Hall effect and magnetic ordering in $RB12$

The concentration of carriers in $LuB12$ is evaluated theoretically by applying ab initio FP-LMTO calculations. Theoretical results are found to be in agreement with high-precision measurements of the Hall coefficient $RH(T)$ carried out on single crystals of the rare-earth dodecaborides $RB12$ $(R=Ho,Er,Tm,Lu)$ at temperatures $1.8–300K$⁠. The nature of the antiferromagnetic ordering in $RB12$ is investigated within an RKKY-like model supplemented by comprehensive electronic structure calculations for paramagnetic, ferromagnetic, and antiferromagnetic phases.