origin of the ‘lattice expansion’ in the nano particles of the above magnetic material has been discussed by Bhowmik [20], as given below.

The XRD pattern of the materials with nano particles are identical with the bulk samples. Al- though small, but a systematic shift in XRD peak positions are observed with decreasing particle size. The absence of any additional lines with respect to standard cubic spinel structure of bulk sample indi- cates that there is no crystallographic phase transformation in the materials containing nano particles.

The agreement of the magnetic parameters (magnetic moment and T C ) of the bulk sample with previ- ously reported value has confirmed that Mn ions are in divalent (Mn 2+ : 3d 5 ) state. The argon atmos- phere during the mechanical milling also rules out the formation of significant amount of Mn ions with higher ionic (3+ or 4+) states.

By comparing the ‘outer shell’ spin configuration of Mn 2+ (3d 5 , moment = 5 µ B ), Mn 3+ (3d 4 , moment = 4 µ ) and Mn 4+ (3d 3 , moment = 3 µ ), it is evident that if Mn 3+ or Mn B 4+ B exists at all, the decrease of lattice parameter is expected [23]. Therefore, the change in valence state or the crystallographic phase transformation are not considered for the ‘lattice expansions’. Hence, the reduction of magnetic moment with decreasing particle size is not attributed to the change in valence state of Mn ions. How- ever, the decrease of magnetic moment in the above magnetic material containing nano particles seems to be consistent with the core-shell model [24].

The core-shell model [24] for ferrimagnetic nano particles suggests that shell contribution will dominate on the properties of nano particles. The microstructure of the shell with more disorder effect may influence the ‘lattice expansion’ in the following two ways :

1. Increasing the free ‘excess volume’ of the incoherent shell, i.e. grain boundary, spins in the interface structure, and

2. Lowering symmetry in oxygen coordination numbers with surface cations. It has already been shown for MnCr 2 O 4 that the increase of lattice volume is highly related to the

change in oxygen coordination number with the cations [21]. Consequently, the lattice pressure on core spins may be reduced by the elastic coupling between the shell spin and the core spin lattices [22].

In fact, various factors such as breaking of long range crystallographic coherent length of bulk material and orientation between the shell spins exhibit inter-atomic spacing, which is different from the bulk lattice. Overall, the macroscopic average of inter-atomic spacing contributes larger lattice param- eter in the nano particles.

Since the ‘superexchange interaction’ in spinel oxide strongly depends on both the bond angle and the bond length of A and B site spins, any change in the ‘spin configuration’ either in shell or core must be reflected in the change of magnetic properties in the nano particles. The gradual decrease of the non-collinear spin structure amongst the B site Cr 3+ moments in the nano particles is reflected by the disappearance of sudden jump in magnetization at 18°K, as observed for the bulk sample [20].

This suggests an increase of B site Cr-Cr distance in the nano particles, which leads to the de- crease of direct antiferromagnetic (J BB ) interactions between Cr moments, and increase of inter-sublattice superexchange interactions (J AB ). The strong J AB with increasing B site Cr - Cr distance has been real- ized in many other spinels. If the ‘lattice expansion’ is related to the increase of Cr - Cr distance via O 2– , it is expected under the assumption T C ~J AB , that T C should be higher for the nano particle sam-

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ples. The experimental data of dc magnetization show magnetic irreversibility and spontaneous mag- netization above 45°K (i.e. T C of the bulk samples) for the nano particle samples. This confirms the enhancement of ferrimagnetic order in MnCr 2 O 4 nano particles. A similar increase of T C with the ‘lattice expansion’ has been observed in other nano particle systems [25].

This work is very important in that the non-collinear ferrimagnetic order is associated with strong

B site direct (antiferromagnetic) cation-cation interactions, which favour non-collinear B site spin struc- ture below 18°K. The increase of T C with decreasing particle size is a consequence of the decrease of non-collinear (B site) spin structure in the nano-particles. The experimental data indicate that the ‘lattice expansion’ has a direct effect on the decrease of non-collinear (B site) spin structure, and hence on enhanced ferrimagnetic order in the nano particles. The observed reduction of magnetic moment, large magnetic irreversibility between MZFC and MFC, and appearance of ‘superparamagnetism’ are some of the disorder effects in nano-particles [20]. The latter is explained by the data on a detailed Mössbauer experiment on the nano particles of magnetite in terms of a 'spin-cating' model in the section - 5.5.2 [6].