Neutron spectroscopic study of crystal-field excitations and the effect of the crystal field on dipolar magnetism in $\mathrm{Li}R{\mathrm{F}}_4$ ($R=\text{Gd}$, Ho, Er, Tm, and Yb)

We present a systematic study of the crystal-field interactions in the $\mathrm{Li}R{\mathrm{F}}_4$ ($R=\mathrm{Gd}$, Ho, Er, Tm, and Yb) family of rare-earth magnets. Using detailed inelastic neutron scattering measurements, we have been able to quantify the transition energies and wave functions for each system. This allows us to quantitatively describe the high-temperature susceptibility measurements for the series of materials and make predictions based on a mean-field approach for the low-temperature thermal and quantum phase transitions. We show that coupling between crystal field and phonon states leads to line-shape broadening in ${\mathrm{LiTmF}}_4$ and level splitting in ${\mathrm{LiYbF}}_4$. Furthermore, using high-resolution neutron scattering from ${\mathrm{LiHoF}}_4$, we find anomalous broadening of crystal-field excitations which we attribute to magnetoelastic coupling.

Figure 1

(a) Crystal structure of $\mathrm{Li}R{\mathrm{F}}_4$. Depending on $R$, the lattice parameters of the tetragonal structure, space group $I{4}_1/a,Z=4$ are approximately $a=b\simeq 5.2\text{Å}$ and $c\simeq 10.5\text{Å}$. The atoms are situated at approximately ${\text{Li}}^{+}$ (4a) $0,1/4,5/8,R^{3+}$ (4b) $0,1/4,1/8$, and ${\text{F}}^{-}$ (16f) $0.22,0.58,0.54$ sites for origin at $\overline{1}$. (b) Coordination of $R$ ions by nearest eight F and four Li ions. The $R\text{-F}$ and $R\text{-Li}$ bond lengths shown are approximately 2.26 and 3.68 Å, respectively. In the $ab$ plane the ions subtend an angle of ${\phi }_1={34}^{\circ },{\phi }_2={37}^{\circ }$, and ${\phi }_3={45}^{\circ }$ from the $a$ axis.

Figure 2

Magnetic properties of selected $\mathrm{Li}R{\mathrm{F}}_4$ compounds. The bars denote the dimension of spin space while the (red squares) blue circles show the (anti)ferromagnetic ordering temperature. Data for transition temperatures are after Refs. [2, 13, 29].

Figure 3

Neutron spectra recorded for ${\mathrm{LiHoF}}_4$ at three different temperatures using TOFTOF spectrometer. The data were recorded for a 14.2-g powder sample of ${\mathrm{LiHoF}}_4$ using $E_i=10.4$ meV. The red line shows the calculated intensity based on the CEF parameters discussed in the text.

Figure 4

(a) Comparison of the time-of-flight spectra measured on TOFTOF for ${\mathrm{LiHoF}}_4$ and ${\mathrm{LiHo}}_x{\mathrm{Y}}_{1-x}{\mathrm{F}}_4,x=0.045$, measured at 13 K. The red line is a fit to the spectrum using Gaussians with black vertical lines indicating the CEF peak positions. (b) Higher-resolution spectrum of the ground state to first-excited state transition for ${\mathrm{LiHoF}}_4$ and ${\mathrm{LiHo}}_x{\mathrm{Y}}_{1-x}{\mathrm{F}}_4,x=0.045$, showing enhanced broadening of the pure compound relative to the diluted one. Data were recorded at 4 K. The FWHM of the elastic line is shown by the black bar at the bottom. The dotted line shows RPA calculations discussed in the text.

Figure 5

Neutron spectra recorded for a single crystal of ${\mathrm{LiErF}}_4$ at 4, 11, 25, and 100 K. Panels (a) and (c) show cuts taken with scattering wave vectors along ${\mathbf{a}}^{*}$ and ${\mathbf{c}}^{*}$, respectively. The red plots show results of simulated neutron scattering cross sections based on the best-fit CEF parameters shown in Table 2. Data for energy transfers less than 8 meV were recorded on FOCUS ($E_i=12$ meV), while high-energy measurements up to 50 meV were obtained using LRMECS ($E_i=80$ meV).

Figure 6

Inelastic neutron spectrum collected from a powder sample of ${\mathrm{LiTmF}}_4$ at 5 K collected using MERLIN spectrometer. Panels (a) and (b) show data collected using 20- and 80-meV incident energy, respectively. Cuts were centered on $\left|\mathbf{Q}\right|=1.4{\text{Å}}^{-1}$ in panel (a) and $3{\text{Å}}^{-1}$ in panel (b). Calculated spectrum based on CEF parameters from Christensen [19] is plotted in red. Transition energies from ground state to excited states are shown by vertical black lines.

Figure 7

(a) Neutron scattering spectrum of ${\mathrm{LiTmF}}_4$ powder showing temperature dependence of the CEF excitation at 3.77 meV. Measurements were obtained using FOCUS with $E_i=7$ meV. The spectra were fit by a Lorentzian function. (b) Linewidth extracted from fitting the CEF excitation at temperatures from 1.5 to 100 K. The solid line is a simulation of the CEF line-shape broadening by a magnetoelastic model described in the text.

Figure 8

Inelastic neutron scattering measurements on a single-crystal sample of ${\mathrm{LiYbF}}_4$ at 10 K using MERLIN. Panel (a) shows a slice through the spectra collected along $(0,0,l)$. The regions A and B are discussed in the text. Panels (b) and (c) show data collected using $E_i=46$ meV cut along directions parallel to $a$ and $c$ axes, respectively. Panels (d) and (e) show CEF modes between 20 and 65 meV measured using 92-meV incident neutrons. The red line shows CEF parameter refinement discussed in the text.

Figure 9

Simulation of the influence of magnetoelastic coupling on the magnetic spectrum of ${\mathrm{LiYbF}}_4$. The dashed plots indicate the unperturbed CEF peak centers. The level scheme for the unperturbed $(g=0)$ and perturbed ($g=0.2$ meV) states by bold and thin lines, respectively.

Figure 10

Splitting of the ground-state multiplet $J$ sublevels of $R$ ions by the CEF as calculated from inelastic neutron scattering measurements. The labels next to the levels denote the symmetry of that level. Double indices indicate that the level is doubly degenerate. Levels plotted in red and blue denote singlet and doublet states, respectively.

Figure 11

Extraction of the ion-independent $A_l^m$ parameter from the $B_l^m$ CEF parameters discussed in the text.

Figure 12

Overview of experimental and theoretical results of magnetization dependence on temperature and field for $\mathrm{Li}R{\mathrm{F}}_4=\text{Gd}$, Ho, Er, and Yb. The leftmost panels show the measured and calculated inverse susceptibility in an applied field 500–5000 Oe. Triangles (circles) denote the moment measured with applied field along the $a \left(c\right)$ axis. The center-left and right panels show the temperature and field dependence of the order parameter for each compound, respectively. The dashed (solid) line indicates calculations which (do not) include the effect of the hyperfine interaction. The rightmost panels are calculations of the low-temperature magnetic phase diagram for each compound. We include available experimental data from susceptibility measurements for ${\mathrm{LiHoF}}_4$ (Ref. [2]) and ${\mathrm{LiErF}}_4$ (Ref. [13]) for comparison. Solid and dashed lines of the phase diagram indicate calculations which include and exclude hyperfine interactions, respectively.