  The recent discovery of n-type Mg$_3$Sb$_2$ thermoelectric has ignited
intensive research activities on searching for potential n-type dopants for
this material. Using first-principles defect calculations, here we conduct a
systematic computational screening of potential efficient n-type lanthanide
dopants for Mg$_3$Sb$_2$. In addition to La, Ce, Pr, and Tm, we find that high
electron concentration ($\geq$ 10$^{20}$ cm$^{-3}$ at the growth temperature of
900 K) can be achieved by doping on the Mg sites with Nd, Gd, Ho, and Lu, which
are generally more efficient than other lanthanide dopants and the anion-site
dopant Te. Experimentally, we confirm Nd and Tm as effective n-type dopants for
Mg$_3$Sb$_2$ since doping with Nd and Tm shows superior thermoelectric figure
of merit zT $\geq$ 1.3 with higher electron concentration than doping with Te.
Through codoping with Nd (Tm) and Te, simultaneous power factor improvement and
thermal conductivity reduction are achieved. As a result, we obtain high zT
values of about 1.65 and 1.75 at 775 K in n-type
Mg$_{3.5}$Nd$_{0.04}$Sb$_{1.97}$Te$_{0.03}$ and
Mg$_{3.5}$Tm$_{0.03}$Sb$_{1.97}$Te$_{0.03}$, respectively, which are among the
highest values for n-type Mg$_3$Sb$_2$ without alloying with Mg$_3$Bi$_2$. This
work sheds light on exploring promising n-type dopants for the design of
Mg$_3$Sb$_2$ thermoelectrics.
