Temperature Variation of the Principal Magnetic Moments of Co⁺⁺ Ions and the Asymmetry of the Crystalline Electric Field in Cobalt Acetate Tetrahydrate

Abstract

THE ground-state of the free divalent cobalt ion is 3d ⁷, ⁴ F _9/2, and the potential due to the crystalline electric field in the neighbourhood of the six co-ordinated cobalt ion conforms to: V = D (x ⁴ + y ⁴ + z ⁴) + Ax ² + By ² − (A + B)z ² the fourth-order terms in the expression represent the cubic, and the quadratic terms the rhombic, part of the field. The observed magnetic properties can then be explained on the assumption that the field is predominantly cubic in symmetry with a feeble rhombic component superposed. If the field is due to an octahedral distribution of water molecules around the Co⁺⁺ ion, the seven-fold orbital degeneracy is split into two triplets and a singlet, and the sign of the cubic field coefficient is such as to make one of the triplets the ground-state, the separation of which from the other triplet is of the order of 10⁴ cm.⁻¹. With such a disposition of the orbital Stark pattern, the components of the lower triplet being further separated to the extent comparable to kT by the rhombic part of the field, and the spin-degeneracy slightly raised through the spin-orbit coupling, the calculations of the principal magnetic moments naturally become very complicated. Schlapp and Penney¹ have, however, made detailed theoretical calculations of the principal magnetic moments of cobalt salts. Assuming the cubic field to be always of the same intensity, and one of the rhombic field constants zero, they assign different values to the other, namely, A = 0, 40, 200, etc. With a small rhombic field the effective magnetic moments naturally become different, but they decrease in more or less the same way as with a purely cubic field when the temperature is lowered. The principal moments separate out further when A is 200, and with the fall of temperature the moment having the largest value increases, reaches a maximum and then falls, while the other moments decrease. From the experimental magnetic data on cobalt salts² it seems that the rhombic field in them is not so strong as to produce a rise in the maximum magnetic moment referred to above.