As a typical strongly-correlated electron system, heavy fermions have attracted intensive attention because of their rich phase diagrams and exotic quantum states such as antiferromagnetism (AFM), superconductivity, and non-Fermi-liquid behavior, where the ground states are tuned by the delicate competition between the Ruderman–Kittel–Kasuya–Yosida (RKKY) and Kondo interactions. A small number of rare-earth based heavy fermion systems exhibit insulating or semiconducting behaviors, thus called Kondo insulator or semiconductor.^[1] Their Fermi level E_F sits right inside the gap formed by hybridization between the localized f and conduction electrons, and the local f moments are generally screened by the conduction electrons with Kondo interactions in a paramagnetic state. For example, the ground state of CeFe₂Al₁₀ is semiconducting and paramagnetic.^[2,3] However, its isoelectronic counterparts CeT₂Al₁₀ (T = Ru and Os) exhibit an unexpected high Nèel temperature T_N = 27.5 K and 28.5 K, respectively. μSR and neutron diffraction measurements have confirmed the AFM order in CeRu₂Al₁₀ with a propagation vector K = (0,1,0),^[4–8] and the ordered magnetic moment μ_AF (≃ 0.3 μ_B/Ce in CeOs₂Al₁₀ and 0.4 μ_B in CeRu₂Al₁₀) is aligned along the c-axis rather than the crystalline electric field (CEF) easy a-axis, indicating a strong anisotropy of the hybridization interactions.^[9,10]

The CeT₂Al₁₀ (T = Fe, Ru, and Os) family crystallizes in an orthorhombic crystal structure of YbFe₂Al₁₀-type (cmcm, Z = 4)^[11] instead of the well-known tetragonal ThMn₁₂-type.^[12] In the unit cell, each Ce atom is situated in a polyhedral cage, consisting of 16 Al atoms and 4 Ru (or Os) atoms and leading to the shortest Ce–Ce distance longer than 5.2 Å. In comparison, its Gd counterpart GdRu₂Al₁₀ has an AFM order below T_N = 18 K with an ordered moment of 7 μ_B/Gd. If the magnetic transition temperatures for rare-earth compounds are assumed to follow the scaling law of their de Gennes factors,^[13–15] the expected Nèel temperature in CeRu₂Al₁₀ is estimated to be only 0.2 K, nearly 100 times smaller than the actual value, arguing against the local origin of the AFM order due to RKKY interactions but favoring an itinerant character of Ce f electrons in CeT₂Al₁₀ instead. The optical studies observed a formation of CDW-like gap along b-axis, probably essential to the abnormal AFM states in both CeRu₂Al₁₀ and CeOs₂Al₁₀.^[16,17] In recent uniaxial pressure experiments, the distance of the Ce–T (T = Ru and Os) along the b axis may be a key parameter to tune T_N.^[18] The magneto-transport study of CeRu₂Al₁₀ suggests an enhanced Nernst coefficient S(T) for its thermoelectric response, similar to the mysterious hidden order in URu₂Si₂.^[19] Despite of these efforts,^[18,20,21] the mechanism of this unusual AFM order in CeT₂Al₁₀ still remains elusive. Point-contact spectroscopy (PCS) can thus serve as a powerful tool to investigate the systematic evolution of the electronic density of states (DOS) across the AFM transition.^[22–24]

In this paper, we have applied point-contact spectroscopy technique to study the high quality CeRu₂Al₁₀ and CeOs₂Al₁₀ single crystals. In both compounds, we have observed two sets of double-peak features at low temperatures far below T_N: One set of double-peak spectra is probably associated with an AFM gap Δ₁, following a mean-field-like temperature behavior, while the other set is likely to be an emergent hybridization gap Δ_h between f and conduction electrons inside the AFM state.

CeRu₂Al₁₀ and CeOs₂Al₁₀ single crystals were grown with the Al self-flux method as described elsewhere.^[18,19] Their resistance R and specific heat C/T vs. temperature T are shown in Figs. 1(a) and 1(b), respectively. The sharp upturns in resistivity and specific heat signal the AFM transition at T_N = 27.5 K and 28.5 K for CeRu₂Al₁₀ and CeOs₂Al₁₀, confirming the high crystal quality as reported. Single crystals from the same batch were broken at room temperature to expose fresh crystal surfaces and then Pt wires were immediately attached on the sample surface with a small drop of conductive silver paint with the averaged Ag grain size ∼ 5 μm, where hundreds of parallel channels between the Ag grains and sample can be assumed and each channel has a much smaller contact area than the total silver paint size around 50–100 μm. This so-called “soft” point-contact method has an advantage of good mechanical and thermal stability against vibrations.^[24] The conductance curves G(V) were recorded with the conventional lock-in technique in a quasi-four-probe configuration, where the sample was always biased positively. The sample was cooled down to 1.8 K and a magnetic field up to 10 T was applied by the Quantum Design PPMS. The exposed surface orientations were later identified by the Laue x-ray diffraction patterns.

Fig. 1.

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	Fig. 1. Temperature dependence of (a) resistance, (b) specific heat C/T, and (c) point-contact zero-bias resistance for both CeRu2Al10 and CeOs2Al10 samples. (d)–(f) Point-contact conductance curves G(V) of CeRu2Al10 at 3.1 K along c, b, and a axes, respectively.

Dozens of contacts have been measured on CeRu₂Al₁₀ and CeOs₂Al₁₀ single crystals, and the resistance of all contacts is in the range of 5–20 Ω. We have to stress that the contact size d should be in the ballistic limit compared with their electronic mean free path l, critical to guarantee the spectroscopic nature of the measured conductance curves. Despite the large ‘footprint’ of the Ag paint with a size around 50–100 μm, hundreds of effective contacts occur in a much smaller region due to the presence of parallel microbridges between the Ag particles and sample. The overall contact area can be estimated by the contact resistance R according to the Sharvin formula^[25]

Figures 1(d)–1(f) show three representative differential conductance curves G(V) at 3.1 K for contacts on CeRu₂Al₁₀ crystals roughly along three principal axes c, b, and a, respectively. They all display an asymmetric double-peak structure around Δ_h ≈ 9 mV (peak to peak distance in Fig. 1(d) as defined in Refs. [26,27]) and another symmetric double-peak feature Δ₁ at around ±25 mV, 30 mV, and 23 mV along a-, b-, and c-axis (half of the peak-to-peak distance in Fig. 1(d) as in the superconductor case), respectively, showing a moderate gap anisotropy. Here, the symmetric double-peak structure displays two characteristic peaks near the gap edges above and below the Fermi energy and depleted density of states inside the gap similar to the superconducting coherence peak, where its peak position is simply taken as the corresponding gap value Δ₁ (we would refer the symmetric double-peak structure as the Δ₁ coherence peaks hereafter). We note that the double-peaks at Δ₁ for I∥ c are relatively weak in intensity compared with other directions, probably implying the two-dimensional nature of the Fermi surface associated with the gap Δ₁. The temperature evolution of point-contact spectra G(V) of CeRu₂Al₁₀ is shown in Fig. 2(a) from 3.5 K to 30.0 K, with the contact along the b-axis crystal orientation. As the temperature increases from 3.5 K, the asymmetric double-peak feature Δ_h evolves into a zero-bias conductance peak (ZBCP) and is barely noticeable at around 21–22 K, while the symmetric double-peak Δ₁ shifts to smaller bias-voltages and the Δ₁ coherence peaks are smeared in intensity and disappear at T > 25.0 K. A V-shape background is observed at 30.0 K above T_N probably due to the Kondo semiconducting gap around the Fermi surface.^[28] For CeRu₂Al₁₀, the temperature dependent Δ₁ gap magnitude in Fig. 2(a) is plotted in Fig. 2(c) in comparison with the Δ1 gap values in other directions. They all follow a BCS mean-field temperature behavior and the gap closes exactly at the Nèel temperature T_N ∼ 27.5 K for CeRu₂Al₁₀. We would thus attribute Δ₁ to the AFM gap below T_N, where the largest AFM gap in the b-axis with the smallest AFM intensity in the c-axis for PCS is consistent with the AFM propagation vector along K = (0,1,0) with the magnetic moment in the c-axis. In addition, we notice that a kink feature at Δ₂ develops in the conductance curve G(V) below T_N as marked by the arrows in Fig. 2(a), suggesting a depleted density of states with the AFM transition in contrast to the Δ₁ coherence peak structure. This kink feature gets more pronounced in another set of G(V) curves as shown in Fig. 2(b) and its voltage position Δ₂ as a function of temperature also follows the mean-field behavior, whose exact origin requires further careful studies.

Fig. 2.

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Fig. 2. (a) and (b) The temperature evolution of soft point-contact conductance curves G(V) as a function of the biased voltage for CeRu2Al10 with surface along b axis and an arbitrary direction, respectively. The curves are vertically shifted for clarity and the dashed lines are a guide for eyes to show the temperature evolution of the AFM gap Δ1 and hybridization gap Δh, respectively. The arrows mark the position of the kink structure Δ2 in the conductance curve G(V). (c) Temperature dependence of the extracted AFM gap Δ1 for CeRu2Al10 in three crystallographic orientations in comparison with the standard mean-field BCS curves and the Δ2 value for the kink structure also follows the BCS behavior.

The asymmetric double-peak feature of CeRu₂Al₁₀ below T_N is characteristic of an emergent hybridization gap Δ_h ∼ 9 meV at 3.2 K, similar to the asymmetric double-peaks for PCS on URu₂Si₂ and UPd₂Al₃.^[29] It probably roots in the modified hybridization between f–c electrons due to the presence of AFM ordering below T_N, yielding a metallic state coexisting with the Kondo semiconducting behaviors. We note that the resistivity below T_N in CeRu₂Al₁₀ is not divergent with decreased temperature as for a typical Kondo semiconductor. In order to quantitatively analyze the hybridization gap Δ_h for CeRu₂Al₁₀ in (001) direction, a co-tunneling model has been adopted to fit the point-contact conductance curves, which has been proven effective in the case of URu₂Si₂ and UPd₂Al₃. Distinct from the general Fano shape in a single Kondo impurity model,^[30] a double-peak resonance separated by a narrow hybridization gap Δ_h is observed instead.^[26,27] Our model formula is , where the first term is the Fano conductance while the second term accounts for the background shape with η as a weighting factor. Figure 3(a) shows one set of G(V) curves for PCS on CeRu₂Al₁₀ along the (001) direction in comparison with their optimal fittings on a parabolic background. A hybridization gap Δ_h = 9 meV is obtained for CeRu₂Al₁₀ at 3.0 K. Its temperature dependence is plotted in Fig. 3(b), and the extracted Δ_h decreases linearly with increasing temperature between 3 K and 19 K, which is in contrast to the BCS-like temperature dependence of Δ₁. A linear extrapolation of Δ_h terminates at approximately 32.5 K, slightly higher than its T_N. Figure 3(c) shows the conductance curves G(V) in different magnetic fields at 1.8 K, where the peak height is gradually suppressed in field but without any obvious change of the peak position.

Fig. 3.

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Fig. 3. (a) Co-tunneling fitting curves (solid lines) in comparison with the temperature dependent conductance curves G(V) (circles). The curves are shifted for clarity. (b) The extracted hybridization gap Δh as a function of temperature from the co-tunneling model fitting (solid squares). A linear extrapolation of the gap closes at 32.5 K (red dashed line) and the black dashed line starts around TN. (c) The point-contact conductance curves G(V) as a function of magnetic field B up to 10 T at T = 1.8 K.

Figures 4(a)–4(c) show the normalized conductance curves G(V) for different CeOs₂Al₁₀ surfaces at 3.0 K, and G_N is the point-contact conductance normalized by the conductance at the highest bias voltage. It is difficult to identify their exact surface orientations due to the limitation of crystal size. In addition to a pronounced parabolic background, the G(V) curves show a similar symmetric double-peak feature associated with the gap Δ₁ in the range of 35–50 mV for different surfaces. At the lower bias-voltage, a symmetric gap-like shoulder feature Δ_h around ±10 mV is commonly observed with more depleted DOS around zero bias, distinguishing itself from that of CeRu₂Al₁₀.

Fig. 4.

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Fig. 4. (a)–(c) The G(V) of CeOs2Al10 at 3.0 K on different cyrstal surfaces. (d) The temperature evolution of the soft point-contact conductance curves G(V) as a function of the biased voltage for CeOs2Al10. The curves are vertically shifted for clarity and the dashed lines are a guide for eyes to show the temperature evolution of the AFM gap Δ1 and hybridization gap Δh, respectively. The arrows mark the position of the kink structure Δ2 in the conductance curve G(V). (e) Temperature dependence of the extracted AFM gap Δ1 for CeOs2Al10 in comparison with the standard mean-field BCS curves and the estimated hybridization gap Δh. (f) Zero-bias conductance curve as a function of temperature G0(T) up to 40 K for a point-contact on CeOs2Al10.

The temperature evolution of point-contact spectra G(V) on CeOs₂Al₁₀ from 1.8 K to 30.0 K is shown in Fig. 4(d). With increasing temperature, the shoulder-like gap feature Δ_h smoothly shifts to smaller bias-voltages and disappears at temperatures above 17 K, while the Δ₁ symmetric double-peaks move to lower bias-voltages and become barely detectable at T > 27 K. CeOs₂Al₁₀ also shows a V-sharp background at temperatures above T_N, consistent with its Kondo semiconductor nature. If we still simply take the Δ₁ peak position as its gap value, the temperature dependence of the AFM gap Δ₁ is plotted in Fig. 4(e) in comparison with the BCS curves. It is clear that the gap Δ₁ in CeOs₂Al₁₀ also follows the mean-field BCS behavior similar to CeRu₂Al₁₀ and it is reasonable to be identified as the associated AFM gap. The shoulder-like gap feature can only be observed at temperatures far below T_N and the dip between the Δ₁ double-peaks becomes flat at the intermediate temperature, corresponding to the kink at 17 K in the temperature-dependent zero-bias conductance curve G₀(T) as in Fig. 4(f). Even though the shoulder-like feature in CeOs₂Al₁₀ should have a common origin as in CeRu₂Al₁₀, most likely due to the new hybridization gap Δ_h, this gap Δ_h opened at much lower temperatures than T_N seems irrelevant or at least a secondary effect of the AFM transition in CeOs₂Al₁₀.

When comparing the conductance curves G(V) between CeRu₂Al₁₀ and CeOs₂Al₁₀, both V-shape backgrounds for temperature above T_N comply with the Kondo semiconductor behavior and the symmetric coherence peaks below T_N can be commonly identified as the AFM gap. Similar gaped structure has been reported in optical conductivity^[16,17] and break junction tunneling measurements,^[31,32] where an AFM gap also develops around T_N and follows the typical mean-field temperature behavior. However, we notice that the reported gap for optical conductivity in CeOs₂Al₁₀ develops below 36 K far above its T_N = 28.5 K and is manifested as a peak at 20 meV. The temperature behavior of the AFM gap in break-junction studies on CeOs₂Al₁₀ is similar to our PCS results and its gap value Δ_AF ∼ 50–60 meV (Δ₁ in our case) seems comparable to ours. The exact origin of the difference among different techniques is unknown and further studies are required. The appearance of Δ₁ coherence peaks in our point-contact results suggests that there should be a Fermi surface instability associated with the AFM transition, where an opened AFM gap modifies the density of states around the Fermi level in a mean-field manner for the abnormal AFM orders in both CeRu₂Al₁₀ and CeOs₂Al₁₀. A drastic drop of the thermopower S(T) from 30 μV/K to –7 μV/K crossing T_N has been observed only along the b axis, also signaling a partial loss of the Fermi surface in the hybridized band around T_N.^[33]

Our directional PCS results on CeRu₂Al₁₀ support the largest AFM gap along the b-axis in the same direction as the AFM propagation vector K = (0,1,0), while the weakest PCS AFM peak intensity is along the c-axis parallel to the ordered magnetic moment. In an itinerant SDW scenario of the AFM order, these observations can be naturally explained by the anisotropic c–f hybridization effect, where the ab-plane hybridization induces a Fermi surface instability connected by the propagation vector K = (0,1,0) and thus yields an AFM transition. Meanwhile, the c-axis magnetic moment is not screened due to a weaker hybridization in this direction considering the small ordered magnetic moment μ Ȭ 0.42 μ_B in CeRu₂Al₁₀. The Ce 4f electrons in CeRu₂Al₁₀ are supposed to be more localized with a larger magnetic moment and less hybridized with a smaller T_N than CeOs₂Al₁₀.^[17] In addition, the opening of a new hybridization gap Δ_h has been observed for both compounds, leading to a metallic nature and interrupting the initial Kondo semiconducting behaviors at low temperatures. Our PCS results on Δ_h are consistent with the claimed V₂ in break-junction tunneling measurements.^[31,32]

The anomalous AFM phase in CeRu₂Al₁₀ and CeOs₂Al₁₀ has been investigated by the soft point-contact spectroscopy. Two sets of double-peak spectra have been observed at low temperatures below T_N on both compounds. The symmetric double-peak feature has been ascribed to a moderately anisotropic mean-field gap Δ₁ and is probably associated with an AFM gap in an itinerant SDW scenario due to the c–f hybridization. In addition, an opening of a new c–f hybridization gap may be a common behavior in such systems with Fermi surface instability. More careful studies are required to clarify the origin of the AFM state and its feedback effect on the c–f hybridization in the Kondo semiconductors CeRu₂Al₁₀ and CeOs₂Al₁₀.