Magnetisation studies of sample D

Following the same protocols for sample C we will now apply the same magnetic analysis to sample D, which has an average particle size from TEM ofdT EM ≈12 nm.

This sample has a particle size mid way through the range already described, and hence test our current size dependent hypotheses.

Parameter Single Langevin Dual Langevin Units µ1 11.7(1) 19.2(7) kµB µ2 n/a 4.7(2) kµB MS1 8.06(4)×10−3 4.64(3)×10−3 emu cm−3 MS2 n/a 4.17(3)×10−3 emu cm−3 b −3.75(5)×10−7 −4.49(5)×10−7 emu cm−3 Oe−1 χ2_red 7.90 1.37 n/a

Table 4.10: Best fit parameters for the Single and dual Langevin models to theT = 200 K data sets shown in figure 4.18.

4.6.1 Langevin analysis

Figure 4.18 shows the M vs H data taken for sample D at 200 K. The magnetisa- tion is reversible with applied field at this temperature with a negligible remanent magnetisation indicating that the material is above its blocking temperature and the super-paramagnetic assumption is applicable. As with sample C, the M vs H

data has been taken at a higher temperature, 200 K, so that the θcorrection term becomes negligible and the low H, M vs T analysis can be removed - hence in- creasing the speed of analysis, a key issue for industrial application. Inspection of figure 4.18 the high H behaviour appears to have a larger diamagnetic signal than samples A to C - however, the diamagnetic contribution is actually the same and it is the scale of the super-paramagnetic contribution that is decreased due to a lower loading of nanoparticles. As previously stated measuring the actual loading of Ni within the Fomblin grease is impractical due to safety reasons but the fact we can observe the super-paramagnetic behaviour at lower loading of Ni does highlight the extreme sensitivity of the SQUID magnetometer to low Ni content.

The M vs H data was fit with both the Single and dual Langevin models, shown as the black and green lines on figure 4.18 respectively, and the best fit parameters are summarised in table 4.10. As with sample A and B it is the dual Langevin model that gives the superior fit (a χ2_red = 1.37 cf. 7.90 for the single Langevin model) and as expected from the shape of the response the value of MS

is reduced compared to previous samples but the diamagnetic susceptibility, b, is comparable.

The values of µfound using the dual Langevin model show a slight increase when compared to samples A and B, but are smaller than sample C. Likewise, assuming the 20 - 80% behaviour as earlier predicts a value ofµaverage= 9.5(3) kµB, again an increase compared to samples A and B but smaller than sample C. Following

Figure 4.18: M vs H data set for sample D taken at T = 200 K. The data has been fit by both a Single and Dual Langevin function model (black and green lines respectively) and the parameters of these fits are listed in table 4.10. Inset - the H

Parameter Value Units µ 12.1(1) µB MS 0.0348(3) emu cm−3 θ 15.0(2) K α 2.2(2)×10−5 K−1.5 β 9.36(3)×10−3 emu cm−3 b −5.21(1)×10−7 emu cm−3 Oe−1 χ2_red 1.28 n/a

Table 4.11: Best fit parameters for the three term model to the M vs T data sets reported in figure 4.19.

the same procedures as earlier this size of magnetic moment would predict an average particle diameter of 7.2(3) nm, cf. dT EM = 12.19(7) nm. This is a reduction of ≈

5 nm - following the trend from samples A, B and C in which the larger diameter had the larger reduction in diameter. If this particle follows the same behaviour as previously seen we will expect to see a strong Curie-tail behaviour in the high H,

M vs T response and expect to find a value ofµshell between 0.4 and 1.1 µB.

4.6.2 Curie behaviour at high H

Figure 4.19 is the M vs T data taken for sample D at H = 10 and 50 kOe (green and orange respectively). As with previous measurements the Curie-tail feature is clear at low temperatures, with a marked increase in M as T approaches 5 K. The two most striking features, however, are the large difference between the 10 and 50 kOe data sets (again due to a low loading of Ni compared to previous samples) and the apparent approach to saturation in the 10 kOe data set. Unlike previous samples, which have a gradual increase in M on decreasing T to 5 K, the 10 kOe data set appears to tend to a constant value in the range 5 to 15 K. This would suggest that the Weiss temperature may have changed sign (mathematically giving an asymptote at finite temperature) and the magnetic species leading to this Curie behaviour have a ferromagnetic correlation. If this is the case the lowT data will not follow the proposed model and data approaching the Weiss temperature will need to be ignored.

The data sets were fit by the three term model as previously described, with both 10 and 50 kOe data sets sharing all free parameters. To allow for the possibility of a positive Curie constant, data within 10 K of the Weiss temperature was excluded from the fit. The resultant best fit is shown on figure 4.19 as the black lines and the

Figure 4.19: M vs T behaviour of sample D taken at H = 10 (green) and 50 kOe (orange). The lines represent the best fit to the data of the three term model and the parameters are summarised in table 4.11.

best fit parameters are summarised in table 4.11. Comparing the values found with samples A to C, the values ofαandbare of consistent size, however,µhas increased and (as predicted) θis now positive.

A change in sign ofθis a sign that the surface magnetic species are now corre- lated ferromagnetically, instead of antiferromagnetically for previous samples. These species still have too large a magnetic moment to arise from a single atom, suggest- ing that this contribution to the magnetisation arises from multiple micro-domain ordered ferromagnetically within the domain and then correlated ferromagnetically to the neighbouring domains.

Corroboration of the value ofθ can also be found by inspection of the zero- field cooled M vs T data (inset to figure 4.19), which shows a sharp peak in the magnetisation (unseen in the three previous samples where θ is negative) at 15 K. While these two values matching is far from conclusive, it does strengthen the case for a ferromagnetic correlation between the surface micro-clusters withθ≈15 K.

Assuming at this stage that the parameters produced from the “three term” model are accurate and following the procedures previously outlined, the predicted average moment per shell, µshell = 35(1) kµB. As previously stated, the Langevin

and TEM predicted particle sizes differ by≈5 nm, accounting for a volume,Vshell= 750(30) nm3, and hence a magnetic moment per atom of µshell = 0.59(3) µB. This

value follows the same size dependence as previously suggested with µshell being

slightly larger than that of sample D and close to the bulk value for Ni.