The dependence of the room-temperature magnetic anisotropy Δχ of lanthanide complexes on the type of the coordination polyhedron and on the nature of the lanthanide ion is quantitatively analyzed in terms of a model approach based on numerical calculations. The aim of this study is to establish general regularities in the variation of the sign and magnitude of the magnetic anisotropy of lanthanide complexes at room-temperature and to estimate its maximal value. Except for some special cases, the variation of the sign of the magnetic anisotropy over the series of isostructural lanthanide complexes is found to obey a general sign rule, according to which Ce(III), Pr(III), Nd(III), Sm(III), Tb(III), Dy(III), and Ho(III) complexes have one sign of Δχ and Eu(III), Er(III), Tm(III), and Yb(III) complexes have the opposite sign. Depending on the specific coordination polyhedron, a maximal magnetic anisotropy is observed for Tb(III), Dy(III), or Tm(III) complexes, and its absolute value can reach ${\text{50\hspace{0.05em}000×10}}^{\text{−6}}\hspace{0.17em}{\mathrm{cm}}^3 {\mathrm{mol}}^{\text{−1}}$ or more. Results of the present study can be helpful for the analysis of the orientational behavior of lanthanide-containing liquid crystals and lanthanide-doped bilayered micelles in an external magnetic field. The use of the Bleaney theory in the quantitative analysis of the magnetic anisotropy of lanthanide compounds is shown to have limitations because of a large ratio between the crystal-field splitting energy of the ground multiplet of the lanthanide ion and the thermal energy at room-temperature.

The dodecaboride ${\mathrm{LuB}}_{12}$ with cage-glass state and rattling modes has been studied to clarify the nature of the large amplitude vibrations of Lu ions. Discovered anisotropy of charge transport in conjunction with distortions of the conventional fcc symmetry of the crystal lattice may be attributed to coherent motion of Lu ions along a singular direction in the lattice. Arguments are presented in favor of cooperative dynamic Jahn-Teller effect in the boron sublattice to be the reason of the rattling mode, lattice distortion, and formation of the filamentary structure of the higher conducting channels—dynamic charge stripes.