Magnetic properties of lithium rare-earth fluorides: Ferromagnetism in LiEr${\mathrm{F}}_4$ and LiHo${\mathrm{F}}_4$ and crystal-field parameters at the rare-earth and Li sites

Single crystals of LiEr${\mathrm{F}}_4$ and LiHo${\mathrm{F}}_4$ have been grown and their magnetic properties measured from 1.3 K to 300 K. LiHo${\mathrm{F}}_4$ turned out to be a nearly ideal Ising ferromagnet with $T_C=1.30\mathrm{}\pm 0.05$ K and a saturation magnetization along the crystalline $c$ axis of $(6.98\mathrm{}\pm 0.02){\mu }_B$. In LiEr${\mathrm{F}}_4$ no ordering was observed, but extrapolation indicates that below 0.5 K it will be ferromagnetic with the magnetic moments in the crytalline $\mathrm{ab}$ plane. From the susceptibilities the crystal-field parameters $B_n^m$ with $(n, m)=(2, 0), (4, 0), (4, 4), (6, 0), (6, 4)$ have been extracted giving for ${\mathrm{Er}}^{3+}$ in LiEr${\mathrm{F}}_4$: 430., -985., 1185., -5., $740.+i135$. (${\mathrm{cm}}^{-1\mathrm{}}$) and for ${\mathrm{Ho}}^{3+}$ in LiHo${\mathrm{F}}_4$: 470., -825., 1050., -10., $760.+i150$ (${\mathrm{cm}}^{-1\mathrm{}}$). The exchange constants were found to be small compared to the dipole interactions. Furthermore the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ NMR spectra have been obtained in these materials as well as in LiTb${\mathrm{F}}_4$ thereby determining the second-order crystal-field parameters at the Li site: $q=0.0363, 0.0354, \mathrm{and} 0.0343$ ${\mathrm{\AA }}^{-3\mathrm{}}$ for the Er, Ho, and Tb compound, respectively. The crystal-field parameters are compared to values calculated from point charges, showing agreement at the Li sites but not at the rare earth sites.