  Substantial amounts of the transition metals Mn, Fe, Co, and Ni can be
substituted for Li in single crystalline Li$_2$(Li$_{1-x}T_x$)N. Isothermal and
temperature-dependent magnetization measurements reveal local magnetic moments
with magnitudes significantly exceeding the spin-only value. The additional
contributions stem from unquenched orbital moments that lead to rare-earth-like
behavior of the magnetic properties. Accordingly, extremely large magnetic
anisotropies have been found. Most notably, the magnetic anisotropy alternates
as easy-plane $\rightarrow$ easy-axis $\rightarrow$ easy-plane $\rightarrow$
easy-axis when progressing from $T$ = Mn $\rightarrow$ Fe $\rightarrow$ Co
$\rightarrow$ Ni. This behavior can be understood based on a perturbation
approach in an analytical, single-ion model. The calculated magnetic
anisotropies show a surprisingly good agreement with the experiment and capture
the basic features observed for the different transition metals.
