Vibron Quasibound State in the Noncentrosymmetric Tetragonal Heavy-Fermion Compound ${\mathrm{CeCuAl}}_3$

We have investigated the noncentrosymmetric tetragonal heavy-fermion antiferromagnetic compound ${\mathrm{CeCuAl}}_3$ ($T_N=2.5\mathrm{K}$) using inelastic neutron scattering (INS). Our INS results unequivocally reveal the presence of three magnetic excitations centered at 1.3, 9.8, and 20.5 meV. These spectral features cannot be explained within the framework of crystal-electric-field models and recourse to Kramers’ theorem for a $4f^1$ ${\mathrm{Ce}}^{3+}$ ion. To overcome these interpretational difficulties, we have generalized the vibron model of Thalmeier and Fulde for cubic ${\mathrm{CeAl}}_2$ to tetragonal point-group symmetry with the theoretically calculated vibron form-factor. This extension provides a satisfactory explanation for the position and intensity of the three observed magnetic excitations in ${\mathrm{CeCuAl}}_3$, as well as their dependence on momentum transfer and temperature. On the basis of our analysis, we attribute the observed series of magnetic excitations to the existence of a vibron quasibound state.

Figure 1

(a) Tetragonal unit cell for ${\mathrm{CeCuAl}}_3$. The arrows represent the active longitudinal optic ($L$-optic) phonon modes at the $H$-point of the Brillouin zone (BZ) with ${}^1\mathrm{H}_3$ symmetry. The displacement vector $\mathbf{u}$ is the same for all other ${\mathrm{Ce}}^{3+}$ ions in the unit cell. (b) The square BZ for the basal plane, showing the location of the $H$ point. (c) Heat capacity (left $y$ axis) of $R{\mathrm{CuAl}}_3$ ($R=\mathrm{Ce}$, black circles and $R=\mathrm{La}$, red squares) and magnetic entropy (right $y$ axis) versus temperature.

Figure 2

Contour plots of the INS data as a function of energy transfer ($E$) and momentum transfer ($Q$): (a) ${\mathrm{CeCuAl}}_3$ and (b) ${\mathrm{LaCuAl}}_3$ at 4.7 K with an incident energy $E_i=40\mathrm{meV}$; (d) ${\mathrm{CeCuAl}}_3$ and (e) ${\mathrm{LaCuAl}}_3$ at 4.7 K with incident energy $E_i=8\mathrm{meV}$. Magnetic scattering in ${\mathrm{CeCuAl}}_3$ at 4.7 K has been estimated by subtracting the data of ${\mathrm{LaCuAl}}_3$ as show in panels (c) and (f) for $E_i=40\mathrm{meV}$ and 8 meV, respectively.

Figure 3

$Q$-integrated 1D cuts of the total scattering from ${\mathrm{CeCuAl}}_3$ (black circles) and ${\mathrm{LaCuAl}}_3$ (red squares) at low $Q=0$ to $4(2.43){\AA }^{-1}$ (a, c) and at high $Q=5$ to $10(6.39){\AA }^{-1}$ (b, d) at 4.7 and 150 K (right side). The inset shows the data from ${\mathrm{CeCuAl}}_3$ and ${\mathrm{LaCuAl}}_3$ with $E_i=8\mathrm{meV}$ ($Q=0$ to $3.6(2.0){\AA }^{-1}$) at 4.7 K.

Figure 4

Energy-integrated $Q$-dependent magnetic scattering from ${\mathrm{CeCuAl}}_3$ at 4.7 K. The solid line (red) represents the square of the ${\mathrm{Ce}}^{3+}$ magnetic form factor and the dotted line (blue) represents the vibron structure factor (see text).

Figure 5

Low-$Q$ ($2.43{\AA }^{-1}$) magnetic scattering in ${\mathrm{CeCuAl}}_3$ at 4.7 K (a) and 150 K (b) at an incident energy $E_i=40\mathrm{meV}$. The green circles in (a) correspond to $E_i=8\mathrm{meV}$ (right $y$ axis). The inset in (b) shows the data with $E_i=6\mathrm{meV}$ at 20 K and $Q=1.7.{\AA }^{-1}$. The thick solid lines represent the fit using the Hamiltonian given by Eq. (1). The dotted lines show the individual components to the fit (see text for details).