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For Fe-I, in total, there’s 5 4-fold rotation axes, of which 3 from the x, y and z and 2 that cross diagonal axes in the plane. For Fe-II, there’s 9, 3 on the cube edges, 2 crossing diagonal axes within each plane (which amounts to 6 total). Every 4-fold axis can be taken as the z-axis of the principle axis system, so eta is zero. Since there’re more than 2 4-fold axes in each case, the electric-field gradient tensor is zero.
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