William J. Veigele' Kaman Nuclear C O ~ O I ~Springs, ~ O
High Field Paramagnetic Susceptibility
Colorado
In a paper by Carlin2 on paramagnetic susceptibility, the Van Vleck formalism3 was used to calculate parallel and perpendicular components of paramagnetic susceptibility, X N and xl. In particular the fornralism was applied to the nickel(I1) ion with a spin S = 1 in a crystal field with axial symmetry. The xl conlponent was determined from the energy eigenvalues
V a n Vleck's Equation for D
>
g$H,, obtaining
Wz S D
+ qrZPH,P/D
from which x, = (2Ngl2BX/D)[I - exp( -D/kT)I/[l
(6)
+ 2 exp(-D/kT)]
Equation (11) is for high magnetic fields, therefore the condition that x = 0 for H = 0 does not obtain. The zero field splitting (given by D)exists because of the ion's crystalline environment, and for a free ion (D= O), eqn. (11) does not vauish but reduces to the pure Zeeman case. Paramagnetic Susceptibility for D
was derived. Paramagnetic susceptibility is defined to be independent of magnetic field thus the derivation of xl should hold also. for D
