Interplay between hybridization gaps and antiferromagnetic gap in the hole-doped Kondo semiconductor Ce(Os1-yRey)2Al10

The Kondo semiconductor CeOs2Al10 undergoes an antiferromagnetic (AFM) order at an unexpectedly high temperature 28.5 K. We have performed break junction tunneling measurements for the hole-doped system Ce(Os1-yRey)2Al10 (y ≤ 0.1). The tunneling spectrum dI/dV for y = 0 displays successive openings of a hybridization gap V1, an AFM gap VAF and another hybridization gap V2 in the density of states (DOS). On cooling from 36 K to TN, both the gap value V1 and the DOS at the Fermi level, EF, decrease by 8% of the values at 36 K. This fact indicates that the development of short-range magnetic correlations reduces the c-f hybridization gap. For y = 0.02, a peak appears in dI/dV at V = 0 concurrently with the disappearance of V2. With increasing y further, the in-gap states develop at EF, in good agreement with the increase in the Sommerfeld coefficient of the heat capacity. Thereby, TN, V1 and VAF decrease and disappear at y = 0.05. These facts provide compelling evidence that the presence of V1 is necessary for the AFM order in CeOs2Al10.


Introduction
A family of cerium-based compounds CeT2Al10 (T = Fe, Os and Ru) belongs to Kondo semiconductors.
For example, the resistivity (T) in the Os compound shows a thermal activation-type temperature dependence at 30 < T < 80 K. Nevertheless, this compound undergoes an antiferromagnetic (AFM) transition at rather high Néel temperature TN of 28.5 K [1,2]. It has remained a mystery that the TN with a small magnetic moment 0.3 B/Ce is higher than TN = 18 K for the Gd counterpart with 7 B/Gd [3]. Below TN, the slope of (T) increases abruptly, most likely by the formation of a superzone gap. The analysis of anisotropic magnetic susceptibility and the x-ray absorption spectra for single crystals determined the crystal-field ground state to be a Kramer's doublet dominated by |Jz> = |± 3/2>, where |Jz> is the c-axis component of the total angular momentum J = 5/2 [4]. The break junction tunneling spectroscopy (BJTS) is a powerful method to detect fine changes in the density of states (DOS) caused by AFM and charge-density-wave (CDW) transitions. The BJTS uses a crack prepared in a sample as an insulating barrier for the semiconductor-insulator-semiconductor (SIS) junction. Cracking the sample in a liquid-helium atmosphere provides a clean interface without any contamination and oxidation of reactive Ce based compounds. Furthermore, the SIS junction is not affected by the Seebeck effect so that symmetric tunneling spectra are observed [5]. The BJTS for the antiferromagnet Ce(Fe0.95Co0.05)2 showed peaks at V = ±10 mV below TN = 45 K due to a superzone gap opening in the DOS at EF [6]. The CDW gap in CeTe2 was found to decrease when a short-range ferromagnetic order develops at low temperatures. This observation in CeTe2 revealed the interplay between the CDW and magnetic order [7].
Recently, BJTS measurements for CeT2Al10 (T = Fe, Os) have revealed openings of two gaps (1 = 150 meV, 2 = 38 meV) in CeFe2Al10 and three gaps (1 = 100 meV, AF = 50 meV,2 = 25 meV) in CeOs2Al10 [8]. In the latter, the AFM gapAF develops below TN. We pointed out that 1 and 2 are proportional to the Kondo temperature TK, and the ratio 1/2 is approximately 4 for the two compounds with T = Fe and Os. These relations,  ∝ TK and 1/2 = 4, agree with those for the double c-f hybridization gaps calculated with the periodic Anderson model for a crystal-field ground state consisting of |Jz> = |± 3/2> [9]. The 5d hole and electron doping effects in Ce(Os1-yRey)2Al10 and Ce(Os1-xIrx)2Al10 systems, respectively, have been studied by the measurements of magnetic properties, optical conductivity and muon spin relaxation (SR) as well as neutron scattering [10][11][12]. It is found that the 4f state in CeOs2Al10 becomes more itinerant by doping of 5d holes, while the 4f state is localized by the doping of 5d electrons. The semiconducting increase in the (T) below 16 K changes to a metallic behavior at a small level of y = 0.02. For y = 0.1, (T) exhibits a broad maximum at around 100 K which is a characteristic of valence fluctuating Ce compounds. On the other hand, (T) for the electron doped sample with x = 0.04 shows a metallic behavior at low temperatures. For x = 0.15, (T) no longer shows the thermal activation behavior above TN nor the increase below TN. In both systems doped with 5d holes and electrons, the suppression of TN is well correlated with that of the thermal activation energy /kB in (T). In contrast, the Sommerfeld coefficient  in the specific heat increases sharply as x and y are increased. Therefore, we concluded that the presence of the hybridization gap V1 is necessary for the AFM order in CeOs2Al10. Although the activation energy in (T) gives a crude estimation of the gap width, it does not provide us with the information on the temperature variation of the gap structure. Note that (T) depends on the scattering process and the DOS only at the Fermi level. It is important to observe how the three gaps V1, VAF and V2 in CeOs2Al10 are changed by doping the 5d holes and electrons.
For this purpose, we have measured the BJTS on the system Ce(Os1-yRey)2Al10 (y ≤ 0.1). We have reported that the sample with y = 0.02 undergoes an AFM transition at 23 K, above which (T) still exhibits the activation-type temperature dependence. For y = 0.05, however, the AFM transition and the gap /kB in (T) disappear. Furthermore, (T) in y = 0.1 shows a characteristic temperature dependence with a broad maximum around 100 K [10].

Sample preparation and break-junction tunneling measurements
For BJTS measurements, polycrystalline samples of Ce(Os1-yRey)2Al10 (y = 0, 0.02, 0.05 and 0.1) were prepared by arc melting and subsequent annealing in an evacuated quartz ampoule at 850 ℃ for 7 days [2]. The atomic composition was determined by electron-probe microanalysis, thereby the real compositions of Re were found to agree with the initial ones. In addition, a small amount of impurity phase Os4Al13 has been detected. The midpoint of the jump in the specific heat has been taken as the AFM ordering temperature TN [10].
The samples were shaped into a plate of 3×2×0.5 mm 3 for BJTS measurements. In order to crack it perpendicularly in the middle, we cut a groove into the surface. The plate was mounted on a flexible substrate, and an adjustable force was applied from its back to make a crack in a liquid-helium chamber. The spectra of dI/dV, where I and V represent the tunneling current and the bias voltage, respectively, have been recorded using a standard lock-in technique by applying V along the long axis of the sample [8]. The different thermal expansions between the sample and the substrate made the junction unstable at elevated temperatures. In fact, we could observe the spectra on heating just to 65 K.

Experimental results
The tunneling spectra dI/dV vs the bias voltage V for Ce(Os1-yRey)2Al10 (y = 0, 0.02 and 0.05) at 4.4 K are shown in Fig. 1. The spectra are normalized by the values at V = 400 mV. The absolute value of dI/dV depends on the junction resistance RJ, which is determined by the thickness of insulating barrier [14]. In the high-bias range at V = 400 mV, the values of RJ are 20 -10000 Ω at 4.4 K whose magnitude is much larger than the sample resistance 10 -50 mΩ measured before breaking. This relation satisfies the condition to measure the voltage drop by the tunneling current in the insulating barrier. By measuring the spectra for many junctions, we confirmed that both the gap structures and the width V P-P hardly depend on RJ [15]. Such a result is in accordance with a principle of the tunneling spectroscopy.
There are three gap structures in the spectrum for y = 0. The peak structures at ± 200, 100 and 50 mV are denoted as V1, VAF and V2, respectively, whose values agree with those obtained for single crystals [8]. The peak structures of VAF change to a shoulder in the spectrum for y = 0.02, where a peak appears at V = 0. This peak structure develops in the spectrum for y = 0.05, where the gaps V1 and VAF disappear. These changes in the spectrum with y indicate that the 5d hole doping suppresses the hybridization gaps and induces an in-gap state at EF. These behaviours are consistent with the gap structures in the DOS calculated on the basis of the periodic Anderson model which takes into a slight dispersion in the f-band in the orthorhombic Kondo semiconductors [16].
The temperature dependences of dI/dV vs V are shown in Fig. 2 for three selected compositions y = 0, 0.02 and 0.1. For y = 0, we present the data obtained with the single crystal [8] because the gap structures are clearer than that obtained with the polycrystal. We note that there is little difference in the gap structures between the two. The voltage difference between the shoulders at ±200 mV at 78.5 K is denoted as V1. On cooling, the shoulders change to peaks. Below TN, other peaks develop at ±100 mV, whose peak-to-peak voltage is denoted as the AFM gap VAF = 200 mV. On further cooling below 16 K, additional peaks appear at ±50 mV, whose peak-to-peak voltage is denoted as V2.
In the spectra for y = 0.02, the dI/dV at 40 K displays shoulders at V1/2. The shoulders change to peaks at 35 K, and transform into shoulders again at T < 30 K. On cooling below 27 K (> TN = 23 K), other shoulders appear at VAF/2. At low temperatures, the dI/dV exhibits a cusp at V = 0, which develops into a peak on cooling. The spectra for y = 0.1 is characterized by one cusp at V = 0. The development of a cusp at V = 0 is a characteristic of a metallic heavy fermion state [17]. It indicates that the 4f state in CeOs2Al10 becomes more itinerant by 5d hole doping. With increasing y, in fact, the behavior of (T) changes from the Kondo semiconducting one to that for the valence fluctuating Ce compounds [10].
The temperature dependences of the gap widths V P-P (= V1, VAF and V2) are plotted in Fig. 3(a). For y = 0, the black and blue data are obtained with a single crystal and a polycrystal, respectively, whose temperature variations are essentially same. The gap width V1 for y = 0 decreases from 430 to 400 mV at around 36 K, which is still above TN = 28.5 K. We recall that the CDW-like charge gap develops in CeOs2Al10 on cooling below 36 K [18]. Similarly for y = 0.02, V1 decreases on cooling from 50 to 27 K (> TN = 23 K). It is reminiscent of the CDW gap in CeTe2 which decreases on cooling below 6.1 K, where a short-range ferromagnetic order develops [6]. By analogy, the reduction in V1 occurring above TN in Ce(Os1-yRey)2Al10 (y = 0, 0.02) may be attributed to the onset of a short-range magnetic correlation. The gap VAF for y = 0 increases gradually below TN, whereas that for y = 0.02 seems to appear suddenly at 27 K. The gap V2 for y = 0 appears below 16 K, but corresponding anomaly is absent for y = 0.02. Figure 3(b) displays the temperature dependences of normalized zero bias conductance, {NZBC} 1/2 = {[dI/dV (V = 0)] / [dI/dV (V = 400 mV)]} 1/2 . We note that the NZBC is proportional to the square of the DOS at the Fermi level, N(EF). The NZBC for y = 0 gradually decreases and bends at around 36 K, which occurs simultaneously with the sudden decrease in V1. It suggests that a part of Fermi surface is lost by the development of the short-range correlation. Besides, the significant change in the Fermi surface on cooling from 36 K manifests in the sharp decrease in the thermopower, which is very sensitive to the energy derivative of quasiparticle density of states at EF, sharply decreases only along the b-axis [19]. For y = 0.02, the decrease in NZBC turns to an increase below 27 K due to the development of ingap states at EF. For y = 0.1 with no AFM transition, the NZBC increases monotonically on cooling. Figure 4(a) displays the y dependences of gap widths V1, VAF and V2 as well as {NZBC} 1/2 . The increase in {NZBC} 1/2 with y is consistent with that in the value as shown in Fig. 4(b). The inverse correlation between TN and  in Fig. 4(b) indicates that the increase of N(EF) suppresses the AFM order.   Moreover, the TN and the gap widths V1 and VAF are largely suppressed at a small hole-doping level y = 0.02, and all disappear at y = 0.05. Therefore, the AFM transition is strongly correlated with the hybridization gap V1. This relation supports our previous argument that the presence of the hybridization gap V1 is necessary for the unusual AFM order [10]. Here, let us compare the c-f hybridization gap V1 with the spin gap which was observed by inelastic neutron scattering [12]. The spin gap exists at 11 meV in the undoped sample with y = 0. For y = 0.03, TN is decreased to 21 K, but the spin gap still exists at the same energy 11meV while the excitation intensity is much reduced. On the other hand, the spin gap disappears in the 5d electrons doped systems Ce(Os1.92Ir0.08)2Al10 with TN = 21 K. It is highly required to examine by the BJTS wherever or not the hybridization gap V1 is correlated with the spin gap.

Summary
We have performed the BJTS measurements for the Ce(Os1-yRey)2Al10 (y ≤ 0.1) to study how the two hybridization gaps V1, V2 and the AFM gap VAF change by doping of the 5d holes in CeOs2Al10 with TN = 28.5 K. For the undoped sample, both the hybridization gap V1 and the magnitude of N(EF) decrease on cooling below 36 K. These reductions occurring above TN are attributed to a short-range correlation. the in-gap states at EF develops further. We found a strong correlation between the variations of TN, V1 and VAF. Thus, we conclude that the presence of the hybridization gap V1 above TN is necessary for the unusual AFM order.