Terahertz conductivity of the heavy-fermion compound UNi${}_2$Al${}_3$

We have studied the optical properties of the heavy-fermion compound UNi${}_2$Al${}_3$ at frequencies between 100 GHz and 1 THz (3 and 35 cm${}^{-1}$), temperatures between 2 and 300 K, and magnetic fields up to 7 T. From the measured transmission and phase shift of radiation passing through a thin film of UNi${}_2$Al${}_3$, we have directly determined the frequency dependence of the real and imaginary parts of the optical conductivity (or permittivity, respectively). At low temperatures the anisotropy of the optical conductivity along the $a$ and $c$ axes is about 1.5. The frequency dependence of the real part of the optical conductivity shows a maximum at low temperatures, around 3 cm${}^{-1}$ for the $a$ axis and around 4.5 cm${}^{-1}$ for the $c$ axis. This feature is visible already at 30 K, much higher than the Néel temperature of 4.6 K, and it does not depend on external magnetic fields as high as 7 T. We conclude that this feature is independent of the antiferromagnetic order for UNi${}_2$Al${}_3$, and this might also be the case for UPd${}_2$Al${}_3$ and UPt${}_3$, where a similar maximum in the optical conductivity was observed previously [Dressel et al., Phys. Rev. Lett. 88, 186404 (2002)].

Figure 1

The frequency dependence of the real part of the optical conductivity ${\sigma }_1$ and permittivity ${\epsilon }_1$ for Drude, Lorentz, and combined Drude and Lorentz response. The parameters used for the Drude behavior are ${\sigma }_{\mathrm{dc}}=25000$ ${\Omega }^{-1}{\mathrm{cm}}^{-1}$ and ${\Gamma }_D/\left(2\pi \right)=$ $0.08$ ${\mathrm{cm}}^{-1}$. For the Lorentz oscillator we chose ${\nu }_0={\omega }_0/\left(2\pi c\right)=5$ ${\mathrm{cm}}^{-1}$, ${\nu }_{P,L}={\omega }_{P,L}/\left(2\pi c\right)=3800$ ${\mathrm{cm}}^{-1}$, and ${\Gamma }_L=11$ ${\mathrm{cm}}^{-1}$.

Figure 2

Transmission spectra along the $a$ axis of the UNi${}_2$Al${}_3$ thin film on YAlO${}_3$ substrate for different temperatures.

Figure 3

Transmission measurements with an external magnetic field were performed in three different configurations of sample and magnetic field, each with two different polarizations of the electric-field vector of the radiation.

Figure 4

Real parts of optical conductivity and permittivity of UNi${}_2$Al${}_3$ along the $a$ axis (left) and $c$ axis (right) for different temperatures. Data points on the ${\sigma }_1$ axis indicate the dc conductivity.

Figure 5

Ratio of ${\sigma }_1$ along the $a$ and the $c$ axis for UNi${}_2$Al${}_3$, as a function of frequency for three exemplary temperatures.

Figure 6

The real part of the optical conductivity ${\sigma }_1$ for UNi${}_2$Al${}_3$ compared to the corresponding data for UPd${}_2$Al${}_3$ from literature.[20]

Figure 7

Transmission spectra at 2 K with electric field polarized along the $a$ axis with external magnetic fields between 0 and 7 T (see Fig. 3, configuration 1). The transmission shows no field dependence within the accuracy of our measurement.

Figure 8

On top, schematics of the YAlO${}_3$ substrate with the main axes in red and black and the UNi${}_2$Al${}_3$ film on YAlO${}_3$ with the main axes of the film in green and blue and the main axes of the underlying substrate in red and black are shown. The orange arrows indicate the polarization of the light during the measurements. The transmission of the bare YAlO${}_3$ substrate along its main axes shows usual Fabry-Perot resonances. By fitting transmission and phase shift (here only transmission is shown) we can determine the optical parameters along the “black” main axis (${\epsilon }_1^b,{\epsilon }_2^b$) and along the “red” main axis (${\epsilon }_1^r,{\epsilon }_2^r$). These parameters are used in the fit of transmission and phase shift of the UNi${}_2$Al${}_3$ film on YAlO${}_3$ to extract ${\sigma }_1$ and ${\sigma }_2$ (or equivalently ${\epsilon }_1$) of UNi${}_2$Al${}_3$ along $a$ and $c$ axis. The double maxima in the transmission of UNi${}_2$Al${}_3$ film on YAlO${}_3$ are caused by the birefringent substrate because the radiation is not polarized along any of its main axes.

Figure 9

Transmission and phase shift of a UNi${}_2$Al${}_3$ film on a YAlO${}_3$ substrate at 4 K along the $c$ axis of UNi${}_2$Al${}_3$. The dotted spectra are measured, and the solid line is a fit optimized around 14 cm${}^{-1}$. This frequency range is enlarged in the insets. By fitting each Fabry-Perot maximum separately we find the frequency dependence of the optical properties.