Electronic Structures of Quaterthiophene and Septithiophene on Cu

Mar 10, 2016 - Electronic Structures of Quaterthiophene and Septithiophene on Cu(111): Spatial Distribution of Adsorption-Induced States Studied by ST...
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Electronic Structures of Quaterthiophene and Septithiophene on Cu(111): Spatial Distribution of Adsorption-Induced States Studied by STM and DFT Calculation Toshiyuki Kakudate,*,†,‡ Shigeru Tsukamoto,§ Osamu Kubo,‡ Masato Nakaya,‡ and Tomonobu Nakayama*,†,‡ †

Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan § Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany ‡

ABSTRACT: The oligothiophene molecule family has a tunable energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) as the function of the number of thiophene units. This tunability is of great use to controlling carrier injection at the molecule/ electrode interface in molecule-based electronic devices. We investigate quaterthiophene (4T) and septithiophene (7T) molecules adsorbed on Cu(111) surfaces by scanning tunneling microscopy and spectroscopy (STM and STS) at room temperature. Both oligothiophene molecules form one-dimensional (1D) chain structures on Cu(111), and each molecule in the 1D structures is observed as a row of bright ovals corresponding to thiophene units. Observed features of 4T and 7T molecules differ from those expected from the HOMO and LUMO of the free-standing molecules, and density-functional calculations of a 4T molecule together with a Cu(111) surface reproduce the experimental STM images as they reflect characteristic spatial distribution of adsorption-induced states. In other words, the adsorption-induced states are spatially protruding out from the molecule and not completely localized in the space between the molecule and the Cu(111) surface. increasing number of thiophene units.15−17 On the other hand, it has been also pointed out that the geometry and electronic structure of oligomers are modified by the adsorption onto metal surfaces.18−20 Although this is considered to be essential for charge carrier injections in the oligothiophene/metal interfaces, it has never been clarified systematically. The adsorption geometries and electronic structures of oligothiophenes on noble metal surfaces such as Cu, Ag, and Au have been intensively investigated by scanning tunneling microscopy and spectroscopy (STM and STS), where bithiophene (2T),21 terthiophene (3T),22 quinquethiophene (5T),23 sexithiophene (6T),24−33 and octithiophene (8T)32−34 have been employed. The STS measurements on 3T22 and 6T18 in a single molecular level reveal that the longer oligothiophene has the smaller HOMO−LUMO gap and that experimentally obtained HOMO−LUMO gaps are consistent with theoretically obtained ones. However, little is known about quaterthiophene (4T) and septithiophene (7T), which are

1. INTRODUCTION Through the recent progress in nanoscience and nanotechnology, organic molecules have been recognized as functional components of electronic devices in the near future owing to the potential application of their unique functionalities.1−10 So far, they have been studied in a variety of applications, for instance, organic field-effect transistors,1−5 organic light-emitting diodes,3−5 and organic photovoltaic cells3−6 as well as flexible organic devices7,8 and single-molecule devices.9,10 For these applications, the relative energy positions of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels with respect to the Fermi level (EF) at the molecule/metal interface are important because the electronic structure at the interface has a large effect on the performance of electron and hole injection.11−13 In organic electronic devices, polythiophenes, oligothiophenes, and their derivatives have been extensively studied as promising molecular assemblies.5,14 One of the useful properties of the oligothiophenes is the tunability of the energy gap: the HOMO−LUMO gap of an oligothiophene decreases with © XXXX American Chemical Society

Received: January 18, 2016 Revised: March 10, 2016

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force components acting on the atoms were less than 0.07 eV/ Å.

composed of four and seven thiophene units, respectively (for the structural formulas, see Figure 1), though alkyl-substituted 4T and 7T have been studied.35,36

3. RESULTS AND DISCUSSION 3.1. Formation of 1D Chain Structures of 4T and 7T Molecules. Figure 2a is an STM image of the terrace of a

Figure 1. Structural formulas of 4T and 7T molecules.

In this study, the adsorption geometries and electronic structures of 4T and 7T molecules on Cu(111) are investigated by STM and STS at room temperature (RT). The STM measurements reveal that both 4T and 7T molecules form characteristic one-dimensional (1D) molecular chain structures on a terrace of Cu(111). Moreover, by STS measurements, the energy difference between the HOMO- and LUMO-derived states of the 7T molecular chain structure is measured to be about 3.0 eV, being smaller than that of the 4T molecular chain structure. It is also found that the oligothiophenes chemically adsorb on the Cu(111) surface through S−Cu bonds, and hybridized states are induced by the adsorption of the molecule onto the surface. The adsorption-induced states observed by STS at the energy close to EF are discussed by comparing the STM images and density-functional calculations.

2. EXPERIMENTAL AND THEORETICAL METHODS All experiments were performed in an ultrahigh vacuum (UHV) chamber with a base pressure of 2.0 × 10−10 Torr. A Cu(111) single-crystal surface was cleaned by repeated cycles of Ar+ ion sputtering for 20 min with an energy of 2.3 keV and annealing for 1 h at 400 °C. 4T and 7T molecules (Tokyo Chemical Industry Co.) were loaded into individual laboratorybuilt evaporators, and careful degassing was carried out in the UHV chamber to remove residual contamination and oligothiophene molecules shorter than 4T or 7T molecules. During the deposition, the substrate temperature was kept at RT, and the pressure was below 1.0 × 10−9 Torr. The STM/ STS measurements were performed using a UHV-STM1 (Omicron) with electrochemically etched Pt−20% Ir tips (Agilent) at RT. Typical parameters in the STM measurements were a sample bias voltage (Vs) in the range of −2.0 to +2.0 V and a tunnel current (It) in the range of 30 to 50 pA. For further clarification of the experimental observations, first-principles calculations within the framework of the densityfunctional theory (DFT) were performed. The calculation method used in this work was based on the real-space finitedifference formalism,37 which employed the projector augmented wave method38,39 to describe the interaction between nuclei and valence electrons. Exchange-correlation interactions were treated using the local density approximation.40 The realspace grid spacing was chosen to be 0.16 Å, which corresponds to a plane-wave cutoff energy of 110 Ry. In the present work, the optimized geometry and electronic structure were calculated not only for isolated 4T and 7T molecules but also for the system comprising a single 4T molecule adsorbed on a Cu(111) surface. Structural relaxation was performed until the

Figure 2. STM images of the terraces of Cu(111) surfaces after the deposition of the oligothiophene molecules: (a, b) 4T; (c) 7T. (a) is taken at Vs = −1.5 V and It = 40 pA, while the inset is at Vs = −0.5 V and It = 30 pA. (b) and (c) are both at Vs = −1.5 V and It = 50 pA.

Cu(111) surface after the deposition of 4T molecules. Several 1D chain structures consisting of rod-like structures (indicated by white rectangles) are observed. The magnified STM image of a 1D chain structure (inset of Figure 2a) shows that each rod-like structure is composed of four ovals, as indicated by the four white arrows. From the fact that 6T and 8T molecules adsorbed on noble metal surfaces have been observed as rows of six and eight ovals in STM images,20,27,29,34 we can conclude that each rod-like structure in Figure 2a is a single 4T molecule. B

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In Figure 3, one can observe the peak labeled as adsorptioninduced states for the 7T chain, which is energetically distinguishable from the surface state (SS) of the Cu(111) surface. This has been also observed for 8T molecular chains in our previous work,20 and the adsorption-induced states have been reported to appear due to the chemical interaction between the molecule and the Cu(111) surface. For the 4T molecule, only two peaks are observed in our STS measurement, as indicated by the black arrows in Figure 4.

Moreover, compared with the structural formula of the 4T molecule shown in Figure 1, the four ovals observed in the magnified STM image are found to correspond to the four thiophene units in a 4T molecule. Note that the longest 1D chain structure composed of 4T molecules obtained in this study is longer than 20 nm as shown in Figure 2b. Such 1D molecular chain structures are also formed when 7T molecules are deposited on a Cu(111) surface, where seven ovals corresponding to the seven thiophene units of a single 7T molecule are clearly observed, as indicated by the seven white arrows in Figure 2c. In the 1D molecular chain structures, each molecule is aligned along the Cu⟨11−2⟩ directions as indicated by the gray arrows in Figures 2a−c. It is notable that the alignment of 4T molecules in this study is different from the preferential alignments of a single 4T molecule and a 4T dimer on Cu(111) theoretically calculated.41 To clarify this disagreements, further investigations on the nature of interaction between the molecules in the 1D chain and interaction between the molecules and the substrate surface are necessary. 3.2. Experimentally Obtained Electronic Structures of 4T and 7T Molecules. We have also measured the STS spectra of both 4T and 7T molecules to investigate their electronic structures. Figures 3a and 3b show the STS spectra

Figure 4. STS spectrum taken from the central parts of 4T molecules in the 1D molecular chain structure on Cu(111).

According to DFT calculations,15−17 a free-standing 4T molecule has a HOMO−LUMO gap of 3.0−3.4 eV, which is larger than that of the 7T molecule. Thus, the two peaks can be interpreted as the adsorption-induced states and 4T LUMOderived state, while the 4T-HOMO derived state would locate outside of the measurement range. 3.3. Theoretically Obtained Electronic Structure of the 4T Molecule on Cu(111) Surface. To investigate the detailed electronic properties of the adsorption-induced states observed in the STS spectra, we have performed first-principles calculations for the ground-state electronic structure of a single 4T molecule adsorbed on a Cu(111) surface (see Figure 5a). The Cu(111) substrate is composed of three Cu(111) layers with an interlayer distance of 2.07 Å. In the directions parallel to the layers, the periodic boundary conditions are imposed, and the supercell size is 26.40 Å × 10.16 Å corresponding to 12 × 4 unit cells of the substrate. Because of the large supercell size, the 4T molecule laid on the Cu(111) surface hardly interacts with those in the neighboring supercells. In the direction perpendicular to the layers, although the periodic boundary condition is imposed, the vacuum space between the atomic slab structures is as large as 20.7 Å, and thus, the unfavorable influence on the molecule from the back side of the slab structure is negligible. Geometrical optimization is carried out for not only the 4T molecule but also the topmost Cu(111) layer, while the second and third layers are fixed. The geometrical optimization reveals that the optimized distance between a S atom and the closest Cu atom is 2.22−2.26 Å. This length implies the existence of chemical covalent bonds between Cu and S atoms; indeed, the covalent bonding picture of Cu−S has been reported for a system comprising a thiophene monomer (1T) adsorbed on Cu(111).42 Figure 5b shows the local density of states (LDOS) as the functions of the energy with respect to EF and the z coordinate perpendicular to the molecular plane. Note that the state densities are calculated by integrating the absolute square of the wave functions over each xy plane of the supercell shown in

Figure 3. STS spectra taken (a) at the central parts of 7T molecule in the 1D structures and (b) at the bare Cu region.

taken from 7T molecules in the 1D chain structure and from the bare Cu region, respectively. In Figure 3a, we can observe three peaks, which are indicated by the black arrows. These peaks can be assigned to the 7T HOMO-derived state, 7T LUMO-derived state, and adsorption-induced states for the following reasons: The energy difference of 3.0 eV between the shoulder peaks located at about −2.0 and 1.0 V is in good agreement with the theoretically obtained HOMO−LUMO gap of 2.5−3.0 eV for a free-standing 7T molecule.15−17 In our previous study on 8T molecules deposited on a Cu(111) surface,20 the STS spectra measured on 8T molecules in a 1D chain structure show the energy difference of about 3.0 eV between the HOMO- and LUMO-derived states and is found to be consistent with the theoretically obtained HOMO− LUMO gap of 2.4−2.9 eV for a free-standing 8T molecule.15−17 Therefore, it is reasonable to assign the shoulder peaks located at about −2.0 and 1.0 V in Figure 3a to the 7T HOMO- and LUMO-derived states, respectively. C

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molecule and the surface layer (dotted line in Figure 5b: z = 0.72 Å) and a decay toward the substrate. In contrast, the other states shown in Figure 5b have less LDOS intensities above the molecular plane and higher intensities inside the Cu substrate. Moreover, each of the four LDOS curves in Figure 5c have the highest intensity at the energy of the unique states as indicated by the black arrow. These calculation results suggest that the electronic states at the energy of −0.4 eV is more observable than the other states even at the position away from the molecular plane. Therefore, we can conclude that the STS peak observed at Vs = −0.5 V (Figure 4) corresponds to the unique electronic states seen at the energy of −0.4 eV in Figures 5b and 5c. According to the discussion on the calculation results, the unique electronic states are characteristic of the 4T molecule adsorbed on Cu(111) surface, and thus, we name the STS peak adsorption-induced states. 3.4. Comparison of STM Image and Molecular Orbital. Here, we discuss the STM images of the oligothiophene molecules in the 1D chain structures on Cu(111) surfaces by comparing with the HOMO and LUMO of the corresponding free-standing molecules. Figure 6a shows the spatial distributions of the HOMO and LUMO of a free-standing 7T molecule obtained theoretically. The higher intensities of the HOMO are observed at above the hydrogen atoms locating at both edges of the molecule, while those of the LUMO appear at along the molecular axis. Such spatial distributions of the molecular orbitals are also confirmed for a free-standing 4T molecule, as shown in Figure 6b. One may straightforwardly suppose from the calculation results that the straight (zigzag) shapes are observed in STM images at negative (positive) Vs with assuming the molecular electronic properties preserved. In fact, we have reported that the straight and zigzag shapes appear in the STM images of 8T molecular films formed on Au(111) surfaces at positive and negative Vs, respectively.20 In this study, however, such dependence of the STM images of the molecules on the polarity of Vs are hardly observed in the STM images. Figure 7a shows the magnified STM images of the 1D chain structure of 7T molecules taken at Vs = ±0.5, ±1.0, and ±2.0 V with a constant It of 50 pA. The rod-like structure composed of straightly aligning seven ovals corresponding to the seven thiophene units of the 7T molecule is clearly recognized at Vs = ±0.5 V. Although the seven ovals blur with increasing magnitude of Vs, the rod-like shape of the molecule is retained regardless of the polarity of Vs as seen in

Figure 5. Calculation model and LDOS of the 4T molecule on a Cu(111) surface. In (a), the yellow, brown, pink, and blue spheres represent S, C, H, and Cu atoms, respectively. (b) The LDOS contour is plotted as the functions of the energy and position perpendicular to the molecular plane. State densities are integrated over each xy plane. In (c), state densities are integrated over the volumes above the xy planes indicated in the panel.

Figure 5a. Figure 5c draws the LDOS curves that are obtained by integrating the LDOS in Figure 5b from z = 2.86, 3.28, 3.70, and 4.13 Å to the end of the supercell in the z direction. In Figure 5b, one can clearly see unique states at around −0.4 eV as indicated by the black arrow, which have the highest intensity above the molecular plane (dashed line in Figure 5b: z = 2.99 Å). The electronic states additionally exhibit following features in space, i.e., a localization at the space between the

Figure 6. Spatial distributions of the local densities of the HOMO and LUMO of the free-standing (a) 7T and (b) 4T molecules, depicted on the plane 7.0 Å above the molecular plane. D

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Figure 7. STM images of the 1D molecular chain structure of the oligothiophenes: (a) 7T molecules taken at Vs = ±0.5, ±1.0, and ±2.0 V with a constant It of 50 pA and (b) 4T molecules taken at Vs = ±0.5, ±1.0, and ±2.0 V with a constant It of 30 pA.

Figure 7a. In Figure 7b, showing the magnified STM images of the 1D chain structure of 4T molecules, the rod-like structure composed of straightly aligning four ovals corresponding to the four thiophene units of the 4T molecule is clearly recognized at Vs = ±0.5 V. For the negative Vs, the rod-like shape of the molecule is retained regardless of magnitude of Vs. In contrast, for the positive Vs, dumbbell-like shapes appear from Vs = +1.0 V. These observations suggest that chemical interaction is induced between the molecule and the substrate surface by the adsorption, and the electronic structure of the molecule at around EF is modified. It has been reported in the previous study on adsorbed 8T molecules on Au(111) and Cu(111) that 8T molecules weakly interact with the Au(111) surface and mostly preserve the electronic structure of the free-standing molecules while, on Cu(111), they chemically interact with the surface and the electronic structure is considerably altered.20 This is consistent with the interpretation of the STS measurements and LDOS calculation results in this study. It can be expected that the adsorption-induced states play an important role in imaging of the oligothiophenes in the 1D chain structures by STM. 3.5. Formation of the Adsorption-Induced States. To investigate more details on the role of the adsorption-induced states in STM images, let us discuss the spatial distribution of the adsorption-induced states peculiar to the system of Figure 5a, which is found at around −0.4 eV in Figures 5b and 5c. In Figure 8, the density of states within the energy range from −0.5 eV to EF is depicted on the xy plane 7 Å above the 4T molecular plane so that the electronic states we are focusing on are included. The adsorbed 4T molecule is clearly visible as a rod-like shape composed of four ovals corresponding to the thiophene rings. This is different from the spatial distributions

of the HOMO and LUMO of a free-standing 4T molecule (Figure 6). Moreover, the two center ovals clearly appear larger than the other ovals, and the gap between the two center ovals is more clearly visible than the other gaps. These features in the spatial distribution of the density of states are in good agreement with those seen in the STM image of 4T molecules at Vs = −0.5 V, as shown in Figure 7b. Therefore, it is reasonable to conclude that the theoretically obtained spatial distribution of the adsorption-induced states corresponds to the experimentally obtained STM image. The formation of the adsorption-induced states would be a result of hybridization between LUMO states of the 4T and 7T molecules and the SS of Cu(111) surface as explained below. In Figure 9a, the isosurface of the absolute square of the

Figure 9. Isosurfaces of (a) the density of the adsorption-induced states of the 4T molecule on a Cu(111) surface and (b) the LUMO wave function of the free-standing 4T molecule. In (a), the isosurface only above the molecule/surface interface is depicted for visibility.

adsorption-induced states above the interface between the molecule and the Cu(111) surface (corresponding to z > 1.96 Å in Figure 5b) is visualized. Figure 9b exhibits the isosurface of the LUMO wave function of a free-standing 4T molecule. By comparing these spatial distributions, we see that the adsorption-induced states preserve the spatial feature of the LUMO of the free-standing molecule. From an energy point of view, as shown in the STS spectra of the 4T and 7T in Figures 3 and 4, the peak corresponding to the adsorption-induced states appears instead of that of the SS of the Cu(111) surface.

Figure 8. Spatial distribution of the LDOS of the 4T molecule on a Cu(111) surface, depicted on the plane 7.0 Å above the molecular plane. The state densities are integrated over the energy range from −0.5 eV to EF. E

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the substrate. In Figures 11a and 11b, the density of the states within the energy ranges from −3.2 to −2.2 eV and from −3.2

Therefore, we surmise that the LUMO states of the 4T and 7T molecules hybridize with the SS of the Cu(111) surface during adsorption processes, and consequently the bonding state is stabilized to appear as the adsorption-induced states just below the SS of the Cu(111) surface. 3.6. Influence of Molecular Orbital on STM Images. As mentioned in section 3.2, the 4T molecule on the Cu(111) surface is observed as a rod-like structure and a dumbbell-like one in the STM images at Vs = −1.0 and +1.0 V (see Figure 7b), respectively. These observations are obviously different from the spatial distributions of the HOMO and LUMO of a free-standing 4T molecule as shown in Figure 6b. In this subsection, we discuss the STM observations in comparison with the density of states within a specific energy ranges, as discussed for the adsorption-induced states in the previous subsection. In Figures 10a and 10b, the density of the states

Figure 11. Spatial distributions of LDOSs of the 4T molecule on a Cu(111) surface, depicted on the plane 7.0 Å above the molecular plane. The state densities are integrated over the energy ranges (a) from −3.2 to −2.2 eV and (b) from −3.2 eV to EF.

eV to EF are depicted on the xy plane 7 Å above the 4T molecule, respectively. The spatial distribution of the density of states in Figure 11a is visible as a zigzag shape and roughly resembles that of the HOMO of the free-standing 4T molecule shown in Figure 6b. However, the spatial distribution of the density of states in Figure 11b is visible as a straight line and similar to that in Figure 8. Moreover, Figure 11b is in good agreement with the STM images of 4T molecules at negative Vs’s, as shown in Figure 7b. This would be attributed to that the adsorption-induced states have higher density above the molecule and stick out more toward the vacuum than the other electronic states, as seen in Figures 5b and 5c. Therefore, the adsorption-induced states most contribute to the tunneling current within the energy range of this study, and this results in the appearance of the straightly aligned four ovals corresponding to the spatial distribution of the adsorption-induced states in the STM images at any negative Vs.

Figure 10. Spatial distributions of LDOSs of the 4T molecule on a Cu(111) surface, depicted on the plane 7.0 Å above the molecular plane. The state densities are integrated over the energy ranges (a) from −1.0 eV to EF and (b) from EF to +1.0 eV.

within the energy ranges from −1.0 eV to EF and from EF to +1.0 eV are depicted on the xy plane 7 Å above the 4T molecule adsorbed on a Cu(111) surface (see Figure 5a), respectively. The former is clearly visible as a rod-like shape composed of four ovals, and the two ovals in the middle appear larger than the other two. This is essentially the same with Figure 8. On the other hand, the latter exhibits a clear dumbbell-like shape composed of two large bright spots. These appearances in the spatial distribution of the density of states coincide well with the corresponding STM images at positive Vs’s in Figure 7b and quite different from the spatial distribution of the HOMO and LUMO of the free-standing 4T molecule. This discussion implies that HOMO and LUMO of the molecule have less influence, and rather the other electronic states close to EF including the adsorption-induced states play an important role in the STM images of the oligothiophene system. This implication is also applicable to the discussion why 4T (7T) molecules are observed as straightly aligned four (seven) ovals in the STM images at negative Vs’s, regardless of the magnitude of Vs. To elucidate this concern, we focus on the HOMO-derived state of the 4T molecule adsorbed on a Cu(111) surface. On the LDOS contour plot of the 4T molecule shown in Figure 5b, the HOMO-derived state corresponds to the electronic states from −3.2 to −2.2 eV, which have higher intensity above the molecule as well as inside

4. CONCLUSIONS The adsorption geometries and electronic structures of 4T and 7T molecules on a Cu(111) surface were investigated by STM and STS at RT. We found that both 4T and 7T molecules adsorbed on the surface along the Cu ⟨11−2⟩ directions formed characteristic 1D molecular chain structures. The STS measurements revealed that the energy difference between the HOMO- and LUMO-derived states of the 7T molecule in the 1D structure was determined to be about 3.0 eV, which was smaller than that of the 4T molecule. In addition, the existence of the adsorption-induced states in the energy gap for each system was confirmed by the detailed analyses of STS spectra and DFT calculations. For further understanding of the adsorption-induced states, experimentally obtained STM images were compared with theoretically obtained ones from the viewpoint of spatial distributions of HOMO, LUMO, and the adsorption-induced states, and we found that the characteristic of adsorption-induced states of the 4T on Cu(111) well explain the observed STM images. The adsorption-induced states were not completely localized in the space between the molecule and the Cu(111) surface but considerably protruding above the molecular plane. The DFT calculations also revealed that the adsorption-induced states F

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preserved the spatial feature of the LUMO of the free-standing molecule. From this result and the STS spectra, it was clarified that the adsorption-induced states were generated by the hybridization of the LUMO states of the oligothiophene molecules and the SS of the Cu(111) surface.



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Corresponding Authors

*(T.K.) Tel and fax +81-22-217-5666; e-mail kakudate@tagen. tohoku.ac.jp. *(T.N.) Tel +81-29-860-4129; fax +81-29-860-4886; e-mail nakayama.tomonobu@nims.go.jp. Present Addresses

T.K.: Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Aobaku, Sendai, Miyagi 980-8577, Japan. O.K.: Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. M.N.: Division of Quantum Science and Energy Engineering, Department of Materials, Physics, and Energy Engineering, Nagoya University, Furo-Cho, Chikusa-Ku, Nagoya, Aichi 4648603, Japan. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported in part by the Grant-in-Aid for Scientific Research (A) (No. 22241030) by Japan Society for the Promotion of Science (JSPS). We greatly appreciate Professor Dr. S. Blügel and Dr. N. Atodiresei of Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA for fruitful discussions.



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