Developments in Ceramic Materials Research

Synthesis, Spectroscopic and Magnetic Studies… 113
However, it is necessary take into occount that similar behavior could be also originate
by a contribution such as a positive zero-field splitting, which was observed from the ESR
data. Both contributions are qualitatively similar and to consider them simultaneously
presents great difficulties. For this reason, we have tried to fit the experimental data under
each of these hypothesis separately. Using the Van Vleck equation an analytical expression
for the magnetic susceptibility as a function of the temperature and the D parameter was
calculated [45]. However, considering the D value obtained from the Weiss temperature (θ=
2/3D), the calculated curve deviates drastically from the experimental ones (dotted line in
Figure 10). Satisfactory fits can be obtained only by using D values higher than 40 K.
However, these results are completely unrealistic considering the ESR measurements.
An expression for the magnetic susceptibility was derived from high temperature
expansion series for an antiferromagnetic Heisenberg simple cubic lattice calculated by
Rushbrooke and Wood [46]. The best fit corresponds to the continuous line in Figure 10 and
was obtained with a J/k value of -0.92 K. The calculated curve agrees rather well with the
experimental one at high temperatures, but deviates appreciably at low temperatures where
the effect of the zero-field splitting is more important. So, we can conclude that both the
antiferromagnetic interactions and the zero-field splitting determine the magnetic behavior
observed for V(PO3)3.
6.3. Magnetic Properties of M(PO3)3 (M= Mo and Cr) and Cr2(P6O18)
The thermal evolution of the molar magnetic susceptibility for Mo(PO3)3 is shown in
Figure 11. A sharp maximum is observed at 4.5 K, indicating the existence of an
antiferromagnetic ordering in this compound. The high temperature data (T> 50 K) are well
described by a Curie-Weiss law [χ=Cm/(T-θ)] with Cm= 1.71 cm 3 Kmol -1 and θ= -6.8 K. The
negative temperature intercept together with the decrease of the effective magnetic moment
observed when the temperature is lowered (3.64μB at 300 K and 1.78μB at 2 K) are in good
agreement with the predominance of antiferromagnetic interactions in this compound (Figure
11).
Considering the structural features of the molybdenum metaphosphate only
superexchange interactions via (PO4) tetrahedra can be expected. Due to the complexity of
three-dimensional arrangement and the consequent presence of different exchange pathways
it is not possible to find a simple magnetic model, representing exactly the characteristics of
the magnetic ordering in this compound. However, taking into account the weakness of the
exchange couplings and the packing of the (MoO6) octahedra, a simple cubic network can be
utilized in order to obtain an approximate value of the exchange parameter. Considering the
usual isotropic magnetic behavior of Mo(III) ions a Heisenberg Hamiltonian was the starting
point, H = 2J Σ SiSj, with i