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Measurements of temperature dependence of “localized susceptibility”
Nuclear Instruments and Methods in Physics Research B 199 (2003) 318–322 www.elsevier.com/locate/nimb
Measurements of temperature dependence of ‘‘localized susceptibility’’ Hidetsugu Shiozawa a, Tsuneaki Miyahara a,*, Hiroyoshi Ishii a, Yasuhiro Takayama a, Kenji Obu a, Takayuki Muro b, Yuji Saitoh c, Tatsuma D. Matsuda a, Hitoshi Sugawara a, Hideyuki Sato a a
Department of Physics, Tokyo Metropolitan University, Minamiosawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan b JASRI/SPring-8, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan c JAERI/SPring-8, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan
Abstract The magnetic susceptibility of some rare-earth compounds is estimated by measuring magnetic circular dichroism (MCD) of rare-earth 3d–4f absorption spectra. The temperature dependence of the magnetic susceptibility obtained by the MCD measurement is remarkably different from the bulk susceptibility in most samples, which is attributed to the strong site selectivity of the core MCD measurement. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 75.20.Hr; 78.70.Dm; 87.64.Ni Keywords: Magnetic circular dichroism; Coherent Kondo material; Curie–Weiss plot
1. Introduction Magnetic circular dichroism (MCD) measurement has been known to be one of the useful techniques for studying various ordered magnetic materials. Especially, the MCD measurement of the X-ray absorption spectra (XAS) gives us the information on local magnetic moments of selected constituent atoms. The recent development of the synchrotron radiation sources enabled us to
* Corresponding author. Tel.: +81-426-77-2494; fax: +81426-77-2483. E-mail address: [email protected] (T. Miyahara).
measure small MCD signals on disordered materials, owing to the high brilliant and very stable polarized X-rays [1,2]. We pointed out an importance of the MCD measurement above the critical temperature and succeeded to demonstrate the XAS-MCD measurement on a disordered magnetic material [1]. We also measured XAS-MCD on rare-earth compounds CePd3 and PrFe4 P12 in the rare-earth 3d–4f excitation region at several temperatures and estimated the magnetic susceptibility [3]. The obtained results were remarkably different from the bulk magnetic susceptibility. These discrepancies might come from the fact that, at core MCD measurement, we directly observe a localized magnetic moment of rare-earth 4f electrons which mainly takes the magnetic features of
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 1 4 2 0 - 9
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
319
the rare-earth compound, on the other hand the bulk magnetic susceptibility contains contributions of other atomic sites or itinerant electrons. In this paper, we report the results of the XASMCD measurements on CeSn3 , CePd3 and CeRu4 Sb12 at rare-earth 3d–4f excitation region. CeSn3 and CePd3 are known as intermediatevalence materials in which the bulk magnetic susceptibility shows a characteristic broad peak around the Kondo temperature TK of about 150 K. CeRu4 Sb12 has a filled skutterudite structure RT4 X12 (R ¼ rare earth; T ¼ Ru; X ¼ Sb), in which the lanthanide atoms fill the voids of CoAs3 (skutterudite) structure. The rare-earth skutterudites are interesting materials because these show various exciting physical properties depending on the constituent atoms, such as superconductivity, semiconductivity and magnetic order [4,5]. On CeRu4 Sb12 , the bulk magnetic susceptibility shows intermediate-valence behavior with a characteristic broad peak around TK of about 100 K and the electrical resistivity shows the Kondo-like behavior. CeRu4 Sb12 is a unique substance which shows non-Fermi liquid behavior in the specific heat, electrical resistivity and thermoelectric power at low temperatures, whereas the most intermediatevalence or Kondo materials show Fermi liquid behavior. On the other hand, on NdFe4 P12 , the results of numerous macroscopic measurements and neutron diffraction investigations indicate ferromagnetic behaviors with the Curie temperature TC of 1.94 K. These various electrical and magnetic features of the rare-earth skutterudites are thought to be the results of the hybridization between the rare-earth 4f states and conduction states. We investigate the magnetic properties of these interesting materials by measuring the core MCD spectra, indicating that the localized susceptibilities are measured.
tive because the scattered electrons with small kinetic energies around 5 eV give the main contribution to the total photoelectron yield. The magnetic field applied to the samples was 1.4 T, which was generated by a magnetic circuit composed of permanent magnets. The direction of the magnetic field was switched in a few seconds by linear motion of the magnet block. In addition, the direction of the circular polarization of incident light was reversed after a series of measurements. This procedure is important to avoid possible errors on MCD signals because the expected MCD signals measured with the disordered magnetic materials are very small. The energy resolution of the beamline monochromator was reduced to 0.15 eV to increase the intensity of the incident light, which was important to detect small MCD signals. The sample temperature was controlled from 10 K to room temperature with a He cryostat equipped with a heater. Polycrystalline CeSn3 , CePd3 and single crystals CeRu4 Sb12 were prepared for the measurements. These samples were grown by an arc-melting method for CeSn3 and CePd3 , Sb-self-flux method with excess Sb for CeRu4 Sb12 [6,7], respectively. The samples were scraped with a diamond file without breaking ultra-high vacuum of a measurement chamber. The vacuum pressure of the measurement chamber was kept under 4 1010 Torr through the measurements.
2. Experimental
Ip ðxÞ /
3. Calculations In this study, we estimate the magnetic moments of the rare-earth 4f electrons by comparing the magnitudes of the measured rare-earth 3d absorption and MCD spectra with the calculated ones. Under the dipole selection rule, the absorption spectrum Ip ðx) is written as J X
P ðM; HÞ
M¼J
The experiments were performed at an undulator beamline BL-25SU of SPring-8. The absorption spectra were taken by measuring the total photoelectron yield from the samples. This measurement is supposed to be essentially bulk-sensi-
X hf jTp ji; J ; Mi2 S f
ðqðEf Þ; Ef Ei x; CðEf ÞÞ; eM=H ; M 0 =H M 0 ¼J e
P ðM; HÞ ¼ PJ
ð1Þ ð2Þ
320
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
Sðq; x; CÞ ¼ ð1=pq2 CÞ
ðx=C þ qÞ2 2
ðx=CÞ þ 1
;
ð3Þ
where ji; J ; Mi is the initial state with total angular moment J and magnetic quantum number M. hf j is the final state after photo absorption. Ei (Ef ) is the energy of the initial (final) state and x is the photon energy. Tp is the dipole transition matrix, where p ¼ 1 ()1) corresponds to the photon spin parallel (anti-parallel) to the direction of the magnetic field applied to the sample. P ðM; H) is the population function of the initial states ji; J ; Mi according to the Boltzmann distribution expðMHÞ, where H is the reduced temperature kT =glB B. q and C are parameters of the Fano profile [8]. The dipole matrix elements and the energies of the initial and final states are obtained by CowanÕs atomic Hartree–Fock (HF) program with relativistic corrections [9]. The Slater integrals are all reduced to 80% of their HF values [10,11]. Magnetic moment is represented as a function of the effective temperature H as follows: lðHÞ ¼ glB
J X
MP ðM; HÞ;
Fig. 1. Ce 3d absorption and MCD spectra of CeSn3 at 22 K.
ð4Þ
M¼J
where lB is the Bohr magneton and g is LandeÕs g-factor.
4. Results and discussion Fig. 1 shows the Ce 3d absorption and MCD spectra of CeSn3 at 20 K, as a typical example for all temperatures. The symbol lþ (l ) means the absorption intensity when the photon spin is parallel (anti-parallel) to the direction of the magnetic field applied to the sample. The MCD signal is defined as the difference lþ l . The absorption and MCD spectral shape are similar to the theoretical ones calculated assuming the 4f1 Hund ground state at all temperatures, except for the weak absorption satellites localized at about 6 eV above Ce M4;5 edges, respectively. These satellites correspond to 4f0 ground state configuration, whose magnitudes are interpreted as the degree of the hybridization between the 4f and conduction states. Fig. 2 shows the temperature dependence of
Fig. 2. Inverse magnetic susceptibility v1 ðT Þ for CeSn3 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CeSn3 [14].
the inverse magnetic susceptibility for CeSn3 obtained by the present MCD measurement. The magnetic susceptibility can be well described by the Curie–Weiss law. On the other hand, the temperature dependence of the bulk magnetic susceptibility, which is inserted in the figure, shows a typical behavior of the intermediate-valence material with a broad peak around TK of 150 K and an upturn at lower temperature [12–14]. It is reasonable to compare the magnetic susceptibility obtained by the present MCD measurement at a magnetic field 1.4 T to the bulk magnetic suscep-
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
tibility because the bulk magnetic susceptibility of the intermediate-valence material generally shows no field dependence in the present temperature range [12]. In this situation, we could suggest that the Curie–Weiss behavior is intrinsic to the MCD measurement in which the magnetic moment of a particular site is selectively observed. In other words, the localized 4f spin moment is not quenched in the present temperature range, which is inconsistent with the fact that CeSn3 is the intermediate-valence material with TK of 150 K. A least-squares fit to a Curie–Weiss law yields the effective magnetic moment leff of 2.44lB which is consistent with the free-ion HundÕs rule multiplet value of 2.54lB Fig. 3 shows the similar behavior on CePd3 . Fig. 4 shows the Ce 3d absorption and MCD spectra of CeRu4 Sb12 at 55 K. The absorption and MCD profile are very close to the calculated ones based on the 4f1 Hund ground state. The estimated inverse magnetic susceptibilities of CeRu4 Sb12 were plotted against the temperature as shown in Fig. 5. The result is not remarkably different from the case for the bulk magnetic susceptibility where the typical behaviors of the intermediate-valence material are observed [15]. A possible reason for the similarity between the present result and bulk magnetic susceptibility is that the 4f states in CeRu4 Sb12 are much more itinerant than those in CeSn3 or CePd3 .
321
Fig. 4. Ce 3d absorption and MCD spectra of CeRu4 Sb12 at 55 K.
Fig. 5. Inverse magnetic susceptibility v1 ðT Þ for CeRu4 Sb12 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CeRu4 Sb12 in a magnetic field of H ¼ 0:1 T [15].
5. Conclusion
Fig. 3. Inverse magnetic susceptibility v1 ðT Þ for CePd3 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CePd3 .
In this study, we have found the remarkable difference between the MCD signals and bulk magnetic susceptibility in most samples. Especially, on the intermediate-valence materials CeSn3 and CePd3 , it was found that the local magnetic moments of Ce 4f sites were not quenched below the bulk ‘‘TK ’’. CeRu4 Sb12 rather shows as similar
322
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
behavior as the bulk measurements, which could be caused by the itinerant character of the 4f states. Acknowledgements This work was performed at the SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal no. 2001B0093-NS-np). References [1] T. Miyahara et al., Jpn. J. Appl. Phys. 38 (Suppl. 38-1) (1999) 396.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
J. Rothman et al., J. Magn. Magn. Mater. 198 (1999) 276. T. Miyahara et al., J. Phys. Soc. Jpn. 70 (2001) 2977. N. Takeda, M. Ishikawa, J. Phys. Soc. Jpn. 69 (2000) 868. M.S. Torikachvili et al., Phys. Rev. B 36 (1987) 8660. N. Takeda, M. Ishikawa, Physica B 259–261 (1999) 92. N. Takeda, M. Ishikawa, Physica B 281–282 (2000) 388. U. Fano, Phys. Rev. 124 1866. R. Cowan, The Theory of Atomic Structure and Spectra, University of California Press, Berkeley, 1981. T. Thole et al., Phys. Rev. B 32 (1985) 5107. J. Goedkoop, X-ray Dichroism of Rare Earth Materials, 1989, ISBN 90-9003127-8. T.-W.E. Tsang et al., Phys. Rev. B 29 (1984) 4185. J. Lawrence, Phys. Rev. B 20 (1979) 3770. K.A. Gschneidner et al., J. Magn. Magn. Mater. 47&48 (1985) 51. E.D. Bauer et al., J. Phys., Condens. Matt. 13 (2001) 5183.
Measurements of temperature dependence of ‘‘localized susceptibility’’ Hidetsugu Shiozawa a, Tsuneaki Miyahara a,*, Hiroyoshi Ishii a, Yasuhiro Takayama a, Kenji Obu a, Takayuki Muro b, Yuji Saitoh c, Tatsuma D. Matsuda a, Hitoshi Sugawara a, Hideyuki Sato a a
Department of Physics, Tokyo Metropolitan University, Minamiosawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan b JASRI/SPring-8, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan c JAERI/SPring-8, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan
Abstract The magnetic susceptibility of some rare-earth compounds is estimated by measuring magnetic circular dichroism (MCD) of rare-earth 3d–4f absorption spectra. The temperature dependence of the magnetic susceptibility obtained by the MCD measurement is remarkably different from the bulk susceptibility in most samples, which is attributed to the strong site selectivity of the core MCD measurement. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 75.20.Hr; 78.70.Dm; 87.64.Ni Keywords: Magnetic circular dichroism; Coherent Kondo material; Curie–Weiss plot
1. Introduction Magnetic circular dichroism (MCD) measurement has been known to be one of the useful techniques for studying various ordered magnetic materials. Especially, the MCD measurement of the X-ray absorption spectra (XAS) gives us the information on local magnetic moments of selected constituent atoms. The recent development of the synchrotron radiation sources enabled us to
* Corresponding author. Tel.: +81-426-77-2494; fax: +81426-77-2483. E-mail address: [email protected] (T. Miyahara).
measure small MCD signals on disordered materials, owing to the high brilliant and very stable polarized X-rays [1,2]. We pointed out an importance of the MCD measurement above the critical temperature and succeeded to demonstrate the XAS-MCD measurement on a disordered magnetic material [1]. We also measured XAS-MCD on rare-earth compounds CePd3 and PrFe4 P12 in the rare-earth 3d–4f excitation region at several temperatures and estimated the magnetic susceptibility [3]. The obtained results were remarkably different from the bulk magnetic susceptibility. These discrepancies might come from the fact that, at core MCD measurement, we directly observe a localized magnetic moment of rare-earth 4f electrons which mainly takes the magnetic features of
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 1 4 2 0 - 9
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
319
the rare-earth compound, on the other hand the bulk magnetic susceptibility contains contributions of other atomic sites or itinerant electrons. In this paper, we report the results of the XASMCD measurements on CeSn3 , CePd3 and CeRu4 Sb12 at rare-earth 3d–4f excitation region. CeSn3 and CePd3 are known as intermediatevalence materials in which the bulk magnetic susceptibility shows a characteristic broad peak around the Kondo temperature TK of about 150 K. CeRu4 Sb12 has a filled skutterudite structure RT4 X12 (R ¼ rare earth; T ¼ Ru; X ¼ Sb), in which the lanthanide atoms fill the voids of CoAs3 (skutterudite) structure. The rare-earth skutterudites are interesting materials because these show various exciting physical properties depending on the constituent atoms, such as superconductivity, semiconductivity and magnetic order [4,5]. On CeRu4 Sb12 , the bulk magnetic susceptibility shows intermediate-valence behavior with a characteristic broad peak around TK of about 100 K and the electrical resistivity shows the Kondo-like behavior. CeRu4 Sb12 is a unique substance which shows non-Fermi liquid behavior in the specific heat, electrical resistivity and thermoelectric power at low temperatures, whereas the most intermediatevalence or Kondo materials show Fermi liquid behavior. On the other hand, on NdFe4 P12 , the results of numerous macroscopic measurements and neutron diffraction investigations indicate ferromagnetic behaviors with the Curie temperature TC of 1.94 K. These various electrical and magnetic features of the rare-earth skutterudites are thought to be the results of the hybridization between the rare-earth 4f states and conduction states. We investigate the magnetic properties of these interesting materials by measuring the core MCD spectra, indicating that the localized susceptibilities are measured.
tive because the scattered electrons with small kinetic energies around 5 eV give the main contribution to the total photoelectron yield. The magnetic field applied to the samples was 1.4 T, which was generated by a magnetic circuit composed of permanent magnets. The direction of the magnetic field was switched in a few seconds by linear motion of the magnet block. In addition, the direction of the circular polarization of incident light was reversed after a series of measurements. This procedure is important to avoid possible errors on MCD signals because the expected MCD signals measured with the disordered magnetic materials are very small. The energy resolution of the beamline monochromator was reduced to 0.15 eV to increase the intensity of the incident light, which was important to detect small MCD signals. The sample temperature was controlled from 10 K to room temperature with a He cryostat equipped with a heater. Polycrystalline CeSn3 , CePd3 and single crystals CeRu4 Sb12 were prepared for the measurements. These samples were grown by an arc-melting method for CeSn3 and CePd3 , Sb-self-flux method with excess Sb for CeRu4 Sb12 [6,7], respectively. The samples were scraped with a diamond file without breaking ultra-high vacuum of a measurement chamber. The vacuum pressure of the measurement chamber was kept under 4 1010 Torr through the measurements.
2. Experimental
Ip ðxÞ /
3. Calculations In this study, we estimate the magnetic moments of the rare-earth 4f electrons by comparing the magnitudes of the measured rare-earth 3d absorption and MCD spectra with the calculated ones. Under the dipole selection rule, the absorption spectrum Ip ðx) is written as J X
P ðM; HÞ
M¼J
The experiments were performed at an undulator beamline BL-25SU of SPring-8. The absorption spectra were taken by measuring the total photoelectron yield from the samples. This measurement is supposed to be essentially bulk-sensi-
X hf jTp ji; J ; Mi2 S f
ðqðEf Þ; Ef Ei x; CðEf ÞÞ; eM=H ; M 0 =H M 0 ¼J e
P ðM; HÞ ¼ PJ
ð1Þ ð2Þ
320
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
Sðq; x; CÞ ¼ ð1=pq2 CÞ
ðx=C þ qÞ2 2
ðx=CÞ þ 1
;
ð3Þ
where ji; J ; Mi is the initial state with total angular moment J and magnetic quantum number M. hf j is the final state after photo absorption. Ei (Ef ) is the energy of the initial (final) state and x is the photon energy. Tp is the dipole transition matrix, where p ¼ 1 ()1) corresponds to the photon spin parallel (anti-parallel) to the direction of the magnetic field applied to the sample. P ðM; H) is the population function of the initial states ji; J ; Mi according to the Boltzmann distribution expðMHÞ, where H is the reduced temperature kT =glB B. q and C are parameters of the Fano profile [8]. The dipole matrix elements and the energies of the initial and final states are obtained by CowanÕs atomic Hartree–Fock (HF) program with relativistic corrections [9]. The Slater integrals are all reduced to 80% of their HF values [10,11]. Magnetic moment is represented as a function of the effective temperature H as follows: lðHÞ ¼ glB
J X
MP ðM; HÞ;
Fig. 1. Ce 3d absorption and MCD spectra of CeSn3 at 22 K.
ð4Þ
M¼J
where lB is the Bohr magneton and g is LandeÕs g-factor.
4. Results and discussion Fig. 1 shows the Ce 3d absorption and MCD spectra of CeSn3 at 20 K, as a typical example for all temperatures. The symbol lþ (l ) means the absorption intensity when the photon spin is parallel (anti-parallel) to the direction of the magnetic field applied to the sample. The MCD signal is defined as the difference lþ l . The absorption and MCD spectral shape are similar to the theoretical ones calculated assuming the 4f1 Hund ground state at all temperatures, except for the weak absorption satellites localized at about 6 eV above Ce M4;5 edges, respectively. These satellites correspond to 4f0 ground state configuration, whose magnitudes are interpreted as the degree of the hybridization between the 4f and conduction states. Fig. 2 shows the temperature dependence of
Fig. 2. Inverse magnetic susceptibility v1 ðT Þ for CeSn3 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CeSn3 [14].
the inverse magnetic susceptibility for CeSn3 obtained by the present MCD measurement. The magnetic susceptibility can be well described by the Curie–Weiss law. On the other hand, the temperature dependence of the bulk magnetic susceptibility, which is inserted in the figure, shows a typical behavior of the intermediate-valence material with a broad peak around TK of 150 K and an upturn at lower temperature [12–14]. It is reasonable to compare the magnetic susceptibility obtained by the present MCD measurement at a magnetic field 1.4 T to the bulk magnetic suscep-
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
tibility because the bulk magnetic susceptibility of the intermediate-valence material generally shows no field dependence in the present temperature range [12]. In this situation, we could suggest that the Curie–Weiss behavior is intrinsic to the MCD measurement in which the magnetic moment of a particular site is selectively observed. In other words, the localized 4f spin moment is not quenched in the present temperature range, which is inconsistent with the fact that CeSn3 is the intermediate-valence material with TK of 150 K. A least-squares fit to a Curie–Weiss law yields the effective magnetic moment leff of 2.44lB which is consistent with the free-ion HundÕs rule multiplet value of 2.54lB Fig. 3 shows the similar behavior on CePd3 . Fig. 4 shows the Ce 3d absorption and MCD spectra of CeRu4 Sb12 at 55 K. The absorption and MCD profile are very close to the calculated ones based on the 4f1 Hund ground state. The estimated inverse magnetic susceptibilities of CeRu4 Sb12 were plotted against the temperature as shown in Fig. 5. The result is not remarkably different from the case for the bulk magnetic susceptibility where the typical behaviors of the intermediate-valence material are observed [15]. A possible reason for the similarity between the present result and bulk magnetic susceptibility is that the 4f states in CeRu4 Sb12 are much more itinerant than those in CeSn3 or CePd3 .
321
Fig. 4. Ce 3d absorption and MCD spectra of CeRu4 Sb12 at 55 K.
Fig. 5. Inverse magnetic susceptibility v1 ðT Þ for CeRu4 Sb12 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CeRu4 Sb12 in a magnetic field of H ¼ 0:1 T [15].
5. Conclusion
Fig. 3. Inverse magnetic susceptibility v1 ðT Þ for CePd3 in a magnetic field of H ¼ 1:4 T. Inset: Inverse of bulk magnetic susceptibility v1 ðT Þ for CePd3 .
In this study, we have found the remarkable difference between the MCD signals and bulk magnetic susceptibility in most samples. Especially, on the intermediate-valence materials CeSn3 and CePd3 , it was found that the local magnetic moments of Ce 4f sites were not quenched below the bulk ‘‘TK ’’. CeRu4 Sb12 rather shows as similar
322
H. Shiozawa et al. / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 318–322
behavior as the bulk measurements, which could be caused by the itinerant character of the 4f states. Acknowledgements This work was performed at the SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal no. 2001B0093-NS-np). References [1] T. Miyahara et al., Jpn. J. Appl. Phys. 38 (Suppl. 38-1) (1999) 396.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
J. Rothman et al., J. Magn. Magn. Mater. 198 (1999) 276. T. Miyahara et al., J. Phys. Soc. Jpn. 70 (2001) 2977. N. Takeda, M. Ishikawa, J. Phys. Soc. Jpn. 69 (2000) 868. M.S. Torikachvili et al., Phys. Rev. B 36 (1987) 8660. N. Takeda, M. Ishikawa, Physica B 259–261 (1999) 92. N. Takeda, M. Ishikawa, Physica B 281–282 (2000) 388. U. Fano, Phys. Rev. 124 1866. R. Cowan, The Theory of Atomic Structure and Spectra, University of California Press, Berkeley, 1981. T. Thole et al., Phys. Rev. B 32 (1985) 5107. J. Goedkoop, X-ray Dichroism of Rare Earth Materials, 1989, ISBN 90-9003127-8. T.-W.E. Tsang et al., Phys. Rev. B 29 (1984) 4185. J. Lawrence, Phys. Rev. B 20 (1979) 3770. K.A. Gschneidner et al., J. Magn. Magn. Mater. 47&48 (1985) 51. E.D. Bauer et al., J. Phys., Condens. Matt. 13 (2001) 5183.