Magnetothermodynamics of α-NiSO4·6H2O. III. Derivation of Spin-Hamiltonian–Molecular-Field Parameters from Experimental Data

Abstract

Magnetothermodynamic data for α‐NiSO₄·6H₂O, with magnetic fields along two axes, the $c$ crystallographic axis ([001] direction) and the [110] direction, have been interpreted using a spin‐Hamiltonian–molecular‐field model for the NI(H₂O)₆^+ 2 complexes. Best values for the spin‐Hamiltonian parameters are $\text{D\hspace{0.17em}=\hspace{0.17em}4.741}{\mathrm{cm}}^{\text{−\hspace{0.17em}1}}$ (singlet–doublet separation for $H$ = 0); $g_z{\text{\hspace{0.17em}=\hspace{0.17em}2.215}}_8{\mathrm{,\; g}}_{\mathrm{xy}}{\text{\hspace{0.17em}=\hspace{0.17em}2.249}}_5$ (principal values for the $g$ tensor of the Ni(H₂O)₆^+ 2 complexes); ${\text{φ\hspace{0.17em}=\hspace{0.17em}39.0}}_0^{°}$ (angle the $z$ magnetic axes of the four Ni(H₂O)₆^+ 2 complexes per unit cell makes with the $c$ tetragonal screw axis—the $x$ magnetic axes are perpendicular to the tetragonal axis); $\text{γ\hspace{0.17em}=\hspace{0.17em}0.272}\mathrm{mole}\mathrm{\hspace{0.17em}/\hspace{0.17em}}{\mathrm{cm}}^3$ (molecular field constant representing an isotropic combined ferromagnetic exchange and dipole–dipole interaction between Ni^+ 2 ions); and $\text{λ\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}281}{\mathrm{cm}}^{\text{−\hspace{0.17em}1}}$ (the spin–orbit coupling constant). For the $c$ axis the temperature‐independent susceptibility $\alpha$ was computed to be 0.75 × 10⁴, while for the [110] direction it was 0.98 × 10^− 4 cm³/mole. However, a best fit to the magnetic‐moment data for the [110] axis was obtained using only the diamagnetic susceptibility, −1.25 × 10^− 4 cm³/mole. A detailed analysis of the methods used in obtaining the parameters from the data is given. The over‐all fit to all of the magnetothermodynamic data is excellent, constituting a “textbook” example of the spin‐Hamiltonian–molecular‐field method.