Calculations of Electric Field Gradients and g Factors for a Single Crystal of Paramagnetic CuCl2·2H2O

Abstract

The electric field gradient tensor at the chlorine site in a single crystal of Cu${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O has been evaluated using the point-charge model and also considering the effects of induced dipoles. The quadrupole coupling constant, asymmetry parameter, and orientation of the principal axes of the field gradient tensor with respect to the crystalline $a$, $b$, $c$ axes are also calculated. The theoretical quadrupole resonance frequency, assuming the antishielding factor of the ${\mathrm{Cl}}^{-}$ ion to be -56.6, comes out as 6.8 Mc/sec which is to be compared with the observed value of 9.05 Mc/sec. The calculated asymmetry parameter and orientation of the principal axes could not be checked for want of an experimental investigation on the Zeeman effect. Using the same model, $g$ factors of the paramagnetic ${\mathrm{Cu}}^{++}$ ion are evaluated considering spin-orbit interaction by calculating the electrostatic potential at the ${\mathrm{Cu}}^{++}$ site and the consequent crystal-field splittings. The agreement between the theoretical and experimental $g$ factors is better than in the case of the chlorine nuclear quadrupole resonance (NQR) frequency, perhaps due to the fact that the final $g$ values calculated are less sensitive to the percentage covalent character. The contribution of induced dipoles is noted to be significant in both cases. The effect of the paramagnetic ${\mathrm{Cu}}^{++}$ ions on the chlorine NQR, particularly in the antiferromagnetic region (below 4°K), is discussed and the importance of careful experimental investigations to detect the Zeeman splittings even in the absence of an external magnetic field analogous to the zero-field nuclear resonance is indicated.