On the Magnetic Behavior of Vanadium, Titanium and Chrome Alum

As Siegert has shown, the fact that the susceptibilities of both titanium and vanadium alum conform to the ``spin-only'' formula demands that the ratio of the fourth-to the second-order part of the noncubic portion of the crystalline potential have a certain critical value. The present paper investigates whether such a ratio can result from (I) the direct effect of the ``distant'' charges, i.e., the atoms more remote than the six waters immediately surrounding the paramagnetic ion, (II) the indirect action of the remote atoms in distorting or polarizing the water cluster so that it is no longer octohedral, or (III) the Jahn-Teller effect, whereby the degeneracy of the cation has repercussions on the arrangement of the surrounding waters, so that they are not cubically grouped. It is concluded that (I) does not yield a sufficiently large splitting. That the mechanism (III) cannot alone be effective is shown by Gorter's relaxation experiments, as well as by the existence of a small splitting of the basic quartet of chrome alum which cannot be due to (III), but which is revealed by adiabatic demagnetization experiments. On the other hand, (II) does give a ratio of fourth- to second-order terms of the proper size and sign, and the corresponding departures from octohedral symmetry in the water cluster need not be large enough to contradict x-ray data. The total splitting is materially amplified by the superposition of (III) on (II). It is gratifying that a model can be found which will thus yield the rather peculiar type of crystalline potential required if the basic orbital states of titanium and vanadium are both nondegenerate, but trigonal, as shown by the susceptibility data. Furthermore, it is shown in Section IV that the model gives a splitting in chrome alum of the order of magnitude 10-1 cm-1 and sign deduced by Hebb and Purcell from the magnetization at low temperatures.