Optical investigation of the antiferromagnetic phase transitions in heavy-electron compounds

Abstract We have investigated the electrodynamic response of the heavy-electron compounds UPd 2 Al 3 ( T N = 14.5 K) and UCu 5 ( T N = 15 K). The complete excitation spectra were obtained by Kramers-Kronig transformation of the optical reflectivities measured on a fairly broad frequency range (i.e. from 15 up to 10 5 cm −1 ), combined with the direct measurement of the conductivity at millimeter and microwave frequencies. In UCu 5 we found an absorption in the far infrared below T N , which is ascribed to excitations across a spin-density-wave-type gap and indicates the itinerant nature of the magnetic phase transition. This feature is absent in UPd 2 Al 3 , in accordance with the local magnetic moment character of the antiferromagnetic order.

The electrodynamics of several heavy fermion (HF) metals have been explored in detail. However, significantly less is known about the electrodynamics of the magnetically ordered states of these materials. Although magnetic-ordering and heavy-electron behaviour seem, at first sight, to be mutually exclusive, various experimental observations in recent years indicate that this is not necessarily so. Both magnetic ordering out of a heavy-electron state and the formation of a heavy-electron state in a magnetically ordered matrix seem possible. Examples of these two distinctly different situations are realized in the lowtemperature properties of U2Zn~7 , URu2Si2, UPd2A13 and UCus, which order antiferromagnetically at 9.7 K, 17 K, 14.5 K and 15 K, respectively. In this paper, we contrast our optical investigations on UCu 5 and on UPd2AI 3 with the goal of understanding the effects of the magnetic phase transitions in more depth.

* Corresponding author.
For our optical investigations we used well-annealed polycrystalline samples of UCu 5 and single crystals of UPd2AI 3. We have performed optical reflectivity measurements on a very broad frequency range, from the ultraviolet (UV) down to the far infrared (FIR) and as a function of temperature, as described in previous works [1,2]. Figs. l(a) and 2(a) summarize the experimental findings in the FIR part of the spectrum, which is relevant for the present discussion. The complete reflectivity spectra were already presented elsewhere [1,2] and particularly our new optical measurements on UPd2A13 single crystals, presented here, confirm the general trend indicated by previous investigations on polycrystalline specimens [1]. A full account of these results will be presented in a forthcoming publication [3]. The optical conductivity trl(to), shown in Figs. l(b) and 2(b), is obtained through Kramers-Kronig (KK) transformations of the R(to) spectra. The spectra were extended to higher frequencies with the usual extrapolations [1,2]. The very delicate low-frequency extrapolation, below the lowest measurable frequency towards zero, was per- formed with the help of the Hagen-Rubens (HR) law [1,2]. First, we discuss the electrodynamic response of UCu 5, where the most remarkable feature is the fairly strong temperature dependence of R(~o) in FIR, and particularly below T N. Indeed, at 25 K the reflectivity has typical metallic behaviour, while at 12 K, where a maximum of p(T) is observed [4], we note a deviation from the usual metallic Drude-like behaviour in R(to) at about 40 cm -1. As shown in Fig. l(a), the magnitude of this anomaly grows with decreasing temperature. For a chosen frequency range around 30 cm -~ the temperature dependence of R(to) produces a very weak bump at 12 K, a well-defined absorption at 9 K and a damped shoulder at 6 K in cry(to) (Fig. l(b)). We consider it important to note that the general behaviour of ~(¢0) in the measured frequency range is completely unaffected by the HR extrapolation. Moreover, it is worth noting that the electrodynamic response of UCu 5 bears several similarities with the optical properties of URu2Si 2 [5].
We claim that the temperature dependence of ~r~ (to) in FIR of UCu 5 is related to the onset of the antiferromagnetic order below TN. The absorption most clearly seen at 9 K is interpreted as being due to a spin density wave (SDW) gap [6], consequently implying the partly itinerant nature of the antiferromagnetic phase transition at T s. The optical conductivity below T N can consistently be ftted by a combination of two contributions, namely a low-frequency 'renormalized' Drude contribution, and a phenomenological harmonic oscillator for the absorption at about 30 cm -1. Based on these assumptions we may then evaluate the resonance frequency which we ascribe to excitations across the SDW gap. Its saturation value is 28 cm I and corresponds to a reduced gap of 2za/ kBT N =2.7. It is remarkable that this ratio is in agreement with a previous evaluation arrived at by an analysis of the anomaly in p(T) around TN, assuming a two-component description of the total conductivity [4].
On the other hand, UPd2AI 3 does not display a similar absorption, the onset of which would be coincident with T N. In fact, we do not find a feature at (or near to) 2A---3.52kBTN, which could be ascribed to'a so-called SDW gap. This peculiar behaviour of trl(to ) is indicative of the fact that the antiferromagnetic transition is not the consequence of the 2k F nesting of the Fermi surface (or part of it) and thus is not an instability leading to a SDW ground state. The DC resistivity also indicates the absence of a Fermi surface anomaly, and p(T) reflects the freezing out of the spin-flip scattering mechanism and the increase in the relaxation time ~" [1]. Similar results were also obtained for U2Zn17 [2]. The absence a SDW energy gap is in accordance with the localised character of the antiferromagnetic order [7]. The temperature dependence in trl(to ) is due to a temperature dependent narrow Drude-like resonance in the FIR range, ascribed to the optical conductivity of the heavy quasiparticle. This behaviour is reminiscent of what has been found in other HF systems, like, for example, in CeAI 3 [8]. The narrow resonance centred at to = 0 can be fitted, again, with the so-called renormalized Drude expression [8], which leads to the values m*/m b ~67 at 6 K and m*/m b -27 at 15 K for the effective mass, in good agreement with evaluations from the specific heat data [1,9].
In conclusion, we have shown that the electrodynamic response in UCu s and UPd2AI 3 is indicative of the different nature of the antiferromagnetic phase transitions, observed in these compounds, which also seems to be reflected in the corresponding different behaviours of p(T). Nevertheless, it remains to be seen what kind of relation might be established between typical itinerant features in the electrodynamic response of these antiferromagnets, par-ticularly of UCu 5 and URu2Si 2, and their rather simple magnetic order, apparently commensurate with the lattice.