The temperature dependence of the nuclear quadrupole coupling parameters, $\frac{\mathrm{eQq}}{h}$, of Al and Ga has been measured in the ferroelectric compound C${\left(\mathrm{N}{\mathrm{H}}_2\right)}_3$Al${\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$·6${\mathrm{H}}_2$O (GAlSH) and three other isomorphous compounds that result when Ga replaces Al and Se${\mathrm{O}}_4$ replaces S${\mathrm{O}}_4$. Measurements were also made on deuterated GAlSH. The temperature dependence of the electron spin resonance (ESR) of ${\mathrm{Cr}}^{3+}$, substituted for Al or Ga in the above five compounds, was also measured. For the five compounds, $\frac{\mathrm{eQq}}{h}$ versus temperature for each compound was similar, small (∼100 kc/sec), linear with temperature, and in some cases changed sign. Within the framework of the ionic model, $\frac{\mathrm{eQq}}{h}$ and $\frac{d\left(\frac{\mathrm{eQq}}{h}\right)}{\mathrm{dT}}$ have been calculated. It is found that the latter is fairly insensitive to the x-ray and charge distribution parameters and depends mainly on the large anisotropic thermal expansion coefficient. Using the theoretically calculated antishielding factor, there is agreement between the calculated and the measured $\frac{d\left(\frac{\mathrm{eQq}}{h}\right)}{\mathrm{dT}}$. The data also indicate that the ratio of the antishielding factors of ${\mathrm{Al}}^{3+}$ and ${\mathrm{Ga}}^{3+}$ are in approximate agreement with the calculated values.

The temperature dependence of the electron spin resonance of ${\mathrm{Cr}}^{3+}$ in the five compounds is again similar to each other. The $g$ values for the Al and Ga compounds are the same within experimental error. The zero-field splitting ($D$ term in the spin-Hamiltonian) of the deuterated GAlSH has a slightly larger variation with temperature than the undeuterated compound. By parametrically eliminating temperature, the relation between $D$ and $\frac{\mathrm{eQq}}{h}$ is studied. The result is two parallel lines, one for the two different sites in the two Al compounds and the other for the Ga compounds. The lines are parallel only if the Ga nuclear quadrupole moment and antishielding factor are normalized to those of Al. Using simple crystal field theory, it is shown that $D$ should be proportional to $\frac{\mathrm{eQq}}{h}$. However, the data show that $D$ and $\frac{\mathrm{eQq}}{h}$ are not simultaneously zero and that the slope is ten times larger than calculated. These two discrepancies are discussed. A calculation of the extra potential seen by the $3d$ electrons, due to the fact that the crystal field induces a quadrupole moment in the core electrons, is discussed. However it does not remove the discrepancy. It appears that the relation between $D$ and the crystalline field is not firmly established.

• Received 26 April 1961

DOI:https://doi.org/10.1103/PhysRev.123.1634