  Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained
in ultracold atom experiments, are investigated. These molecules are known to
exhibit a degree of quantum chaos, due to the strong anisotropic mixing of
their angular spin and rotation degrees of freedom. Within a model of these
molecules, we identify different realms of this anisotropic mixing, depending
on whether the spin, the rotation, or both, are significantly mixed by the
anisotropy. These realms are in turn generally correlated with the resulting
magnetic moments of the states.
