Kondo scaling of the pseudogap in CeOs₄Sb₁₂ and CeFe₄P₁₂

CeOs₄Sb₁₂ and CeFe₄P₁₂ are classified as Kondo semiconductors, which show coupled changes in electrical transport, thermodynamic and magnetic properties with a low-temperature semiconductor-like electrical resistivity. We have carried out core level and valence band photoemission spectroscopy on single crystal CeOs ₄Sb₁₂ and CeFe₄P₁₂ to study their electronic structure and the evolution of states at the Fermi level as a function of temperature (∼10-300K). The Ce3d core level spectra show the presence of f⁰, f¹ and f² final states with very different relative intensities in the two compounds. Single-impurity Anderson model calculations provide f electron counts of n_f = 0.97 and 0.86 per Ce atom, suggestive of a low-and high-T_K (= single ion Kondo temperature) for CeOs₄Sb₁₂ and CeFe ₄P₁₂, respectively. The high-resolution temperature-dependent near-Fermi level spectra show pseudogaps of energy ∼ 50meV and ∼ 110meV in the valence band density of states(DOS) of CeOs ₄Sb₁₂ and CeFe₄P₁₂, respectively. The temperature dependence of the DOS at the Fermi level follows the change in effective magnetic moment estimated from magnetic susceptibility for both materials, confirming the Kondo nature of the pseudogap in CeOs ₄Sb₁₂ and CeFe₄P₁₂. A compilation of measured pseudogaps using photoemission and optical spectroscopy identifies the charge gaps Δ_C for Ce-based Kondo semiconductors and provides a direct relation with T_K given by Δ_C ∼ 2k _BT_K. In conjunction with the known behaviour of the spin gaps Δ_S ∼ k_BT_K, the results establish the coupled energy scaling of the spin and charge gaps in Kondo semiconductors.