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Evidence for Gamma_8 Ground-State Symmetry of Cubic YbB12 Probed by Linear Dichroism in Core-Level Photoemission

We have successfully observed linear dichroism in angle-resolved Yb3+ 3d5/2 core-level photoemission spectra for YbB12 in cubic symmetry. Its anisotropic 4f charge distribution due to the crystal-field splitting is responsible for the linear dichroism, which has been verified by spectral simulations using ionic calculations with the full multiplet theory for a single-site Yb3+ ion in cubic symmetry. The observed linear dichroism as well as the polarization-dependent spectra in two different photoelectron directions for YbB12 are quantitatively reproduced by theoretical analysis for the Gamma_8 ground state, indicating the Gamma_8 ground-state symmetry for the Yb3+ ions mixed with the Yb2+ state.

Rare earth-based strongly correlated electron systems show various interesting phenomena such as competition between magnetism and unconventional superconductivity, charge and/or multipole ordering, and formation of a narrow (∼meV) gap at low temperatures. Among them, YbB 12 is known as a Kondo semiconductor 1-5 , which has recently been recognized as a candidate for topological insulators 6 , as intensively discussed for another Kondo semiconductor SmB 6 7-9 . The mean valence of YbB 12 has been estimated as ∼ 2.9+ by bulk-sensitive 3d core-level hard X-ray photoemission (HAXPES) spectroscopy 10 . In order to discuss mechanisms of the gap opening at low temperatures 5,[11][12][13][14][15][16] and the possibility of topological insulator, it is essential to verify the ground-state symmetry of the Yb 3+ [4f 13 (one hole)] state determined by crystal-field (CF) splitting. Nevertheless, it is unclear for YbB 12 . Its eight-fold degenerated Yb 3+ 4f 7/2 levels are considered to be split into two quartets 17 (normally, two doublets and a quartet) due to CF in YbB 12 . The ground state of the Yb 3+ ions is commonly asserted to be in a so-called Γ 8 symmetry 5,18 , but a possible accidentally degenerated Γ 6 + Γ 7 ground state is not completely excluded. In this letter, we show the evidence for the Γ 8 symmetry of the Yb 3+ sites in the ground state of YbB 12 on the basis of linear dichroism in angle-resolved core-level photoemission.
Generally, it is difficult to experimentally determine the 4f ground-state symmetry. Inelastic neutron scattering is useful but other excitations like phonon excitations often hamper to observe magnetic 4f −4f excitations. Linear dichroism (LD) in 3d−to−4f soft Xray absorption spectroscopy (XAS) for single crystals is powerful owing to the dipole selection rules, as reported for Ce compounds [19][20][21][22] . However, it is not applicable for compounds in cubic symmetry, in which there is no anisotropic axis relative to the electric field of an incident light. On the other hand, the selection rules work also in photoemission process while the excited electron energy is much higher than that in the absorption. Furthermore, there is another controllable measurement parameter as "photoelectron detection direction" relative to the singlecrystalline axis in addition to the polarization direction of the excitation lights in photoemission. Indeed, using LD in 3d core-level HAXPES spectra, determination of the Yb 3+ 4f ground state have been succeeded for tetragonal YbCu 2 Si 2 and YbRh 2 Si 2 23 . LD in the cole-level HAXPES for cubic Yb compounds is also expected to be observed, as discussed below.
In the case of Yb 3+ ions in tetragonal symmetry, the eightfold degenerate J = 7/2 state splits into four dou- blets as where the coefficients 0 ≤ b ≤ 1, 0 ≤ c ≤ 1 defining the actual charge distributions and CF splitting energies depend on the CF parameters B 0 2 , B 0 4 , B 4 4 , B 0 6 , and B 4 6 in Stevens formalism 24 . In the cubic symmetry, the eightfold degenerate J = 7/2 state splits generally into two doublets and one quartet as The Γ 6 and Γ 7 states correspond to the tetragonal Γ 1 6 (with b = 7/12) and Γ 2 7 (with c = 1/2) states, respectively. Since the CF splitting in the cubic symmetry can be recognized as the special case for the tetragonal symmetry, it is natural to expect the observation of LD in core-level photoemission for cubic Yb compounds at least Γ 6 or Γ 7 ground state, for which the 4f charge distribution is deviated from a spherical symmetry and thus anisotropic as shown in Fig. 1. The Γ 6 , Γ 7 , and Γ 8 4f charge distributions are elongated along the [100], [111], and [110] directions, respectively. Actually, we have performed ionic calculations including the full multiplet theory 25 and the local CF splitting using the XTLS 9.0 program 26 . All atomic parameters such as the 4f -4f and 3d-4f Coulomb and exchange interactions (Slater integrals) and the 3d and 4f spin-orbit couplings have been obtained using Cowan's code 27 based on the Hartree-Fock method. The Slater integrals (spin-orbit couplings) are reduced to 88% (98%) to fit the core-level photoemission spectra 10 .
Simulated polarization-dependent Yb 3+ 3d 5/2 corelevel HAXPES spectra in the cubic symmetry at two photoelectron directions ([100], [111]) are shown in Fig. 1. In the case of YbB 12 , since the accidentally degenerated Γ 6 + Γ 7 states could be a candidate for the ground state, the simulations assuming the Γ 6 + Γ 7 ground state and its 4f hole spatial distribution are also shown. LD defined by the difference in spectral weight between the s-and ppolarization configurations is reversed between the [100] and [111] directions for all states displayed here. LD for the Γ 6 ground state has the same tendency as that for the Γ 8 ground state. On the other hand, LD for Γ 8 is the smallest since the 4f hole spatial distribution for the Γ 8 state is the nearest to a spherical shape among these three eigenfunctions. LD assuming the Γ 6 + Γ 7 state is reversed to that for the Γ 8 state. These simulations indicate that the symmetry of Yb 3+ state can be determined by LD in the core-level photoemission.
We have performed LD in HAXPES 28,29 at BL19LXU of SPring-8 30 using a MBS A1-HE hemispherical photoelectron spectrometer.
A Si(111) double-crystal monochromator selected linearly polarized 7.9 keV radiation within the horizontal plane, which was further monochromatized by a Si(620) channel-cut crystal. In order to switch the linear polarization of the excitation light from the horizontal direction to the vertical direction, two single-crystalline (100) diamonds were used as a phase retarder placed downstream of the channel-cut crystal. P L of the polarization-switched X-ray after the phase retarder was estimated as −0.93, corresponding to the vertically linear polarization components of 96.5%. Since the detection direction of photoelectrons was set in the horizontal plane with an angle to incident photons of 60 • , as shown in Figs. 1(a),(b), the experimental configuration at the horizontally (vertically) polarized light exci- tation corresponds to the p-polarization (s-polarization). The excitation light was focused onto the samples using an ellipsoidal Kirkpatrik-Baez mirror. In order to precisely detect LD in the Yb 3d core-level photoemission spectra, we optimized the photon flux so as to set comparable photoelectron count rates between the s-and ppolarization configurations. Single crystals of YbB 12 synthesized by the traveling-solvent floating-zone method 3,4 were fluctuated along the (100) plane in situ, where the base pressure was ∼1×10 −7 Pa. The experimental geometry was controlled by using a newly developed two-axes manipulator 31 , where the normal emission direction parallel to the [100] direction in Fig. 1(a) was changed to the photoelectron detection of the [111] direction in Fig. 1(b) by azimuthal rotation of 45 • and polar rotation by ∼55 • . The sample and surface qualities were checked on the basis of the absence of any core-level spectral weight caused by possible impurities including oxygen and carbon. The energy resolution was set to 400 meV. The measuring temperature is 9 K that is sufficiently lower than the excited state ( > ∼ 250 K) 18 . The polarization-dependent Yb 3+ 3d 5/2 HAXPES spectra along the [100] direction of YbB 12 are shown in Fig. 2. A single peak at a binding energy of ∼1519 eV and a multiple-peak ranging from 1524 to 1534 eV exist in all the spectra. Since the 4f subshell is fully occupied in the Yb 2+ sites with a spherically symmetric 4f distribution, the former single peak is ascribed to the Yb 2+ states. The 3d 9 4f 13 final states for the Yb 3+ compo- Shirley-type background has been subtracted from the raw spectra (Fig. 2). (c) 4f -hole spatial distribution for the Yb 3+ ion with the Γ8 symmetry. (d) Crystal structure of YbB12 32 nents show an atomic-like multiplet-split peak structure in the 1524 − 1534 eV range. We show the spectra in the expanded scale ranging from 1524.5 to 1530.5 eV in the Fig. 2(b). A slight but intrinsic LD is seen in the highest and second-highest peaks in the raw spectra.
Comparison of the polarization-dependent Yb 3+ 3d 5/2 HAXPES spectra of YbB 12 and their LD with the photoelectron directions of [100] and [111] to the simulated ones for the Γ 8 ground state are shown in Fig. 3. Socalled Shirley-type backgrounds are subtracted from the raw spectra as shown in Fig. 2, and the backgroundsubtracted spectra are normalized by both Yb 2+ and Yb 3+ 3d 5/2 spectral weights. The highest peak is slightly stronger in the p-polarization configuration (p-pol.) than in s-polarization one (s-pol.), and the second highest peak is stronger in the s-pol. for both experimental and simulated spectra along the [100] direction. These tendencies are reversed for the data along the [111] direction. As shown in Figs. 3(a) and (b), the observed LD as well as the spectra are quantitatively reproduced by the simulations for the Γ 8 ground state, for which the 4f charge distribution is shown in Fig. 3(c). If the 4f ground state of YbB 12 were in the Γ 6 symmetry, LD would much larger than the experimental one. The sign of LD for the Γ 7 or the accidental degenerated Γ 6 + Γ 7 ground states is completely inconsistent with our experimental results. Such a quantitative reproducibility of LD as well as the corelevel spectra by the simulations surely indicates the Yb 3+ (4f 13 ) ions in the Γ 8 symmetry mixed with a small quantity (∼ 10%) of the Yb 2+ (4f 14 ) component 10 in the ground state of YbB 12 . Our finding of the Γ 8 4f symmetry for the Yb 3+ sites in the ground state is consistent with the prediction by a band-structure (local density approximation + on-site Coulomb repulsion, LDA+U ) calculation, where the Γ 6 and Γ 7 states are in the occupied side 5 . One might consider that the Γ 6 and Γ 7 states are possibly mixed in the ground state for the valence-fluctuating system due to the hybridization between the 4f and valence-band orbitals at low temperatures well below the Kondo temperature (∼ 240 K for YbB 12 1-4 ). As widely recognized for the local electronic structures of transition metal-oxides, on the other hand, it should be noted that the so-called crystal-field splitting actually seen for realistic materials is a consequence of the anisotropic hybridization effects in addition to static ligand potentials. The latter would be much smaller than the former for YbB 12 since the ligand-field potential on the Yb sites is to some extent nearer to a spherically symmetric one, being caused by the crystal structure 1,2,32 where the Yb ion is surrounded by the truncated octahedron made of 24 boron ions as shown in Fig. 3(d). The 4f -hole spatial distributions are elongated along the centres of the truncated octahedron faces for the Γ 6 and Γ 7 states whereas they are along the edges of the hexagonal faces for the Γ 8 state, which leads to the conclusion that the 4f holes in the Γ 8 state are relatively stabilized by the hybridizations compared to those in the Γ 6 and Γ 7 states with different symmetry, as suggested by the LDA+U calculation. Then the possible Γ 6 and/or Γ 7 state mixture would be experimentally insignificant in our data.
In summary, we have successfully determined the 4f symmetry of the Yb 3+ sites in the ground state for cubic YbB 12 as the Γ 8 symmetry by the LD in Yb 3+ corelevel HAXPES at two different photoelectron directions. Our result also suggests that the Yb 3+ ion model under the effective CF, in which the hybridization effects are implicitly taken into account, is available even for the valence-fluctuating system at low temperatures well below the Kondo temperature. The applicability of LD in the core-level HAXPES even to the system in cubic symmetry (not restricted to systems with lower symmetry) demonstrated here would be promissing for revealing the strongly correlated orbital symmetry of the ground state in partially filled subshell, of which the charge distributions are deviated from the spherical symmetry.
We thank H. Yomosa, S. Fujioka, K. Yano, Y. Nakata, Y. Nakatani, T. Yagi, S. Tachibana, Y. Nakamura, H. Aratani, and K. Kodera for supporting the experiments. We are also grateful to K. Miyake, A. Tsuruta, Y. Saitoh, A. Yasui, and A. Fujimori for fruitful discussions. This work was supported by a Grant-in-Aid for Scientific Research (23654121), Grants-in-Aid for Young Scientists (23684027, 23740240), and a Grant-in-Aid for Innovative Areas (20102003) from MEXT and JSPS, Japan, and by Toray Science Foundation. The hard X-ray photoemission was performed at SPring-8 under the approval of JASRI (2014A1149, 2014B1305).