My first understanding of 'van Vleck paramagnetism' refers to open shell configurations short of half filling by one electron. In LS coupling we then have L=S and by the third Hund's rule we obtain a singlet ground state. There is nevertheless a finite paramagnetic susceptibility because of the Zeeman Hamiltonian couples singlet and triplet states (by nonzero off-diagonal elements).
Having started to deal with crystal field states I have learned that more generally, non-diagonal Terms of Zeeman-Hamiltonians are being called 'van Vleck terms'. In case they couple non-degenerate states this produces a second order contribution to the paramagnetic moment and susceptibility. As I see it, this is what constitutes the so-called 'single ion anisotropy'.
However, I have come across abstracts & papers referring to e.g. Tm as a 'van Vleck ion'. Does this imply a singlet ground state (how would Tm do that ?) or more generally express the notion of an 'ion with single ion anisotropy' (due to van Vleck terms)?
Van Vleck's own paper on Thulium garnets may provide some insights:
M. M. Schieber et al, J. Phys. Chem. Solids, vol 27, pp 1041 (1966).
Here the Tm3+ ion CF ground state is indeed a singlet. The 4f configuration is even (4f^12) J=6, L=5, S=1, so there is no problem with that.
THanks for the reference, Carsten. I'll give it a look.
In my personal nomenclature, though, a non-degenerate state is not automatically a singlet (just J=0 is). So in the given case my guess is, that the ground state is the M_J=0 state of the J=6 multiplet? (Well, I'll give it a close look anyway.)
A singlet CF state is automatically non-magnetic as it is invariant under time reversal. Only through mixing with other states (singlet, doublet or triplet) can it acquire a magnetic moment. For this reason 4f shells with odd electron count (=half-integer J) are always at least doubly degenerate, as an electric field cannot break the degeneracy of two states that are related by time reversal. Nor can any other time-reversal even interaction.
The notion of van Vleck is not so much anisotropy, but a higher lying state with larger magnetic moment than the ground state. E.g. there are effective Ising system with very large uniaxial anisotropy but a large moment in the ground state. The susceptibility does not change a lot as function of applied field, so people don't call them van Vleck.
Look at Lea Leask and Wolf to find the exact composition of the different CF eigenstates. A symmetric or antisymmetric combination of M_J=j and M_J=-j also has zero net moment.
The Raising Of Angular Momentum Degeneracy
Of f-Electron Terms by Cubic Crystal Fields
K.R. Lea, J.M. Leask, and W.P. Wolf
J. Phys. Chem. Solids, 23, 1281-1405, 1962.
The term Van Vleck paramagnetism comes historically from terms appearing in the perturbative development of the magnetic susceptibility done by Van Vleck (you can see also J. Jensen A. Mackinstosh "Rare Earth Magnetism"). The first term in the susceptibility is the Van Vleck contribution, which becomes constant at zero temperatura, whereas the second term, the Curie contribution, diverges according to 1/T in the low-temperatura limit. The case of LLW is valid for cubic systems.
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