Optical Probing of the Antiferromagnetic Phase Transitions in the Heavy-Electron Compounds U2Zn17 and UCu5

We have investigated the complete electrodynamic response of the heavy-electron compounds U2Zn17 and UCu5. Particular emphasis has been devoted to the optical evidence of the antiferromagnetic phase transitions at 9.7 K and 15 K for U2Zn17 and UCu5, respectively. In UCu5, we found an absorption in the far infrared, which is ascribed to excitations across a spin-density-wave-type gap. This feature is absent in U2Zn17. We argue that UCu5 belongs to a characteristically different class of antiferromagnets than U2Zn17 which represents the class of heavy-electron compounds with localized magnetic moments.

diffraction experiments reveal rather conventional types of arrangements of the ordered moments, in both cases of the order of l p g per U ion[3-51. These phase transitions are indicated by distinct anomalies of the specific heat and abrupt changes in the temperature dependence of the magnetic susceptibility. The ordering temperatures may also be identified by non-monotonous variations of the temperature dependence of the electrical resistivity.
For Uz Zn17, the positive slope 6p/6T suddenly increases with decreasing temperature, manifesting lesser scattering of conduction electrons at moment fluctuations. For UCu5 the behaviour is distinctly different [2,6]. The slope @/ST is negative in the paramagnetic state.
Within a small temperature interval it displays a tendency towards divergence but finally changes discontinuously to a large negative value, i.e. p( T) increases considerably with decreasing temperature just below TN. Decaying magnetic scattering and the onset of coherence as the heavy-electron state develops well below TN result in a maximum of p ( T ) approximately 3 K below the Nt5el temperature. Nevertheless, the p ( T ) variation close to but below TN implies that the energy spectrum of the itinerant charge carriers is considerably affected by the phase transition, in contrast to what is observed in UzZn17 111.
In this paper we report on a, to our knowledge, first attempt to study these features in more depth by probing the effects of the phase transitions with optical methods. From our observations we conclude that Uz Zn17 undergoes an antiferromagnetic phase transition involving mainly local magnetic moments. In contrast, UCu5 exhibits an excitation spectrum characterized by the sudden appearance of absorption in the far-infrared (FIR) spectral range at a temperature coincident with T N , which we tend to ascribe to a SDW gap.
However, our experimental results on UCu5 provide a rather puzzling contrast between the SDW-like picture emerging from our optical work and the commensurability of the magnetic order [3,4]. In principle, optical experiments are a very suitable tool because an incommensurate antiferromagnetic order should lead to a spin density wave (SDW) formation and an opening of a gap at the Fermi level c F , leading to a distinct absorption in the excitation spectrum at 24 = 3.52kB T N . Such a SDW arises as a result of a Fermi-surface instability, due to the degeneracy between occupied levels on one side and empty levels on the other side of the Fermi-distribution edge. In the case of a commensurate antiferromagnetic order we would not expect a gap at E F for partially filled bands. In fact, the degeneracy would be destroyed by the periodic crystal potential with large band structure gaps, except at the unlikely situation where the latter potential is very small [7].
Well-annealed polycrystalline samples of U2 Zn17 and UCu5 have been used for our optical investigations. Previous experiments on UzZn17 have shown that all features of low-temperature properties are independent of whether they are measured on poly-or single-crystalline material. For UCu5 we have investigated the same specimen, previously used for studies of low-temperature transport properties [6]. We have performed opticalreflectivity measurements on a very broad frequency range, from the ultraviolet (UV) down to the far infrared (FIR) and, in both cases, as a function of temperature. To this end, we used four spectrometers with overlapping frequency ranges, as described in previous work@]. Both samples were polished in order to obtain flat and shiny surfaces.
In fig. 1 we present the reflectivity spectra on the whole measured frequency range for both compounds a t 300 K (note the logarithmic frequency scale). The insets display the R ( w ) spectra at several temperatures above and below TN in the FIR range (note the linear frequency scale). At frequencies above the mid-IR there is no temperature dependence discernible in the reflectivity spectra of both compounds. The optical conductivity r 1 ( w ) is obtained through Kramers-Kronig (KK) transformations of the R( w ) spectra. The spectra were extended to higher frequencies with the usual extrapolations R ( w ) -1 / w 2 for w c 3 . lo5 em-' and R ( w )l / w 4 for higher frequencies. The very delicate low-frequency extrapolation, below the lowest measurable frequency (i.e. 17 em-') towards zero, was performed with the help of the Hagen-Rubens (HR) relation R ( w ) = 1 -2 q x , using the measured 0d.c. data [1,2,6]. We discuss this in more detail below. Figure 2 displays the complete excitation spectra in terms of the optical conductivity on a logarithmic frequency scale. The FIR part is shown in fig. 3 for several temperatures. The excitation spectra in the mid-IR frequency range are characterized by a dominant absorption, centered at 3000 and 4000 em-' for UCu5 and Uz Zn17, respectively. At higher frequencies, i.e. in the ultraviolet, some weak structures may be identified. A complete band structure calculation would be of help for a precise identification of these absorptions; we tend to ascribe them to electronic interband transitions.
First, we discuss the electrodynamic response of UCu5, with particular emphasis on the  FIR spectral range. The most remarkable feature is the fairly strong temperature dependence of R(w) in FIR. The inset of fig. la) displays this frequency range, of particular relevance for the present discussion. It may be seen that the variation of the temperature dependence of R ( w ) is considerable below TN . Indeed, at 25 K the reflectivity has the typical metallic behaviour, while at 12 K, where a maximum of p ( T ) is observed [2,6], we note a deviation from the usual metallic Drude-like behaviour in R ( w ) at about 40 em-'. As shown in the inset of fig. la), the magnitude of this anomaly grows with decreasing temperature. It is interesting to observe that, nevertheless, the lowest part of R(o) ( fig. la)) at each temperature matches very well a HR extrapolation to 100% reflectivity at w = 0 and taking into account the previosly measured ( T ) values [6]. Considering fig. 3a), one may also check the fairly good correspondence between the FIR conductivity, i.e. 5 1 (o + 0) limit, and the measured ad.&. values of this sample [6], which calls for the good consistency of the KK transformations.
For a chosen frequency range around 30cm-' the temperature dependence of R ( w ) produces a very weak bump at 12 K, a well-defined absorption at 9 K and a damped shoulder at 6 K in al(w) (fig.3~)). The low-frequency optical conductivity, which is merely the consequence of the HR extrapolation, can be described with a renormalized Drude behaviour, defined by enhanced effective mass m* and relaxation time T*. We shall return to this aspect later. We consider it important to note that the general behaviour of c1 (w) in the measured frequency range is completely unaffected by the HR extrapolation. I t is well known that the evaluation of this part of the spectrum is fairly delicate and that G-' (U) may be strongly altered by ways of different extrapolations. We checked this aspect by performing the KK transformations without the extension of the spectra in the form of the HR extrapolation. The bump or absorption at about 30 em-' in o1 (0) turns out to be even more enhanced in that case. Thus, we consider the performed extrapolation as a safe approach for the analysis of the optical spectra, leading therefore to a rather cautious interpretation.
We claim that the temperature dependence of o1 (w) in FIR of UCu5 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 SDW gap [7], consequently implying the partly itinerant nature of the antiferromagnetic phase transition at TN. The optical conductivity below TN can consistently be fitted by a combination of two contributions, namely a low-frequency <<renormalized. Drude contribution, and a phenomenological harmonic oscillator for the absorption at about 30 em-'. Details of the phenomenological fit will be presented elsewhere. Based on these assumptions we may then evaluate the resonance frequency which we ascribe to excitations across the SDW gap. Its saturation value is 28cm-' and corresponds to a reduced gap of 2 4 k B TN = 2.7. It is remarkable that this ratio is in agreement with a previous evaluation arrived at by an analysis of p ( T ) around TN , assuming a two-component description of the total conductivity [61. This latter analysis also suggests that only 20% of the total charge carrier concentration above TN is involved in the SDW phase transition. Hence, the remaining free charge carriers (i.e. -80%) contribute to the optical conductivity with the low-frequency Drude behaviour. This contribution overlaps the SDW gas absorption.
Indeed at 6 K, the SDW gap appears at best as a shoulder. At 6 K, ud.c, is two times larger than at TN and the renormalized Drude contribution partially smears the SDW gap absorption. There is a compelling similarity with the optical properties of URu, Si, 191 and UNiz Si, [lo], where, in analogy to the situation in Cr[11], a SDW gap was also identified.
We now compare the electrodynamic response of UCu6 with that of U, Zn17. As we have already mentioned above, we find no appreciable variation of the temperature dependence of R(w) in FIR when crossing the antiferromagnetic phase transition temperature of UzZn17 with decreasing temperature, Down to our lowest frequency (i.e. 17cm-l) there is no indication of an absorption appearing below TN (fig.3b)). Unless an eventual SDW gap absorption develops at very and thus anomalously low frequencies, we tend to ascribe U, Zn17 to the class of materials with an antiferromagnetic phase transition involving local magnetic moments. Nevertheless, it cannot a priori be excluded that this localized antiferromagnetic order still opens gaps in the electronic band structure, due to the crystal potential and depending on the degree of interaction between possible new boundaries of the Brillouin zone (BZ) and the Fermi surface (i.e. depending on whether the zone boundaries only touch or cut the Fermi surface) [12]. However, this possibility is very unlikely since the magnetic BZ of UzZn17 has been claimed to be identical with the chemical zone [5].
The electrodynamic response of Uz Znl7 is reminiscent of our recent experimental findings on UPdzA13 [13]. In U2Zn17, as indicated by fig. 2b) and particularly by fig. 3b), the w + 0 limit of R(o) and, above all, of o1(w) at low temperatures would be consistent with a HR extrapolation with a very low Ud,c. value. This is, however, in contrast with the p ( T ) results. Therefore, we performed a measurement of the surface resistance R, at 35 and 100 GHz with the cavity perturbation technique [8]. One can then calculate u1 ( fig. 4) from R, with the assumption that X, = R, , X, being the surface reactance. Even though the latter assumption might be too crude [8], it is, nevertheless, gratifying that at low temperatures we obtain a fairly strong frequency dependence of ul(w), with the development of a narrow resonance centered at zero frequency. As in UPdzA13 [13], a fit with the usual renormalized Drude model can fully describe this part of the excitation spectrum. The small amount of spectral weight associated with the narrow renormalized Drude resonance is indicative of an enhancement of the effective mass of the quasi-particles, in agreement with the thermodynamic results [l].
In conclusion, we have shown that the electrodynamic response in UCu5 and UzZnI7 is indicative of the different nature of the antiferromagnetic phase transitions observed in these compounds. There is, however, an interesting analogy between the excitation spectrum of UCu5 and URuz Si,, and between that of U2 Znl, and UPd2A13, which seems to be reflected in the corresponding different behaviours of p( 2'). Nevertheless, it remains to be seen what kind of relation might be established between typical itinerant features in the electrodynamic response of these antiferromagnets, particularly of UCu5 and URuzSi3, and their rather simple magnetic order, apparently commensurate with the lattice. * * *