LiV{sub 2}O{sub 4}: A heavy fermion transition metal oxide Page: 74 of 181

                                
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Figure 4.10 illustrates the HTSE predictions of Eq. (4.21) for S = 1/2 using these b~ coefficients for
nm"x = 1 to 6. The theoretical xHTSE(T) predictions with nm' = 2, 3 and 6 exhibit broad maxima
as seen in our experimental X(T) data. The prediction with n"' = 6 is evidently accurate at least for
kBT/J > 1.6; at lower T, the theoretical curves with n"' = 5 and 6 diverge noticably from each other
on the scale of Fig. 4.23. Our fits given below of the experimental data by the theoretical XPin (T)
prediction were carried out over temperature ranges for which kBT/J Z 1.6. The Weiss temperature 0
in the Curie-Weiss law is given for coordinatioin number z = 6 and S = 1/2 by
zJS(S+1) _      3J
3kb              .                              2
To fit the HTSE calculations of XsPin (T) to experimental data, we assume that the experimentally
determined intrinsic susceptibility x(T) is the sum of a T-independent term xo and xHSE(T),
x(T) = Xo + XHSE(T)                                  (4.25)
with XHSE(T) given by Eq. (4.21) and the b~ coefficients for S = 1/2 in Eq. (4.23). The three
parameters to be determined are Xo, g and J/k$. The fitting parameters for samples 1-7, 4A and 4B
using nm' = 6, and for sample 1 also using n"' = 2 and 3, are given in Table 4.2 for the 50-400K
and 100-400 K fitting ranges. The fits for these two fitting ranges for sample 1 and n"' = 6 are shown
in Fig. 4.11. Both g and J/kB tend to decrease as the lower limit of the fitting range increases. The
HTSE fits for all the samples yielded the ranges C = NAg2ps/(4kB) = 0.36-0.48cm3K/(molV) and
0 = -20 to -42K. These ranges are in agreement with those reported previously (see Table 1.5). xo
was found to be sensitive to the choice of fitting temperature range. For the 50-400K range, xo was
negative for some samples. Recalling the small negative value of the core diamagnetic contribution in
Eq. (4.15) ana the larger positive value of the Van Vleck susceptibility in Eqs. (4.16) and (4.19), it is
unlikely that xo [defined in Eq. (4.29)] would be negative. Negative values of Xo occur when the low-T
limit of the fitting range is below 100 K, and may therefore be a spurious consequence of the crossover
between the local moment behavior at high T and the HF behavior at low T.
To eliminate Xo as a fitting parameter, we fitted dX/dT by the HTSE prediction for that quantity.
In order to generate the experimental dX/dT, we first employed the following function to obtain an
analytic expression for x(T),
a        +x(T)  a1 + a2T + aT2 + a4T3 + asT4
a6+arT+asT2+asT3+T4                                   4.6
The X(T) of samples 1 and 6 for the entire T ranges 2-400K and 1.8-400K, respectively, can be fitted
well by Eq. (4.26) and the a, coefficients are listed in Table 4.3. The rms deviation of the fit from the