Crystal fields in YbInNi${}_4$ determined with magnetic form factor and inelastic neutron scattering

The magnetic form factor of YbInNi${}_4$ has been determined via the flipping ratios $R$ with polarized neutron diffraction, and the scattering function $S(Q,\omega )$ was measured in an inelastic neutron scattering experiment. Both experiments were performed with the aim of determining the crystal-field scheme. The magnetic form factor clearly excludes the possibility of a ${\Gamma }_7$ doublet as the ground state. The inelastic neutron data exhibit two almost equally strong peaks at 3.2 meV and 4.4 meV which points, in agreement with earlier neutron data, toward a ${\Gamma }_8$ quartet ground state. Further possibilities such as a quasiquartet ground state are discussed.

Figure 1

Ytterbium magnetic amplitudes $|\mathbf{m}(\mathbf{Q})|$ measured with an applied field of 2 T at $T$ $=$ 5 K (a) and $T$ $=$ 20 K (b). The full blue squares correspond to (00l), the full red circles to (hh0), and the black open squares to other reflections with even indices.

Figure 2

Comparison of simulated ytterbium magnetic amplitudes $|\mathbf{m}(\mathbf{Q})|$ at $T$ $=$ 5 K for different ground states. The full symbols are the measured values for ($00l$) (blue squares) and ($\mathit{hh}0$) (red circles); the lines are simulations for the ($00l$) (blue) and ($\mathit{hh}0$) (red) directions for the different crystal-field propositions. The black line corresponds to the spherical form factor. The values for $\sin \theta /\lambda$ $=$ 0 (black triangles) come from magnetization.

Figure 3

Scattering function of YbInNi${}_4$ for $\left|\mathbf{Q}\right|$ in between 0.35 Å${}^{-1}$ and 2.3 Å${}^{-1}$ at 2 K (open black circles) and 5 K (full blue circles), and of LuAuCu${}_4$ (open red squares), also at 5 K. The insets represent the elastic scattering divided by 42. The extra scattering in the YbInN${}_4$ data between 2.5 meV and 6 meV is attributed to magnetic scattering.

Figure 4

Temperature evolution of the scattering function of YbInNi${}_4$ for 12 meV incident energy and $\left|\mathbf{Q}\right|$ in between 0.35 Å${}^{-1}$ and 2.3 Å${}^{-1}$. The insets represent the elastic scattering divided by 42, the dashed lines show crystal-field excitations resulting from a crystal-field fit, and the solid lines are the total fitted magnetic scattering. Note, the fitting region was restricted to energy transfers below $-$2 meV and above 2.5 meV to avoid the strong elastic and the spurious scattering at the tail of the elastic line.

Figure 5

Simulated inelastic scattering function at 5 K for a quasiquartet (left) and quartet (right) ground-state crystal-field model.