Surface States of LaB 6 (001) Studied by Inverse Photoemission

We have newly developed an inverse photoemission (IPE) spectrometer with high eﬃciency and measured k resolved IPE spectra of LaB 6 (001) to study the unoccupied surface states. The surface states were found to be located at 0.2 eV above the Fermi level at the Γ point and showed energy dispersion along the Γ–M direction of the surface Brillouin zone (BZ). The dispersion of the unoccupied surface states is inconsistent with the recently reported theoretical calculation. The discrepancy is considered that the calculation adopted smaller interlayer spacing between topmost La layer and B subsurface as it is in the system. [DOI: 10.1380/ejssnt.2005.367]


I. INTRODUCTION
Before the fascinating physical properties of rare earth compounds have become objectives of the studies of solid state physics, lanthanum hexaboride (LaB 6 ) has attracted much attention as an excellent electron emitter with high electron emissivity and unusually low work function [1]. Since then, atomic and electronic structures of LaB 6 surface has been investigated to clarify the origin of its characteristics [2][3][4][5] and/or to reveal the roles of 4f electrons in the other rare earth hexaborides with 4f electrons [6,7]. So far, the atomic and electronic structures of LaB 6 surface have been studied with various surface sensitive experiments such as photoelectron spectroscopy (PES), low energy electron diffraction (LEED), X-ray photoelectron diffraction (XPD), etc. The energy dispersion of the valence bands obtained from angle-resolved PES spectra showed agreement with the band structure calculated previously except several respects [3,8], and these discrepancies were removed by the results of more reliable band calculation [9]. The surface states of LaB 6 (001), (011) and (111) were found at 2 eV below the Fermi level with considerable dispersion, which are considered to be originated from B 2p dangling bonds accompanying the displacement of La atoms from the surface [2,4,5]. Monnier and Delley [10] have made the calculation of the surface band structure of LaB 6 which reproduces the observed low work function and identified an unreported surface empty state partly responsible for high electron emissivity.
Recently, present authors have achieved ARPES experiments of LaB 6 (011) surface using synchrotron radiation including resonance photoemission at the photon energy around La 4d threshold [11]. They showed that the surface states observed very close to the Fermi level and at binding energy of 2.3 eV reveal enhancements when they * This paper was presented at International Symposium on Surface Science and Nanotechnology (ISSS-4), Saitama, Japan, 14-17 November, 2005. † Corresponding author: morihon@post.kek.jp overlap with La 5d and B 2p derived band, respectively, which gives rise to the surface resonance states. It was also observed that both states showed 5p-5d and 4d-4f resonant photoemission near the La 5p and 4d threshold, respectively. The surface states of LaB 6 (011) have not only the characteristics of the La 5d states but of La 4f states. Though 4f states of La lie a few eV above the Fermi level, the results show that the La 4f states contribute to the valence states over wide range of energy. As for the binding energy of the La 4f states of LaB 6 , Mori et al. [12] observed X-ray bremsstrahlung isochromat spectroscopy (XBIS) spectra of LaB 6 and showed nearly localized 4f states with their binding energy to be 5 eV above the Fermi level. To further clarify the characteristics of the electronic structures of LaB 6 surface, the more detailed information on the states above the Fermi level is needed.
In the following, we study the unoccupied surface electronic states of LaB 6 (001) by k-resolved IPE experiments. Since k-resolved IPE spectra give us not only the binding energies of unoccupied states but also their energy dispersion of the system, the results may reveal the surface electronic states and could clarify the origin of high electron emissivity and low work function of LaB 6 (001).

II. EXPERIMENTAL
The LaB 6 single crystal used in our experiments was grown by the floating zone method and the surface of the sample was cleaned by flash heating at about 1400 • C. The cleanliness of the surface was kept so that the intensity of impurities such as sulfur, nitrogen, oxygen, etc. was below the detection limit of the Auger electron spectroscopy (AES) measurements. We observed clear (1×1) LEED patterns for a clean sample surface. The pressure during IPE measurements was 1 × 10 −10 Torr.
The IPE experiments were performed using newly designed and constructed spectrometer. The spectrometer consists of a thermal electron gun with a transport lens system and a photomultiplier (PM) for the photon detection. The electron gun system can easily be replaced with a GaAs polarized electron source, so that whole system could be used with polarized electrons. The energy of detecting photons is 9.3 eV, which is determined by SrF 2 window in front of PM and KCl film evaporated on the anode of PM as high and low cut filter, respectively. The energy resolution of the detector is 0.46 eV and the total energy resolution of the system is 0.60 eV in FWHM. The quantum efficiency of the detector is about 2.5×10 −2 counts/photon. The conspicuous feature of our detector is its large acceptance angle (1.2 sr) of the first anode of the PM, which enables us to obtain excellent intensity 600 CPS at the Fermi level of gold film irradiated by 1µA of incident electrons. Fig. 1 shows the IPE spectra of LaB 6 (001) clean and contaminated surfaces measured with normal incidence. The spectrum of clean surface consists of a prominent peak very close to the Fermi level, a broad feature like a shoulder around 3.1 eV and a double peak structure with separation of 1.5 eV near 6 eV above the Fermi level. Upon oxygen adsorption, the intensity of the prominent peak at the Fermi level reduces, with which we could assign the peak as a surface electronic states of LaB 6 (001). And the intensities of the shoulder around 3.1 eV and the double peak near 6 eV do not show appreciable change compared with the peak at the Fermi level. This indicates these features are electronic sates of bulk LaB 6 (001).

III. RESULTS AND DISCUSSION
Comparing with theoretical band calculation, we could assign the shoulder to be originated from the hybridization between La 5d and B 2p and/or between La 4f and B 2p and the two peaks as due to 4f empty states of La atom, which could be observed in IPE experiments. The binding energies of 4f states are 5.3 and 6.8 eV, which have been observed as a single peak with broad feature at about 5 eV in XBIS spectra measured [12]. The observed spectral feature is similar to that observed in IPE of La metal by Fedorov et al [13]. They observed a 4f signal at about 5 eV above the Fermi level, which was split into two components; the low energy (4.6 eV) and high energy Intensity (arb. units) IG. 2: k-resolved IPE spectra from LaB6(001) clean surface, for varying angles of electron incidence along the Γ-M direction. The angle of incidence θ is measured relative to the surface normal.
(5.2 eV) peak, which were assigned to be originated from surface and bulk electronic states, respectively. Hence they claimed that the double peak structure is an intrinsic property of empty 4f states. However, upon oxygen adsorption, the two peaks show almost similar change. So the separation of two peaks is rather due to 4f 7/2 and 4f 5/2 spin orbit splitting energy. We have assigned the two peaks as the spin orbit partner of La 4f states, which could be observed as an R 4f 1 electron configuration in IPE of LaB 6 . In the band calculation, La 4f originated states are localized within 2eV about 3 eV above the Fermi level. The excess energy of observed 4f states corresponds to the energy adding single electron to the system. Fig. 2 shows IPE spectra observed with changing the incidence angle of electron beam from -12 • to 54 • within (010) plane of LaB 6 (001) surface, which correspond to observe unoccupied electronic states along the Γ-M direction of the surface BZ. In the figure, the surface empty state near the Fermi level shows remarkable energy dispersion. It should also be remarked in the figure that features originated from La 4f states show energy dispersion, although it is small reflecting their localized nature of 4f states like other rare earth hexaborides. In addition, we could observe several broad features with large energy Recently, Monnier and Delley [10] have made an ab initio calculation of the surface band structure of LaB 6 and showed that the surface electronic states originated from topmost La layer may cause the low work function of the LaB 6 , while B 2p originated bands show energy dispersion around 2 eV below the Fermi level. Comparing with the results of angle-resolved photoemission experiments [2], they showed that the calculation could successfully reproduce the energy dispersion of the B 2p originated occupied surface states. According to their calculation, unoccupied surface states just above the Fermi level are localized on topmost La layer and may show appreciable dispersion and cross the Fermi level along the Γ-M direction in the surface BZ. In fig. 3, the feature observed by IPE shows appreciable band dispersion with its minimum energy at the Γ point and the maximum energy at M point in the surface BZ, which is inconsistent with that of La surface state expected by the calculation. Instead, we could observe a band near the Fermi level with energy dispersion crossing it in the vicinity of the M point. In the calculation, they have assumed the equilibrium distance between outermost La layer and the subsurface B layer to be smaller than that suggested for rigidly cleaved surface. Their calculated surface phonon spectral density reproduced the vibrational modes observed by high resolution electron energy loss spectroscopy (HREELS) [14,15]. However it was not the low frequency modes correlated the vibration of topmost La atoms, but the high frequency modes originated B networks that HREELS observed clearly. The discrepancy may be caused by much reduction of the calculated distance between topmost La layer and B subsurface. The proper consideration of interlayer spacing between topmost La layer and B subsurface will increase the energy of La 5d states and cause better agreement with the experimental observation.

IV. CONCLUSION
We have newly developed a IPE spectrometer with high efficiency and measured k-resolved IPE spectra of LaB 6 (001). We have observed La originated 4f empty states which are consistent with that observed in La metal. We have observed energy dispersion of empty surface electronic states and found that the surface state near the Fermi level is originated from surface La layer, of which the energy dispersion is inconsistent with the recent band calculation. The discrepancy has been considered that the calculation adopted smaller interlayer spacing as it is.