Charge dynamics in the Kondo insulator Ce3Bi4Pt3

We report the reflectivity and optical conductivity of the Kondo insulator Ce3Bi4Pt3. For temperatures less than 100 K, depletion of the conductivity below about 300 cm−1 signifies the development of a charge gap. The temperature dependence of the disappearance of the spectral weight scales with the quenching of the Ce 4f moments.

Some mixed valent compounds show a semiconducting behavior at low temperatures. Recently, renewed interest has been focused on the nature of the small gap responsible for the insulating ground state [1]. Since the periodic Kondo Hamiltonian has been used to describe the mixed valent compounds, the notion Kondo insulator has been coined.
We address the crucial issue about the nature of the Kondo insulator gap. With no electron-electron correlation (U = 0), a small gap is expected due to the coherent hybridization between d and f bands [2]. Essentially, this gap is not different from bonding antibonding gaps of conventional band structure c~,lculat'~c, ns. When the correlation is switched on (Urr~0), the Kondo coupling J disturbs the conduction electrons and strongly effects the gap value. In that case the temperature dependence of the magnetic interaction may correlate with the temperature dependence of the gap. By ';at infrared measurements [3], we probe the temperature-dependent evolution of the charge response (ad~o)) and the gap formation for the Kondo insulator Ce3Bi4Pt3.
In Fig. l(a) the infrared reflectivity is shown for selected temperatures. In the high-temperature region * Corresponding author. 1100-300 K) the reflectivity does not show much temperature dependence. Below 100 K the reflectivity begins to show strong temperature dependence, and exhibits characteristics of gap development at low frequency. In Fig. I(b) the real part of the optical conductivity, a~), is shown as a function of frequency. Between about 100 and 300 K the conductivity is nearly constant as a function of frequency in the far infrared. Changes of the conductivity are modest above 100 K; however, below this temperature spectral weight begins to disappear from the lowfrequency region signifying the development of a charge gap or pseudogap.
The conductivity is strongly depleted up to a characteristic frequency of about 300 cm ~ at low temperature, which corresponds to roughly 400 K. The data show, however, that the development of the gap primarily occurs only below the much lower temperature of 100 K indicating a severe departure from a picture of gap disappearance based on rigid bands and simple thermal activation of carriers.
Ce3Bi4Pt3 exhibits the gradually magnetic -nonmagnetic transition of mixed valent, dense Kondo systems [4]. In addition, inelastic neutron scattering measurements [5~ have detected a spin gap at an energy of As = 160 cm-~ opening at temperatures below 100 K. The simultaneou~ formation of spin and charge gap 0921-4526/94/$07.00 () 1994 Elsevier Science B.V. All rights reserved SSDI 0921-45261931E0208-X (b) Real part of the optical conductivity a~ltn) for different temperatures (from below: 25, 50, 75, 100 and 300 K). A gap is opening below 100 K; the prominent feature Ac seems to be independent of temperature.
below 100 K provokes the proposition that the charge gap is triggered by the magnetic-nonmagnetic transition. On assuming the Curie law with a temperature-dependent magnetic moment/~,rf (T), we can calculate the effective magnetic moment/~fd T) of the localized, magnetic 4f states exploiting the experimental [4] magnetic susceptibility Z (see Fig. 2 gives the magnetic susceptibility data from Ref. [4]; the round points are from the neutron data of Ref. [5]. Right axis: The diamond-shaped points represent the localized charge carrier as a function of temperature as calculated by the optical sum rule (Eq. {2)). The thin line indicates the linear temperature dependence below T*.
a convincing agreement has emerged as depicted in Fig. 2.
In contrast to ordinary heavy fermions where the local 4f states delocalize below the coherence temperature T*, the Kondo insulators show a localization of the charge carrier to the local moments.
We now address the physical nature of Ac. Theoretical estimations of hybridization gaps give a direct gap A direct of the order of tenths of eV and an indirect gap zI indirect ,..., 1/2 (zldircct)2/O "~ TK, with D the width of the conduction band [6]. With TK = 320K for Ce3Bi4Pt3 [4] and the gap temperature Ac/ka = 450 K, the arguing of the optical gap coinciding with the transport gap seems reasonable. On the other hand, the linear extrapolation of the steep part of ax((ld to zero gives a value of the order of 100 K. Similar temperatures of the transport gap have been predicted on suggesting an opening transport gap [7]. Another possibility ~s to interpret A~ as the energy needed to excite a bound charge out from a local Kondo singlet (Ac'~ kBTKI. The temperature independence of Ac is explained by the fixed Kondo energy TK. In conclusion, we have presented explicitly the formation of a charge gap for the mixed valent Kondo insulator Ce3Bi4Pt 3 at low temperature. The gap formation is characterized by (i) a temperature-independent gap with a energy Ac similar to the single ion Kondo energy kaTz and !ii) a loss of spcctral weight ~caling with the quenching of the local 4f moments.