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Ab initio calculation of X-ray magnetic circular dichroism spectra
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 477–478
Ab initio calculation of X-ray magnetic circular dichroism spectra Manabu Takahashia,*, Jun-ichi Igarashib b
a Faculty of Engineering, Gunma University, Tenjin 1-5-1, Kiryu, Gunma 376-8515, Japan Synchrotron Radiation Research Center, Japan Atomic Energy Research Institute, Mikazuki, Sayo, Hyogo 679-5148, Japan
Abstract X-ray magnetic circular dichroism spectra at the K edge of Mn in the ferromagnetic phases of Mn3 GaC and Mn3 ZnC are calculated by taking account of the spin–orbit interaction (SOI) in the LDA scheme. The calculated spectra show excellent agreement with the recent experiment, demonstrating that they arise from the p orbital polarization. We make clear the mechanism of its induction by selectively turning off the SOI on specified states. r 2003 Elsevier B.V. All rights reserved. PACS: 78.70.Dm; 75.25.þz; 75.10.Lp Keywords: X-ray magnetic circular dichroism; X-ray absorption spectroscopy; K-edge absorption
X-ray magnetic circular dichroism (XMCD) has been widely used to investigate magnetic states [1]. For the K edge of transition-metal compounds, the 1s-core electron enters into unoccupied 4p states by photoabsorption. Since the 4p states are not the states of constituting the magnetic order, the relation of the XMCD signal to the magnetic order has to be clarified. One of the present authors and Hirai have analyzed the XMCD at the K edge of ferromagnetic metals, Fe, Co, and Ni, and have found that the spectra come from the 4p orbital polarization induced by the mixing to the 3d states at neighboring sites [2]. The above mechanism is a consequence of an extended character of 4p states, and is closely related to the mechanism of the resonant X-ray scattering (RXS) at the K edges of transition metals in several compounds [3,4]. In this paper, for clarifying further the mechanism of inducing 4p orbital polarizations, we analyze the XMCD spectra at the K edges in the ferromagnetic phase of Mn3 GaC and Mn3 ZnC through an ab initio calculation. We use the Korringa–Kohn–Rostoker *Corresponding author. Tel.: +81-277-30-1926; fax: +81277-40-1026. E-mail address: [email protected] (M. Takahashi).
(KKR) method within the muffin-tin (MT) approximation in the local density approximation (LDA) scheme, and take account of the spin–orbit interaction (SOI). We neglect the core–hole potential in the final state, which is unimportant except for the Fermi-edge singularity. Both materials take ‘‘inverse’’ perovskite structure [5]. They have a ferromagnetic phase above 168 K in Mn3 GaC and above 233 K in Mn3 ZnC [6]. We carry out the band calculation assuming a ferromagnetic phase with the magnetization fixed to the opposite of the ½1 1 1 direction, thereby neglecting small magnetic anisotropy. The spin and orbital angular momenta are given by 0:73ð1:088Þ_ and 0:042ð0:019Þ_ in the d symmetric states, respectively, for Mn3 GaC ðMn3 ZnCÞ: They are consistent with the experiment [5]. Fig. 1 shows the XMCD spectra mc ðoÞ at the Mn K edge in Mn3 GaC; in comparison with the experiment [6]. The XMCD spectra are in good agreement with the experiment; dips A, B, and peak C correspond well with the experimental ones A0 ; B0 ; and C0 : The small peak at the Fermi level in the experiment is not reproduced in the calculation. The XMCD spectra come from the orbital polarization in the p symmetric states. With turning off the SOI on the p symmetric states at Mn sites, we find that dip A keeps the similar shape while dip B almost vanishes. On
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.422
ARTICLE IN PRESS M. Takahashi, J.-i. Igarashi / Journal of Magnetism and Magnetic Materials 272–276 (2004) 477–478
478
Mn K edge in Mn3GaC expt.
0
µc (arb. units)
2 calc.
x103
C
0 −2
A
B
2 killed Mn p SOI
x103
0
0
x103 D
−2
E
2
x103
0 killed Mn p SOI
−2
−2
2
2 killed Mn d SOI
x10
3
killed Mn d SOI
x103
0
0
−2
−2 −10
E’
−2
B’ calc.
x103 D’
0
A’
−1 2
2 expt.
x103
C’
µc (arb. units)
1
Mn K edge in Mn3ZnC
−10 0 10 Relative Energy (eV)
20
Fig. 1. XMCD spectra at the Mn K edge in Mn3 GaC in comparison with the experiment [6]. The origin of energy corresponds to the excitation to the Fermi level. Lower two panels show the spectra calculated with turning off the SOI on the p and d symmetric states at Mn sites, respectively.
the other hand, with turning off the SOI only on the d symmetric states at Mn sites, we find dip A is drastically reduced but dip B and peak C remains similar. The 3d orbital polarization cannot polarize the p orbital in the same Mn site, because the p–d Coulomb interaction is spherically averaged inside the MT sphere. Thus, we conclude that the 3d orbital polarization at neighboring Mn sites induces the p orbital polarization corresponding to dip A through the p–d hybridization. Fig. 2 shows the XMCD spectra mc ðoÞ at the K edge in Mn3 ZnC; in comparison with the experiment [6]. The spectral shape is quite similar to that for Mn3 ZnC; except for a large peak at the Fermi level (peak D). The calculation reproduces well the experimental shape
0 10 Relative Energy [eV]
20
Fig. 2. XMCD spectra at the Mn K edge in Mn3 ZnC in comparison with the experiment [6].
including the peak D at the Fermi level. The analysis similar to the case of Mn3 GaC leads us to conclude that peak D and dip E are generated by the 3d orbital polarization at neighboring Mn sites (see the lower two panels).
References G. Schutz, . R. Wienke, Hyperfine Interaction 50 (1989) 457. J. Igarashi, K. Hirai, Phys. Rev. B 50 (1994) 17820. Y. Murakami, et al., Phys. Rev. Lett. 81 (1998) 582. M. Takahashi, J. Igarashi, P. Fulde, J. Phys. Soc. Japan 68 (1999) 2530. [5] D. Fruchart, E.F. Bertaut, J. Phys. Soc. Japan 44 (1978) 781. [6] S. Uemoto, et al., J. Synchrotron Radiat. 8 (2001) 449. [1] [2] [3] [4]
Journal of Magnetism and Magnetic Materials 272–276 (2004) 477–478
Ab initio calculation of X-ray magnetic circular dichroism spectra Manabu Takahashia,*, Jun-ichi Igarashib b
a Faculty of Engineering, Gunma University, Tenjin 1-5-1, Kiryu, Gunma 376-8515, Japan Synchrotron Radiation Research Center, Japan Atomic Energy Research Institute, Mikazuki, Sayo, Hyogo 679-5148, Japan
Abstract X-ray magnetic circular dichroism spectra at the K edge of Mn in the ferromagnetic phases of Mn3 GaC and Mn3 ZnC are calculated by taking account of the spin–orbit interaction (SOI) in the LDA scheme. The calculated spectra show excellent agreement with the recent experiment, demonstrating that they arise from the p orbital polarization. We make clear the mechanism of its induction by selectively turning off the SOI on specified states. r 2003 Elsevier B.V. All rights reserved. PACS: 78.70.Dm; 75.25.þz; 75.10.Lp Keywords: X-ray magnetic circular dichroism; X-ray absorption spectroscopy; K-edge absorption
X-ray magnetic circular dichroism (XMCD) has been widely used to investigate magnetic states [1]. For the K edge of transition-metal compounds, the 1s-core electron enters into unoccupied 4p states by photoabsorption. Since the 4p states are not the states of constituting the magnetic order, the relation of the XMCD signal to the magnetic order has to be clarified. One of the present authors and Hirai have analyzed the XMCD at the K edge of ferromagnetic metals, Fe, Co, and Ni, and have found that the spectra come from the 4p orbital polarization induced by the mixing to the 3d states at neighboring sites [2]. The above mechanism is a consequence of an extended character of 4p states, and is closely related to the mechanism of the resonant X-ray scattering (RXS) at the K edges of transition metals in several compounds [3,4]. In this paper, for clarifying further the mechanism of inducing 4p orbital polarizations, we analyze the XMCD spectra at the K edges in the ferromagnetic phase of Mn3 GaC and Mn3 ZnC through an ab initio calculation. We use the Korringa–Kohn–Rostoker *Corresponding author. Tel.: +81-277-30-1926; fax: +81277-40-1026. E-mail address: [email protected] (M. Takahashi).
(KKR) method within the muffin-tin (MT) approximation in the local density approximation (LDA) scheme, and take account of the spin–orbit interaction (SOI). We neglect the core–hole potential in the final state, which is unimportant except for the Fermi-edge singularity. Both materials take ‘‘inverse’’ perovskite structure [5]. They have a ferromagnetic phase above 168 K in Mn3 GaC and above 233 K in Mn3 ZnC [6]. We carry out the band calculation assuming a ferromagnetic phase with the magnetization fixed to the opposite of the ½1 1 1 direction, thereby neglecting small magnetic anisotropy. The spin and orbital angular momenta are given by 0:73ð1:088Þ_ and 0:042ð0:019Þ_ in the d symmetric states, respectively, for Mn3 GaC ðMn3 ZnCÞ: They are consistent with the experiment [5]. Fig. 1 shows the XMCD spectra mc ðoÞ at the Mn K edge in Mn3 GaC; in comparison with the experiment [6]. The XMCD spectra are in good agreement with the experiment; dips A, B, and peak C correspond well with the experimental ones A0 ; B0 ; and C0 : The small peak at the Fermi level in the experiment is not reproduced in the calculation. The XMCD spectra come from the orbital polarization in the p symmetric states. With turning off the SOI on the p symmetric states at Mn sites, we find that dip A keeps the similar shape while dip B almost vanishes. On
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.422
ARTICLE IN PRESS M. Takahashi, J.-i. Igarashi / Journal of Magnetism and Magnetic Materials 272–276 (2004) 477–478
478
Mn K edge in Mn3GaC expt.
0
µc (arb. units)
2 calc.
x103
C
0 −2
A
B
2 killed Mn p SOI
x103
0
0
x103 D
−2
E
2
x103
0 killed Mn p SOI
−2
−2
2
2 killed Mn d SOI
x10
3
killed Mn d SOI
x103
0
0
−2
−2 −10
E’
−2
B’ calc.
x103 D’
0
A’
−1 2
2 expt.
x103
C’
µc (arb. units)
1
Mn K edge in Mn3ZnC
−10 0 10 Relative Energy (eV)
20
Fig. 1. XMCD spectra at the Mn K edge in Mn3 GaC in comparison with the experiment [6]. The origin of energy corresponds to the excitation to the Fermi level. Lower two panels show the spectra calculated with turning off the SOI on the p and d symmetric states at Mn sites, respectively.
the other hand, with turning off the SOI only on the d symmetric states at Mn sites, we find dip A is drastically reduced but dip B and peak C remains similar. The 3d orbital polarization cannot polarize the p orbital in the same Mn site, because the p–d Coulomb interaction is spherically averaged inside the MT sphere. Thus, we conclude that the 3d orbital polarization at neighboring Mn sites induces the p orbital polarization corresponding to dip A through the p–d hybridization. Fig. 2 shows the XMCD spectra mc ðoÞ at the K edge in Mn3 ZnC; in comparison with the experiment [6]. The spectral shape is quite similar to that for Mn3 ZnC; except for a large peak at the Fermi level (peak D). The calculation reproduces well the experimental shape
0 10 Relative Energy [eV]
20
Fig. 2. XMCD spectra at the Mn K edge in Mn3 ZnC in comparison with the experiment [6].
including the peak D at the Fermi level. The analysis similar to the case of Mn3 GaC leads us to conclude that peak D and dip E are generated by the 3d orbital polarization at neighboring Mn sites (see the lower two panels).
References G. Schutz, . R. Wienke, Hyperfine Interaction 50 (1989) 457. J. Igarashi, K. Hirai, Phys. Rev. B 50 (1994) 17820. Y. Murakami, et al., Phys. Rev. Lett. 81 (1998) 582. M. Takahashi, J. Igarashi, P. Fulde, J. Phys. Soc. Japan 68 (1999) 2530. [5] D. Fruchart, E.F. Bertaut, J. Phys. Soc. Japan 44 (1978) 781. [6] S. Uemoto, et al., J. Synchrotron Radiat. 8 (2001) 449. [1] [2] [3] [4]