Important Roles of Te 5p and Ir 5d Spin-orbit Interactions on the Multi-band Electronic Structure of Triangular Lattice Superconductor Ir1-xPtxTe2
D. Ootsuki, T. Toriyama, M. Kobayashi, S. Pyon, K. Kudo, M. Nohara, T. Sugimoto, T. Yoshida, M. Horio, A. Fujimori, M. Arita, H. Anzai, H. Namatame, M. Taniguchi, N. L. Saini, T. Konishi, Y. Ohta, T. Mizokawa
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b Journal of the Physical Society of Japan
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Important Roles of Te 5 p and Ir 5 d Spin-orbit Interactions on theMulti-band Electronic Structure of Triangular Lattice SuperconductorIr − x Pt x Te Daiki Ootsuki , Tatsuya Toriyama , Masakazu Kobayashi , Sunseng Pyon , KazutakaKudo , Minoru Nohara , Takuya Sugimoto , Teppei Yoshida , Masafumi Horio , AtsushiFujimori , Masashi Arita , Hiroaki Anzai , Hirofumi Namatame , Masaki Taniguchi , ,Naurang L. Saini , Takehisa Konishi , Yukinori Ohta , and Takashi Mizokawa Department of Physics & Department of Complexity Science and Engineering, Universityof Tokyo, 5-1-5 Kashiwanoha, Chiba 277-8561, Japan Department of Physics, Chiba University, Inage-ku, Chiba 263-8522, Japan Department of Physics, Okayama University, Kita-ku, Okayama 700-8530, Japan Graduate School of Human and Environmental Studies, Kyoto University, Sakyo-ku, Kyoto606-8501, Japan Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-hiroshima739-0046, Japan Graduate School of Science, Hiroshima University, Higashi-hiroshima 739-8526, Japan Department of Physics, University of Roma ”La Sapienza” Piazzale Aldo Moro 2, 00185Roma, Italy Graduate School of Advanced Integration Science, Chiba University, Inage-ku, Chiba263-8522, Japan
We report an angle-resolved photoemission spectroscopy (ARPES) study on a triangular lat-tice superconductor Ir − x Pt x Te in which the Ir-Ir or Te-Te bond formation, the band Jahn-Teller e ff ect, and the spin-orbit interaction are cooperating and competing with one another.The Fermi surfaces of the substituted system are qualitatively similar to the band structurecalculations for the undistorted IrTe with an upward chemical potential shift due to electrondoping. A combination of the ARPES and the band structure calculations indicates that theTe 5 p spin-orbit interaction removes the p x / p y orbital degeneracy and induces p x ± ip y typespin-orbit coupling near the A point. The inner and outer Fermi surfaces are entangled bythe Te 5 p and Ir 5 d spin-orbit interactions which may provide exotic superconductivity withsinglet-triplet mixing. /
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KEYWORDS: spin-orbit coupling, Ir − x Pt x Te , orbital degeneracy, angle-resolved photoemission spec-troscopy, . . . d and 5 d transition-metal compounds with t g orbital degeneracy exhibit rich and inter-esting physical properties due to the competition and / or the collaboration between the spin-orbit interaction and the (band) Jahn-Teller e ff ect. For example, in perovskite-type Ca RuO ,the Jahn-Teller splitting between the Ru 4 d t g yz / zx and xy orbitals collaborates with the4 d t g spin-orbit coupling to stabilize the yz + ixy or zx + ixy orbital to give the magneticanisotropy.
1, 2)
In other perovskite-type Sr IrO , the strong spin-orbit interaction of the Ir 5 dt g orbitals is dominating and provides the unique j / state.
3, 4)
On the other hand, in spinel-type CuIr S , the band Jahn-Teller e ff ect and the Ir-Ir bond dimerization play essential rolesin the charge-orbital ordering with the Ir 5 d t g spin-orbit interaction being apparently inac-tive. The di ff erence between the perovskite-type and spinel-type systems can be attributedto that between the corner sharing and edge-sharing Ir X octahedra. Yet, in Na IrO with theedge-sharing of Ir X octahedra, whereas the j / state is suggested,
8, 9) based on the ab-initio calculation, it has recently been proposed that the j / and j / states are mixed due to forma-tion of Ir 5 d molecular orbitals. In this context, it is highly desirable to study the Ir 5 d t g electronic states in various Ir compounds in a systematic way.The discovery of superconductivity in doped or intercalated IrTe by Pyon et al. andby Yang et al. have added a new family of Ir chalcogenides to the list of fascinating 4 d and 5 d electron systems. IrTe undergoes a structural phase transition at ∼
270 K from thetrigonal (P-3m1) to the monoclinic (C2 / m) structure. IrTe and its derivatives show an in-teresting interplay between lattice instabilities and superconductivity in the triangular lattice.Since the Ir 5 d -to-Te 5 p charge-transfer energy is found to be small, the Te 5 p orbitalscan play significant roles as proposed by Fang et al. and Oh et al.
15, 16)
Also the multi-bandelectronic structure of the Ir 5 d and Te 5 p orbitals in IrTe can induce the (band) Jahn-Tellerinstability and the Peierls instability. In the case of Ir − x Pt x Te , the Ir-Ir bond,
11, 18) the Ir-Tebond, and / or the Te-Te bond can be a ff ected by the Pt doing. In addition, the large Ir 5 d spin-orbit interaction can entangle the spin and orbital degrees of freedom in IrTe and mayinduce nontrivial topological states. In order to reveal possible roles of the Ir 5 d and Te 5 p spin-orbit interactions in the Ir − x Pt x Te , we have performed angle-resolved photoemissionspectroscopy (ARPES) of Ir . Pt . Te and compared the ARPES results with theoreticalcalculations with and without the Ir 5 d and Te 5 p spin-orbit interactions.Single crystal samples of Ir − x Pt x Te were prepared using a self-flux method.
15, 19)
The /
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DRAFT photoemission measurements were performed at beamline 9A, Hiroshima Synchrotron Ra-diation Center using a SCIENTA R4000 analyzer with circularly polarized light. The totalenergy resolutions were set to 18 meV, 22 meV, and 29 meV for excitation energies of h ν =
23 eV, 26 eV, and 29 eV, respectively. The angular resolution was set to ∼ ◦ that givesthe momentum resolutions of ∼ − , 0.016 Å − , and 0.017 Å − for h ν =
23 eV, 26 eV,and 29 eV, respectively. The incident beam is 50 ◦ o ff the sample surface. The base pressureof the spectrometer was in the 10 − Pa range. The samples were cleaved at 20 K under theultrahigh vacuum. The samples were oriented by ex situ
Laue measurements. The spectrawere acquired within 8 hours after the cleavage. Binding energies were calibrated using theFermi edge of gold reference samples. For the band structure calculations, we employ thecode WIEN2k based on the full-potential linearized augmented-plane-wave method andpresent the calculated results obtained in the generalized gradient approximation (GGA) forelectron correlations, where we use the exchange-correlation potential of Ref.21.
The spin-orbit interaction is taken into account for both Ir and Te ions when necessary. We use thecrystal structure and atomic positions measured for IrTe at room temperature. In the self-consistent calculations, we use 264 k -points in the irreducible part of the Brillouin zone withan anisotropic sampling to achieve better convergence. Mu ffi n-tin radii ( R MT ) of 2.50 (Ir) and2.42 (Te) Bohr are used and we assume the plane-wave cuto ff of K max = . / R MT .In Fig. 1, the ARPES spectra along the A-H direction of Ir . Pt . Te are compared withthose of IrTe above the structural transition temperature. The ARPES spectra are comparedwith the band dispersions obtained for undistorted IrTe using the GGA calculation with theIr 5 d and Te 5 p spin-orbit interactions. As for Ir . Pt . Te , it is assumed that the Pt dopingintroduces 0.05 electron per Ir and that the chemical potential is shifted upwards in the bandstructure for undistorted IrTe . The experimental and theoretical band dispersions are in qual-itative agreement for IrTe above the transition temperature as well for Ir . Pt . Te . Nearthe Fermi level, as predicted by the calculation, the inner band forms the small hole pocketsaround the A point (the inner Fermi surfaces) while the outer band forms the large Fermi sur-face (the outer Fermi surface). If the Pt doping supplies electrons to the Ir 5 d and Te 5 p bands,the entire band should be shifted downwards in going from IrTe to Ir . Pt . Te . Indeed, thecalculation for Ir . Pt . Te is shifted downwards assuming the rigid band model and agreesvery well with the experimental result. The energy shift between IrTe and Ir . Pt . Te isconsistent with the rigid band shift of the calculated results, indicating that the Pt dopingprovides electrons to the Ir 5 d and Te 5 p bands.Figure 2(a) and (b) show the Fermi surface maps for Ir . Pt . Te taken at 23 eV with /
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DRAFT right-handed and left-handed circularly polarized light, respectively. The six hole pocketsaround the A point (the inner Fermi surfaces) and the large Fermi surface (the outer Fermisurface) are partly observed as predicted by the band structure calculation. As for the innerFermi surfaces, the upper three hole pockets tend to be emphasized with the right-handedcircularly polarized light, while the lower three hole pockets gain their intensity with theleft-handed circularly polarized light. The asymmetric intensity due to the transition-matrixelement e ff ect is partially removed by summing the Fermi surface maps, and the six foldsymmetry of the six hole pockets are more clearly seen as displayed in Fig. 2(c). Here, thetransition-matrix element e ff ect still remains since the incident light is 50 ◦ o ff the samplesurface.Figures 3(a), (b) and (c) show the evolution of the Fermi surfaces by changing the photonenergy. The momentum perpendicular to the surface ( k z ) is ∼ π/ c , 9 π/ c , and 8 π/ c for 23eV, 26 eV, and 29 eV, respectively. The Fermi surface maps extracted from the ARPES dataare compared with the theoretical Fermi surfaces which are obtained by the rigid band shiftof the GGA calculation with and without the spin-orbit interactions for undistorted IrTe for k z = π/ c , 9 π/ c , and 8 π/ c , respectively. The calculations with and without the spin-orbitinteractions indicates that the e ff ect of the spin-orbit interaction is more significant for theinner Fermi surfaces than the outer one. At 23 eV, the area of the inner Fermi surfaces is wellreproduced by the calculation with the spin-orbit interactions as shown in Fig. 3(a). The e ff ectof the spin-orbit interaction is more pronounced at 29 eV. Without the spin-orbit interactions,even the geometry of the calculated Fermi surfaces is di ff erent from the ARPES results. Onthe other hand, the Fermi surfaces calculated with the spin-orbit interaction are consistentwith the ARPES results.In Fig. 3(d), the Fermi surface map is compared with the calculation with (without) the Te5 p (Ir 5 d ) spin-orbit interaction and that with (without) the Ir 5 d (Te 5 p ) spin-orbit interaction.The calculation with the Ir 5 d spin-orbit interaction agrees with the ARPES results than thecalculation with the Te 5 p spin-orbit interaction, indicating that the Ir 5 d spin-orbit interactionis more important than the Te 5 p spin-orbit interaction for the area of the inner Fermi surfaces.The band dispersions along the A-H and A-L directions are compared with the calculatedresults with and without the spin-orbit interactions in Figs. 4(a) and (b). The spin-orbit bandsplitting at -0.5 eV between the inner bands around the A point and that at -0.25 eV betweenthe inner and outer bands in the A-H cut are clearly observed in the APRES results (indicatedby the arrows), as predicted by the GGA calculation with the spin-orbit interactions. TheGGA calculation predicts that, around the A point, the inner bands near the Fermi level are /
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DRAFT mainly derived from the Te 5 p x and 5 p y orbitals. Therefore, the band splitting at -0.5 eVaround the A point can be attributed to the p x ± ip y type spin-orbit coupling. In going fromthe A point to the H point, the inner bands dominated by the Te 5 p x and 5 p y orbitals tend tohave some contribution of the Ir 5 d e π g orbitals. On the other hand, the outer Fermi surface ismainly constructed from the Te 5 p z orbitals with some contribution of the Ir 5 d a g orbitals.The band splitting at -0.25 eV between the inner and outer bands in the A-H cut would be dueto the p z ± ip x type or p z ± ip y type Te 5 p spin-orbit coupling with some contribution of the Ir5 d spin-orbit coupling. In order to clarify the di ff erent roles of the Ir 5 d and Te 5 p spin-orbitinteractions, the band dispersions along the A-H and A-L directions are compared with thecalculation with (without) the Te 5 p (Ir 5 d ) spin-orbit interaction and that with (without) theIr 5 d (Te 5 p ) spin-orbit interaction in Figs. 4(c) and (d). Although the intensity of the outerband is very small in Figs. 4(a) and (c), the dispersion of the outer band can be seen in theenlarged plot of Fig. 4(e). The band splitting at -0.5 eV around the A point is dominated by theTe 5 p spin-orbit interaction which provides the p x ± ip y type spin-orbit coupling as discussedabove. On the other hand, although the band splitting at -0.25 eV between the inner and outerbands in the A-H cut is induced by the Te 5 p spin-orbit interaction, the magnitude of thesplitting is much more enhanced by the inclusion of the Ir 5 d spin-orbit coupling. Therefore,as for the spin-orbit coupling between the inner and outer bands, the coupling between the Ir5 d a g and Ir 5 d e π g orbitals has a substantial contribution although the inner and outer bandsare dominated by the Te 5 p character.In Ir − x Pt x Te , the inner and outer bands are very close to each other near the Fermi levelalong the A-H direction, and the Te 5 p and Ir 5 d spin-orbit interactions introduce the strongentanglement between the spin and orbital parts of the electrons. The recent ARPES study onSr RuO revealed that the strong spin-orbital entanglement provides mixing of spin-singletand spin-triplet Cooper pairs and may cause an exotic superconducting state. Since themagnitude of the spin-orbit interaction in Ir . Pt . Te is much stronger than that in Sr RuO ,one can expect stronger mixing between spin-singlet and spin-triplet Cooper pairing in theIr . Pt . Te .In conclusion, we have studied the multi-band electronic structure of triangular latticesuperconductor Ir − x Pt x Te using ARPES. The Pt doping introduces the electrons to the Ir5 d and Te 5 p bands and the simple rigid band model is consistent with the observed banddispersions and the Fermi surfaces. The inner and outer Fermi surfaces with the strong Te 5 p character are very close to each other along the A-H direction, and the strong Te 5 p and Ir 5 d spin-orbit interaction in this particular momentum region results in the mixing between the /
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DRAFTFig. 1. (color online) (a) ARPES spectra of IrTe along the A-H direction taken at 300 K above the structuraltransition temperature. The solid curves indicate the band dispersions obtained for undistorted IrTe using theGGA calculation with the Te 5 p and Ir 5 d spin-orbit interactions. (b) ARPES spectra of Ir . Pt . Te along theA-H direction taken at 20 K. The solid curves indicate the calculation shifted by the electron doping by Pt. (c)Schematic drawings for the crystal structure visualized using the software VESTA and the first Brillouin zoneof Ir . Pt . Te . spin-singlet and spin-triplet Cooper pairs in Ir − x Pt x Te .The authors would like to thank Profs. A. Damascelli and H.-J. Noh for valuable dis-cussions. This work was partially supported by Grants-in-Aid from the Japan Society of thePromotion of Science (JSPS) (22540363, 23740274, 24740238, 25400356) and the FundingProgram for World-Leading Innovative R&D on Science and Technology (FIRST Program)from JSPS. T.T. and D.O. acknowledge supports from the JSPS Research Fellowship forYoung Scientists. The synchrotron radiation experiment was performed with the approval ofHiroshima Synchrotron Radiation Center (Proposal No.13-A-6). /
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DRAFTFig. 2. (color online) (a) Fermi surface map for Ir . Pt . Te with right-handed circularly polarized light. (b)Fermi surface map for Ir . Pt . Te with left-handed circularly polarized light. (c) Sum of the Fermi surfacemaps. Fig. 3. (color online) (a) Fermi surface map for Ir . Pt . Te at 23 eV compared with the GGA calculationswith and without the spin-orbit interactions. (b) Fermi surface map for Ir . Pt . Te at 26 eV compared withthe GGA calculations with and without the spin-orbit interactions. (c) Fermi surface map for Ir . Pt . Te at 29eV compared with the GGA calculations with and without the spin-orbit interactions. (d) The GGA calculationwith (without) the Te 5 p (Ir 5 d ) spin-orbit interaction and that with (without) the Ir 5 d (Te 5 p ) comapred withthe Fermi surface map at 23 eV. 7 /
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DRAFTFig. 4. (color online) ARPES spectra of Ir . Pt . Te along the A-H direction (a) and along the A-L direction(b) compared with the GGA calculations with and without the spin-orbit interactions. The red dots and lightblue curves indicate the band dispersions calculated with and without the spin-orbit interaction, respectively.The arrows indicate spin-orbit splitting. ARPES spectra of Ir . Pt . Te along the A-H direction (c) and alongthe A-L direction (d) compared with the GGA calculation with (without) the Te 5 p (Ir 5 d ) spin-orbit interactionand that without (with) the Te 5 p (Ir 5 d ). The red closed circles and the blue open circles indicate the banddispersions calculated with the Ir 5 d and Te 5 p spin-orbit interactions, respectively. The arrows indicate spin-orbit splitting. (e) Second derivative plot of momentum distribution curves(MDC) for the region indicated bythe box in panel (a). The open circles indicate the peak position obtained from MDC.8 /
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