RAPID COMMUNICATIONS PHYSICAL REVIEW B 93, 121111(R) (2016) High-pressure induced modifications in the hybridization gap of the intermediate-valence compound SmB 6 K. Nishiyama, 1 T. Mito, 1, * G. Prist´ aˇ s, 1, 2 T. Koyama, 1 K. Ueda, 1 T. Kohara, 1 S. Gab´ ani, 2 K. Flachbart, 2 H. Fukazawa, 3 Y. Kohori, 3 N. Takeshita, 4 N. Shitsevalova, 5 and H. Ikeda 6 1 Graduate School of Material Science, University of Hyogo, Hyogo 678-1297, Japan 2 Institute of Experimental Physics, Slovak Academy of Science, 04001 Koˇ sice, Slovakia 3 Graduate School of Science, Chiba University, Chiba 263-8522, Japan 4 National Institute of Advanced Industrial Science and Technology, Ibaraki 305-8562, Japan 5 Institute for Problem of Material Science, National Academy of Science of Ukraine, 03680 Kiev, Ukraine 6 Department of Physics, Ritsumeikan University, Kusatsu 525-8577, Japan (Received 12 March 2014; revised manuscript received 2 March 2016; published 28 March 2016) We have carried out the measurements of high-pressure 11 B-nuclear magnetic resonance on the intermediate- valence compound SmB 6 to investigate the effects of pressure on Sm 4f states and the quasiparticle band. From the measurements of spin-lattice relaxation time, just below the critical pressure P c of nonmagnetic-magnetic phase transition, we find that quasiparticle bandwidth clearly decreases with pressure, while the insulating gap is almost constant or slightly increases. The latter is consistent with the result of a band-structure calculation. These pressure induced modifications in the band structure indicate the enhancement of the density of states of the quasiparticles when approaching P c . The pressure dependence of the Sm 4f states and the origin of the insulating gap are well explained in terms of exchange interactions between conduction and 4f electrons. DOI: 10.1103/PhysRevB.93.121111 Lanthanide-based compounds classified as heavy fermion (HF) compounds show a rich variety of physical properties, for example, magnetic ordering, enhanced effective mass of electrons, and intermediate valence (IV), depending on the magnitude of exchange interactions J cf between conduction and 4f electrons. In such a material, if the Fermi level sits in a gap derived from hybridization between conduction and 4f electrons, the material behaves as a semiconductor, which is called a “Kondo insulator.” SmB 6 is one of a few materials in which one finds many important features arising from the interactions between conduction and f electrons. Sm ions in this compound are in an IV state: the valence at room temperature is ∼2.6[1,2]. The electrical resistivity, which is almost temperature in- dependent above ∼50 K, increases by several orders of magnitude as temperature decreases below ∼50 K. This is evidence for opening of a relatively small insulating gap (50–100 K) [3,4]. The gap is suppressed by the application of pressure, and subsequently SmB 6 becomes metallic, according to transport measurements [5]. Simultaneously, it shows a magnetically ordered ground state above critical pressure P c (= 6–10 GPa) [6–8]. The appearance of the metallic and magnetic phase above P c should involve drastic changes in the Sm 4f sates and the structure of related bands. However, to date, because of a lack of many basic characteristics near P c , for example the specific heat and the susceptibility, the detailed 4f states under pressure have not been clarified. Moreover, quite recently the surface conducting states at low temperatures in SmB 6 have attracted much attention as one of the candidates for topological Kondo insulators [9]. To uncover such a novel physics as well, one needs reliable understanding of fundamental bulk properties. * mito@sci.u-hyogo.ac.jp Let us recall the simple description of J cf which is useful to understand pressure induced changes between localized and delocalized characters. For a 4f 1 electron system, J cf is expressed as J cf ∼ |V | 2 ε F − E f , (1) when the Coulomb repulsion U between two f electrons in the same orbital is sufficiently large. Here, ε F is the Fermi energy, E f is the energy level of the 4f electron, and V is assumed k-independent hybridization. Generally, the application of pressure increases |V | in any 4f n electron systems. For the Ce 3+ ion, E f rises with pressure due to an increase in the Coulomb repulsion, leading to a decrease in ε F − E f . Consequently, J cf (therefore Kondo temperature T K ) increases with pressure, as indeed observed in many Ce-based compounds under pressure. On the other hand, for the Yb 3+ state with a 4f 13 configuration, one can consider E f to be a 4f hole level. Therefore E f lowers as a function of pressure, and both |V | and ε F − E f are expected to increase with pressure. In this context, the P dependence of J cf in Yb-based compounds is nontrivial. However, from the fact that many Yb-based compounds show the localization of the 4f hole under pressure, E f is supposed to be more sensitive to pressure than |V |. For the Sm 3+ state with a 4f 5 configuration, the situation may be similar to the case of the Yb 3+ state owing to spin- orbit coupling, namely, it has one 4f hole within the J = 5/2 multiplet. Note that Eq. (1) is valid in the so-called HF systems where E f is deep enough to ε F , which may not be the case in the IV compounds including SmB 6 at ambient pressure. However, |V | and ε F − E f are crucial factors controlling the 4f states between the localized and delocalized regimes in the IV systems, and the right-hand side of Eq. (1), |V | 2 /(ε F − E f ), will be still a meaningful parameter on the condition that U is sufficiently larger than |V |. 2469-9950/2016/93(12)/121111(5) 121111-1 ©2016 American Physical Society