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.
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