  Nuclear magnetic resonance (NMR) was recently shown to measure the bulk band
inversion of Bi$_2$Se$_3$ through changes in the $^{209}$Bi nuclear quadrupole
interaction, and the corresponding tensor of the local electric field gradient
was found to follow, surprisingly, the direction of the external magnetic field
if the sample is rotated. This manifests a hidden property of the charge
carriers in the bulk of this topological insulator, which is explored here with
another material, Bi$_2$Te$_3$. It is found that two electric field gradients
appear to be present at $^{209}$Bi, one rests with the lattice, as usual, while
a second follows the external field if it is rotated with respect to the
crystal axes. These electronic degrees of freedom correspond to an effective
rotation of $j$-electrons, and their level life time is believed to be
responsible for a new quadrupolar relaxation that should lead to other special
properties including the electronic specific heat.
