Magnetic properties of a mixed-valence (III/IV) terbium fluoride KTb3F12

The mixed-valence terbium (III/IV) fluoride ${\mathrm{KTb}}_3{\mathrm{F}}_{12}$ crystallizes with the tetragonal symmetry, space group $\text{I4/m.}$ Below $T_N\text{=3.6±0.1\hspace{0.05em}}\mathrm{K}$ this compound exhibits an antiferromagnetic collinear structure with $\text{k=0}$ characterized by ferromagnetic chains of edge-sharing ${\mathrm{Tb}}^{\text{4+}}$ polyhedra and an antiferromagnetic order between the nearest chains. The magnetic moments of the ${\mathrm{Tb}}^{\text{4+}}$ ions deduced from neutron diffraction are equal to 6.95(4) ${\mu }_B$ at 1.4 K and aligned along the c axis. The ${\mathrm{Tb}}^{\text{3+}}$ ions lie in a special position with zero magnetic moments due to a symmetry cancellation effect of the internal molecular field. In other words, ${\mathrm{Tb}}^{\text{3+}}$ ions present a zero time-averaged magnetic moments in the ordered state, whereas $T_N$ corresponds to the long-range antiferromagnetic ordering of the moments of the ${\mathrm{Tb}}^{\text{4+}}$ ions. From the thermal variation of the reciprocal magnetic susceptibility a molar Curie constant of 27.97(1) emu K mol⁻¹ has been obtained, in good agreement with the theoretical value of 27.64 expected for two ${\mathrm{Tb}}^{\text{4+}}$ and one ${\mathrm{Tb}}^{\text{3+}}$ free ions. The ${\mathrm{Tb}}^{\text{4+}}$ contribution to the magnetization is approximated by the Langevin function and then the ${\mathrm{Tb}}^{\text{3+}}$ contribution is obtained by subtracting the calculated ${\mathrm{Tb}}^{\text{4+}}$ contribution to the total magnetization.