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High-resolution photoemission study of electron–electron interaction in the Ni(1 1 1) surface state
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) e743–e744 www.elsevier.com/locate/jmmm
High-resolution photoemission study of electron–electron interaction in the Ni(1 1 1) surface state Mitsuharu Higashiguchia,, Kenya Shimadab, Masashi Aritab, Yuichi Miuraa, Naohisa Tobitaa, Xiaoyu Cuia, Yoshihiro Aiurac, Hirofumi Namatameb, Masaki Taniguchia,b a Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739-0046, Japan c National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
b
Available online 28 November 2006
Abstract High-resolution angle-resolved photoemission study of the surface state in ferromagnetic Ni(1 1 1) has been performed to evaluate the strength of many-body interactions. We could not observe a kink structure in the energy band dispersion derived from the electron–phonon interaction. The imaginary part of the self-energy was evaluated; it increases significantly with increasing energy, indicating a strong electron–electron interaction. r 2006 Elsevier B.V. All rights reserved. PACS: 71.18.+y; 79.60.i; 79.60.Bm Keywords: Angle-resolved photoemission spectroscopy; Ni(1 1 1); Surface state; Electron–electron interaction
The ferromagnetic surface state has attracted much interest since it is a spin-polarized two-dimensional electronic system, which may form the basis for spintronics devices utilizing spin-polarized interfaces. Angle-resolved photoemission spectroscopy (ARPES) is one of the most powerful methods to directly study the surface electronic states of solids. Recent high-resolution ARPES enables us to evaluate the magnitudes of the many-body interactions acting on the quasi-particles near the Fermi level (EF), such as electron–phonon and electron–electron interactions. The Shockley state (SS) exists in Ni(1 1 1) at the G point of the surface Brillouin zone (BZ) [1–3]. On the basis of a band-structure calculation [2], it should be the majority-spin SS. Two-photon and single-photon ARPES (Dk ¼ 6–8 102 A˚1, DE ¼ 16 meV) studies with a laser have been conducted, and elucidated a parabolic SS together with a surface resonance dispersing to deeper binding energy [1]. Corresponding author.
E-mail address: [email protected] (M. Higashiguchi). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.11.116
In the present paper, we will examine many-body interactions in the SS by means of high-resolution ARPES. The experiment was performed on the helical undulator beamline (BL-9) of the compact electron-storage ring (HiSOR) at Hiroshima University [4]. A high-resolution hemispherical electron-energy analyzer (R4000, GAMMADATA-SCIENTA) was used. The total energy resolution was set at DE ¼ 5 meV and the angular resolution at Dy ¼ 0:10 (DkJ ¼ 0.004 A˚1). Since one of the minority-spin Fermi surfaces does not have a gap in the L point of the BZ, we optimized the excitation energy to hn ¼ 6.9 eV in order to avoid overlap between the SS and bulk-derived bands. The Ni(1 1 1) single crystal was cleaned by cycles of Ar+ ion sputtering and subsequent annealing. During measurements, the sample was mounted on a lowtemperature five-axis goniometer [5], and ARPES spectra along the GK direction were examined. The sample temperature was set at 7.5 K. Fig. 1(b) shows an intensity plot of the SS along the GK direction. Black corresponds to the strongest spectral intensity. One can see clearly a free-electron-like energy-
ARTICLE IN PRESS M. Higashiguchi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e743–e744
e744
MDC at EF
a
90
Κ
Binding Energy (meV)
0
50
| 2 Im Σ | (meV)
Exp. Γ
70
b 100
-0.05
Ni(111) hν=6.9eV T=7.5K 0.00
0.05
Fit
80
60 80
Fig. 1. The ARPES results of Ni(1 1 1) SS. (b) intensity plot along GK direction: circles indicate peak positions. (a) MDC at EF (dots) obtained from (b); solid line exhibits the fit to a Lorentzian on a linear background.
band dispersion, which agrees well with the previous measurements [1]. In order to discuss many-body interactions, we have estimated the imaginary part of the self-energy (Im S) using the equation, j2 Im Rj ¼ dE ¼ ðdE=dkÞdk, where dE/dK represents a group velocity, and dk is the width of the momentum distribution curves (MDCs) [6]. By fitting each MDC with a Lorentzian on a linear background as shown in Fig. 1(a), the peak position and dk have been determined. The peak positions thus evaluated are indicated by circles in the intensity plot. The Fermi energy m for the SS is evaluated to be m ¼ 135 meV. The MDC width at EF is evaluated to be dk0.027 A˚1, which gives an inelastic mean-free path (l) of electrons in the SS as l36 A˚. In the obtained energy dispersion, one cannot clearly see a kink structure, or a sudden change of the group velocity derived from the electron–phonon interaction, as seen in the SS of Mo(1 1 0) [7]. Fig. 2 shows values of |2Im S| evaluated along the GK direction. Since the electron–phonon interaction is negligible, |2Im S| can be expressed by the sum of the contributions from the electron–electron interaction (Im Sel–el) and electron-impurity interaction (Im S0): |2Im S| ¼ |2Im Sel–el|+|2Im S0|. On the basis of the quasi-particle decay rate of the electron gas with a cylindrical Fermi surface, |2Im Sel–el| is given by |2Im Sel–el| ¼ 2bo2[14+ln 2+12|ln (o/m)|] [8], where the 2b value gives a measure of the electron–electron interaction strength. Near EF, logarithmic correction yields |2Im Selel|bo2| ln (o/m)|(o0), which is different from the expression |2Im Sel–el|2bo2 found for three-dimensional electron systems [6].
40
20
0
Binding Energy (meV)
0.10
k // [110] (Å-1)
60
Fig. 2. Experimentally obtained values j2Im Sj of SS along the GK. Solid line shows a fit assuming j2Im Sj ¼ j2Im Sel–elj+j2Im S0j.
We fit the observed |2Im S| values assuming that they were equal to |2Im Sel–el|+C, where C represents |2Im S0|. We obtained 2bGK ¼ 2.970.3 eV1, C ¼ 62.5 meV along the GK direction. In our previous study, we evaluated 2b 1.470.3 eV1 for the bulk-derived S1m band assuming |2Im Sel–el|2b[(pkBT)2+o2] [6]. The width of the SS becomes significantly broader compared to that of the bulk-derived S1m band. This indicates that the electron–electron interaction in the SS is significant. In conclusion, a low-energy ARPES study of the shockly state in Ni(1 1 1) was performed. We found a significant energy-dependent broadening of the linewidth of the surface state, which indicates significant electron–electron interactions. This work was partly supported by a Grant-in-Aid for Scientific Research (No. 17654060) and for COE Research (13CE2002) by MEXT of Japan. M.H. thanks the JSPS for the financial support. We thank NBARD for liquid He. The experiments were done under the approval of HSRC (proposal No. 05-A-57).
References [1] [2] [3] [4] [5] [6]
J. Kutzner, et al., Phys. Rev. B 56 (1997) 16003. N. Memel, Phys. Rev. B 55 (1997) 5634. M. Donath, et al., Phys. Rev. Lett. 70 (1993) 2802. M. Arita, et al., Surf. Rev. Lett. 9 (2002) 535. Y. Aiura, et al., Rev. Sci. Instrum. 74 (2003) 3177. M. Higashiguchi, et al., Phys. Rev. B 72 (2005) 214438, and references therein. [7] T. Valla, et al., Phys. Rev. Lett. 83 (1999) 2085. [8] C. Hodges, H. Smith, J.W. Wilkins, Phys. Rev. B 4 (1971) 302.
Journal of Magnetism and Magnetic Materials 310 (2007) e743–e744 www.elsevier.com/locate/jmmm
High-resolution photoemission study of electron–electron interaction in the Ni(1 1 1) surface state Mitsuharu Higashiguchia,, Kenya Shimadab, Masashi Aritab, Yuichi Miuraa, Naohisa Tobitaa, Xiaoyu Cuia, Yoshihiro Aiurac, Hirofumi Namatameb, Masaki Taniguchia,b a Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739-0046, Japan c National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
b
Available online 28 November 2006
Abstract High-resolution angle-resolved photoemission study of the surface state in ferromagnetic Ni(1 1 1) has been performed to evaluate the strength of many-body interactions. We could not observe a kink structure in the energy band dispersion derived from the electron–phonon interaction. The imaginary part of the self-energy was evaluated; it increases significantly with increasing energy, indicating a strong electron–electron interaction. r 2006 Elsevier B.V. All rights reserved. PACS: 71.18.+y; 79.60.i; 79.60.Bm Keywords: Angle-resolved photoemission spectroscopy; Ni(1 1 1); Surface state; Electron–electron interaction
The ferromagnetic surface state has attracted much interest since it is a spin-polarized two-dimensional electronic system, which may form the basis for spintronics devices utilizing spin-polarized interfaces. Angle-resolved photoemission spectroscopy (ARPES) is one of the most powerful methods to directly study the surface electronic states of solids. Recent high-resolution ARPES enables us to evaluate the magnitudes of the many-body interactions acting on the quasi-particles near the Fermi level (EF), such as electron–phonon and electron–electron interactions. The Shockley state (SS) exists in Ni(1 1 1) at the G point of the surface Brillouin zone (BZ) [1–3]. On the basis of a band-structure calculation [2], it should be the majority-spin SS. Two-photon and single-photon ARPES (Dk ¼ 6–8 102 A˚1, DE ¼ 16 meV) studies with a laser have been conducted, and elucidated a parabolic SS together with a surface resonance dispersing to deeper binding energy [1]. Corresponding author.
E-mail address: [email protected] (M. Higashiguchi). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.11.116
In the present paper, we will examine many-body interactions in the SS by means of high-resolution ARPES. The experiment was performed on the helical undulator beamline (BL-9) of the compact electron-storage ring (HiSOR) at Hiroshima University [4]. A high-resolution hemispherical electron-energy analyzer (R4000, GAMMADATA-SCIENTA) was used. The total energy resolution was set at DE ¼ 5 meV and the angular resolution at Dy ¼ 0:10 (DkJ ¼ 0.004 A˚1). Since one of the minority-spin Fermi surfaces does not have a gap in the L point of the BZ, we optimized the excitation energy to hn ¼ 6.9 eV in order to avoid overlap between the SS and bulk-derived bands. The Ni(1 1 1) single crystal was cleaned by cycles of Ar+ ion sputtering and subsequent annealing. During measurements, the sample was mounted on a lowtemperature five-axis goniometer [5], and ARPES spectra along the GK direction were examined. The sample temperature was set at 7.5 K. Fig. 1(b) shows an intensity plot of the SS along the GK direction. Black corresponds to the strongest spectral intensity. One can see clearly a free-electron-like energy-
ARTICLE IN PRESS M. Higashiguchi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) e743–e744
e744
MDC at EF
a
90
Κ
Binding Energy (meV)
0
50
| 2 Im Σ | (meV)
Exp. Γ
70
b 100
-0.05
Ni(111) hν=6.9eV T=7.5K 0.00
0.05
Fit
80
60 80
Fig. 1. The ARPES results of Ni(1 1 1) SS. (b) intensity plot along GK direction: circles indicate peak positions. (a) MDC at EF (dots) obtained from (b); solid line exhibits the fit to a Lorentzian on a linear background.
band dispersion, which agrees well with the previous measurements [1]. In order to discuss many-body interactions, we have estimated the imaginary part of the self-energy (Im S) using the equation, j2 Im Rj ¼ dE ¼ ðdE=dkÞdk, where dE/dK represents a group velocity, and dk is the width of the momentum distribution curves (MDCs) [6]. By fitting each MDC with a Lorentzian on a linear background as shown in Fig. 1(a), the peak position and dk have been determined. The peak positions thus evaluated are indicated by circles in the intensity plot. The Fermi energy m for the SS is evaluated to be m ¼ 135 meV. The MDC width at EF is evaluated to be dk0.027 A˚1, which gives an inelastic mean-free path (l) of electrons in the SS as l36 A˚. In the obtained energy dispersion, one cannot clearly see a kink structure, or a sudden change of the group velocity derived from the electron–phonon interaction, as seen in the SS of Mo(1 1 0) [7]. Fig. 2 shows values of |2Im S| evaluated along the GK direction. Since the electron–phonon interaction is negligible, |2Im S| can be expressed by the sum of the contributions from the electron–electron interaction (Im Sel–el) and electron-impurity interaction (Im S0): |2Im S| ¼ |2Im Sel–el|+|2Im S0|. On the basis of the quasi-particle decay rate of the electron gas with a cylindrical Fermi surface, |2Im Sel–el| is given by |2Im Sel–el| ¼ 2bo2[14+ln 2+12|ln (o/m)|] [8], where the 2b value gives a measure of the electron–electron interaction strength. Near EF, logarithmic correction yields |2Im Selel|bo2| ln (o/m)|(o0), which is different from the expression |2Im Sel–el|2bo2 found for three-dimensional electron systems [6].
40
20
0
Binding Energy (meV)
0.10
k // [110] (Å-1)
60
Fig. 2. Experimentally obtained values j2Im Sj of SS along the GK. Solid line shows a fit assuming j2Im Sj ¼ j2Im Sel–elj+j2Im S0j.
We fit the observed |2Im S| values assuming that they were equal to |2Im Sel–el|+C, where C represents |2Im S0|. We obtained 2bGK ¼ 2.970.3 eV1, C ¼ 62.5 meV along the GK direction. In our previous study, we evaluated 2b 1.470.3 eV1 for the bulk-derived S1m band assuming |2Im Sel–el|2b[(pkBT)2+o2] [6]. The width of the SS becomes significantly broader compared to that of the bulk-derived S1m band. This indicates that the electron–electron interaction in the SS is significant. In conclusion, a low-energy ARPES study of the shockly state in Ni(1 1 1) was performed. We found a significant energy-dependent broadening of the linewidth of the surface state, which indicates significant electron–electron interactions. This work was partly supported by a Grant-in-Aid for Scientific Research (No. 17654060) and for COE Research (13CE2002) by MEXT of Japan. M.H. thanks the JSPS for the financial support. We thank NBARD for liquid He. The experiments were done under the approval of HSRC (proposal No. 05-A-57).
References [1] [2] [3] [4] [5] [6]
J. Kutzner, et al., Phys. Rev. B 56 (1997) 16003. N. Memel, Phys. Rev. B 55 (1997) 5634. M. Donath, et al., Phys. Rev. Lett. 70 (1993) 2802. M. Arita, et al., Surf. Rev. Lett. 9 (2002) 535. Y. Aiura, et al., Rev. Sci. Instrum. 74 (2003) 3177. M. Higashiguchi, et al., Phys. Rev. B 72 (2005) 214438, and references therein. [7] T. Valla, et al., Phys. Rev. Lett. 83 (1999) 2085. [8] C. Hodges, H. Smith, J.W. Wilkins, Phys. Rev. B 4 (1971) 302.