Theory of the Variations in Paramagnetic Anisotropy Among Different Salts of the Iron Group

A theoretical explanation is given of why nickel salts are nearly isotropic magnetically, while those of cobalt exhibit over 25 percent anisotropy even though the ${\mathrm{Ni}}^{++}$ and ${\mathrm{Co}}^{++}$ ions are both in $F$ states and are adjacent in the periodic table. The cause is an inversion of the levels in the crystalline Stark effect in passing from the configuration $d^8{}_{}{}^3{}_{}{}^{}F\left({\mathrm{Ni}}^{++}\right)$ to $d^7{}_{}{}^4{}_{}{}^{}F\left({\mathrm{Co}}^{++}\right)$. If the crystalline field has only rhombic symmetry, but with the deviations from cubic symmetry comparatively small, extension of the methods in Penney and Schlapp's preceding paper shows that a nearly isotropic level will be the ground level in ${\mathrm{Ni}}^{++}$, but an anisotropic one in ${\mathrm{Co}}^{++}$. It is to be particularly noted that the inversion exists purely in virtue of the difference between the configurations $d^7$ and $d^8$, and does not require different crystalline fields in Ni and Co compounds. The theory predicts that hydrated Ni salts conform closer to Curie's law than those of Co, and have a Curie constant more nearly equal to the "spin only" value $\frac{4NS(\mathrm{S}+1){\left(\frac{\mathrm{he}}{4\pi \mathrm{mc}}\right)}^2}{3k}$. This agrees with experiment. Other pairs of ions are cited in the iron group in which the inversion phenomenon is encountered, with attendant diversity in magnetic behavior. The nearly perfect magnetic isotropy of manganous salts is trivial, as the ground state of ${\mathrm{Mn}}^{++}$ is ${}_{}{}^6{}_{}{}^{}S$; the slight anisotropy may be due to a small amount of incipient $j-j$ coupling or to distortion of the constancy of orbital angular momentum by the crystalline field, so that the orbital magnetic moment does not vanish completely in $S$ states.