- Email: [email protected]
p–f mixing in CeSb, studied by resonant X-ray scattering
ARTICLE IN PRESS
Physica B 345 (2004) 74–77
p–f mixing in CeSb, studied by resonant X-ray scattering A. Stunaulta,*, C. Vettiera, L.P. Regnaultb, F. de Bergevinc, L. Paolasinic, J.Y. Henryb a
Institut Laue Langevin, 6 rue Jules Horowitz, BP 156X, F-38042 Grenoble, Cedex, France b CEA-Grenoble, DRFMC/SPSMS/MDN, F-38054 Grenoble, Cedex 9, France c ESRF, BP 220, F-38043 Grenoble, Cedex, France
Abstract X-ray magnetic scattering experiments have been performed in CeSb at the Ce and Sb L edges. In the non-resonant regime, we observe charge satellites reflecting the lattice modulation associated with the periodicity of paramagnetic G8 planes. At the Ce L2 edge we observe strong magnetic resonances, due to the antiferromagnetic stacking of the ferromagnetic G7 : The study at the Sb L1 edge shows a magnetic dipole resonance, which supports the model of strong p–f mixing, used to explain the origin of the long-range magnetic order of CeSb. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Gg; 71.27.+a; 78.70.Ck Keywords: Cerium; p–f mixing; Resonant magnetic X-ray scattering
1. Introduction CeSb stands at the borderline between welllocalized and itinerant f-electron systems, and presents a fascinating variety of anomalous electronic and magnetic properties, despite the rather simple rock-salt structure. At low temperature, CeSb becomes antiferromagnetic, and goes through a number of magnetic phases, all more simply described as a stacking of ferromagnetic (G7 ground state) and paramagnetic (G8 ground state) Ce planes along the four-fold axes of the high-temperature phase [1]. The magnetic moments point along the propagation vectors. The *Corresponding author. Tel.: +33-4762-0-7657; fax: +334762-07-688. E-mail address: [email protected] (A. Stunault).
long-range magnetic order is associated with a tetragonal distortion, and the Ce and Sb sites have the same tetragonal symmetry. The different Ce ground states lead to different interatomic distances, and different 4f orbital distributions, at the origin of superstructure diffraction satellites. Both the lattice modulation [2], and the modulation of the 4f electron orbital states [3] have been demonstrated by X-ray scattering experiments. The magnetic properties of CeSb have been accounted for by the existence of strong p–f mixing [4]: the valence p electrons (mainly from the pnictide, Sb), hybridize strongly with the Ce 4f electrons, leading to a reduction of the crystal field splitting, an extremely large magnetic anisotropy, and the peculiar sequence of low temperature antiferromagnetic phases.
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.11.024
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
75
To get a better insight of the role of the cerium and antimony ions in the long-range magnetic order, we present a resonant X-ray magnetic study of CeSb at the Ce and Sb L edges.
For satellites of the (0 0 2) and (0 0 4) reflections, vanishing intensity for domains propagating in the (h k 0) plane is consistent with longitudinal lattice modulation, Q and u being almost perpendicular.
2. Experiments
4. Cerium L edges
The experiments were performed at the ID20 beamline of the ESRF. The sample was a 4 4 2 mm3 crystal, with the surface a cleaved (0 0 1) plane, and mounted in a displex cryostat with the (1 1 0) and (0 0 1) directions in the vertical scattering plane when all angles were set to zero. The whole study was performed at 12 K, the lowest reachable temperature. At this temperature, the magnetic structure was frozen in the AFP3 antiferro-para-magnetic phase [1], with a propagation vector tm =(0 0 4/7) corresponding to a (mmkkm0kmmkkm0k) stacking sequence. The associated lattice modulation has a propagation vector tc =(0 0 2/7) [3]. With these propagation vectors, first-order magnetic satellites sit at the same position as the second-order lattice distortion ðtm ¼ 2tc Þ; while first-order charge satellites are located at the third-order magnetic satellites positions ðtc ¼ 2 3tm Þ:
At the Ce L2 and L3 edges, we used a LiF(2 2 0) crystal to analyze the polarization. The results at both edges are qualitatively similar and we show here only the results at the L2 edge, where the intensities strongest, due to reduced absorption by the kapton and beryllium windows along the beam path. We present here only the data at the L2 edge. Fig. 1 shows the data obtained at the (0 4/7 4) and (0 2/7 4) positions in both the s–s and s–p polarization channels. s and p represent the components of the X-ray beam polarization perpendicular and parallel to the scattering plane, respectively. Strong resonances of similar line shape are observed at both positions in the s–p channel, with a maximum 2.5 eV above the edge. The position relatively to the absorption edge shows that this resonance is mainly dipole (2p–5d) [5]. The intensity reaches 11 000 counts/s at the (0 4/7 4) reflection, and is about 10 times weaker at the (0 2/7 4), which mainly reflects the ratio of the magnetic structure factors. In the s–s channel, at the (0 4/7 4) position, the resonance peaks at an energy 3 eV below the edge and is of purely quadrupole origin (2p–4f), as expected from the resonant scattering cross sections [6]. The non-zero background is the nonresonant lattice modulation intensity. At the (0 2/7 4) in s–s; the signal is dominated by the lattice modulation, with a dip reflecting the variation of the absorption through the edge. Similar measurements performed at positions corresponding to the other two domains (along a and c), show weaker intensities, especially along c, as a signature of less populated domains.
3. Non-resonant scattering At a photon energy of 7.84 keV, away from all Ce and Sb absorption edges, a scan along c shows satellites at positions (0 0 472/7), and (0 0 474/7), similarly to the results in [2]. Polarization analysis of the scattered beam, using the (0 0 6) reflection of a pyrolitic graphite crystal shows that the polarization is un-rotated and confirms that these satellites arise from charge scattering and reflect lattice modulations. We could not observe satellites from the other two domains propagating in the [a, b] plane (surface of the crystal) although these domains, with moments in the plane, are expected to be more populated. This can be explained by the direction of the lattice modulation: the scattering amplitude is given by Q . u, where Q is the scattering wave vector and u represents the direction of the lattice modulation.
5. Antimony L edges At the Sb L edges, the polarization was analyzed using an Al(2 0 0) crystal. By analogy with
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
76 12000
(0 4/7 4) σ−π
10000 8000 6000 4000 2000 0 (0 4/7 4) σ−σ
160 140 120 100 80
Intensity (cts/s/200mA)
60 1200
(0 2/7 4) σ−π
1000 800 600 400 200 0 (0 2/7 4) σ−σ
550 500 450 400 350 300
10000 9000 8000 7000 6000 5000 4000 3000 6.150
6.155
6.160 6.165 Energy (keV)
6.170
6.175
Fig. 1. (0 2/7 4) and (0 4/7 4) satellites at the Ce L2 edge. The data are obtained by scanning the energy while keeping the scattering vector constant (fixed Q scans). The bottom panel shows the measured fluorescence. The vertical line marks the position of the absorption edge.
Fig. 2. Fixed Q energy scans at the (0 2/7 4) and (0 4/7 4) satellites at the Sb L1 edge. The vertical line marks the position of the absorption edge. The scale for the integrated intensities has been chosen to reflect approximately to the measured peak intensities in counts/second.
observations in the 5f compounds UAs and UGa3, where a strong dipole resonance was observed at the K edge (1s–4p) [7], we first concentrated on the L1 edge (Fig. 2).
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
In the s–p channel, a double dipole (2s–5p) resonance is observed for both the (0 2/7 2) and (0 4/7 2) reflections, with two maxima, at the edge and 2.5 eV above the edge, respectively. However, the intensity is only seven times weaker at the (0 2/7 2) reflection than at the (0 4/7 2), which is less than expected from the magnetic structure factors. In s–s dipole resonant intensities are observed above the non-resonant charge. Leakage only from the s–p channel (E3% due to the imperfect selection of the polarization by the analyzer) cannot account for the observed resonance. Moreover, the resonant intensity is higher at the (0 2/7 2). The dipole resonance in the s–s channel cannot be of magnetic origin [6] but must be rather related to anisotropy in the 4p Sb charge distribution, leading to Templeton scattering [8]. In s–p; the stronger intensity at (0 4/7 2) points to a magnetic origin, although contribution from the charge distribution is not excluded. Only careful evaluation of the absorption and study of other satellites and of the azimuthal dependence will allow the separation of both effects. We checked that the resonant intensities vanish at the same temperature as either the non-resonant signal, or the Ce L edge resonances, confirming the connection to the Ce long-range magnetic order. Finally, we observed a much weaker resonance in s–p (E1 count/s at the (0 4/7 2) position) at the L3 edge, but not at the L2 edge.
77
6. Conclusion The present experimental results show that, in compounds where the cerium moment is saturated, resonant X-ray scattering experiments may be easily feasible, with strong resonant intensities. The main result however is the observation of a resonance at the antimony L1 edge, both in s–s and s–p: The s–p dipole resonance can be at least partially attributed to the induced spin polarization of the Sb p-electrons, like UAs and UGa3 [7], which supports the model of strong p–f hybridization in CeSb. The s–s resonance unambiguously reflects the anisotropy of the 4p charge distribution.
References [1] J. Rossat-Mignod, et al., J. Magn. Magn. Mat. 31–34 (1983) 398. [2] D.F. McMorrow, et al., J. Phys.: Condens. Matter 9 (1997) 1133; Iwasa, et al., Physica B 281–282 (2000) 437. [3] K. Iwasa, et al., Phys. Rev. Lett. 88 (2002) 207201. [4] H. Takahashi, et al., J. Phys. C 18 (1985) 2697; H. Kitazawa, et al., J. Magn. Magn. Mat. 31–34 (1983) 421. [5] A. Stunault, et al., Phys. Rev. B 65 (2002) 064436. [6] J.P. Hannon, et al., Phys. Rev. Lett. 61 (1988) 1245. [7] D. Mannix, et al., Phys. Rev. Lett. 86 (2001) 4128. [8] D.H. Templeton, et al., Acta Crystallogr. A 36 (1980) 237.
Physica B 345 (2004) 74–77
p–f mixing in CeSb, studied by resonant X-ray scattering A. Stunaulta,*, C. Vettiera, L.P. Regnaultb, F. de Bergevinc, L. Paolasinic, J.Y. Henryb a
Institut Laue Langevin, 6 rue Jules Horowitz, BP 156X, F-38042 Grenoble, Cedex, France b CEA-Grenoble, DRFMC/SPSMS/MDN, F-38054 Grenoble, Cedex 9, France c ESRF, BP 220, F-38043 Grenoble, Cedex, France
Abstract X-ray magnetic scattering experiments have been performed in CeSb at the Ce and Sb L edges. In the non-resonant regime, we observe charge satellites reflecting the lattice modulation associated with the periodicity of paramagnetic G8 planes. At the Ce L2 edge we observe strong magnetic resonances, due to the antiferromagnetic stacking of the ferromagnetic G7 : The study at the Sb L1 edge shows a magnetic dipole resonance, which supports the model of strong p–f mixing, used to explain the origin of the long-range magnetic order of CeSb. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Gg; 71.27.+a; 78.70.Ck Keywords: Cerium; p–f mixing; Resonant magnetic X-ray scattering
1. Introduction CeSb stands at the borderline between welllocalized and itinerant f-electron systems, and presents a fascinating variety of anomalous electronic and magnetic properties, despite the rather simple rock-salt structure. At low temperature, CeSb becomes antiferromagnetic, and goes through a number of magnetic phases, all more simply described as a stacking of ferromagnetic (G7 ground state) and paramagnetic (G8 ground state) Ce planes along the four-fold axes of the high-temperature phase [1]. The magnetic moments point along the propagation vectors. The *Corresponding author. Tel.: +33-4762-0-7657; fax: +334762-07-688. E-mail address: [email protected] (A. Stunault).
long-range magnetic order is associated with a tetragonal distortion, and the Ce and Sb sites have the same tetragonal symmetry. The different Ce ground states lead to different interatomic distances, and different 4f orbital distributions, at the origin of superstructure diffraction satellites. Both the lattice modulation [2], and the modulation of the 4f electron orbital states [3] have been demonstrated by X-ray scattering experiments. The magnetic properties of CeSb have been accounted for by the existence of strong p–f mixing [4]: the valence p electrons (mainly from the pnictide, Sb), hybridize strongly with the Ce 4f electrons, leading to a reduction of the crystal field splitting, an extremely large magnetic anisotropy, and the peculiar sequence of low temperature antiferromagnetic phases.
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.11.024
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
75
To get a better insight of the role of the cerium and antimony ions in the long-range magnetic order, we present a resonant X-ray magnetic study of CeSb at the Ce and Sb L edges.
For satellites of the (0 0 2) and (0 0 4) reflections, vanishing intensity for domains propagating in the (h k 0) plane is consistent with longitudinal lattice modulation, Q and u being almost perpendicular.
2. Experiments
4. Cerium L edges
The experiments were performed at the ID20 beamline of the ESRF. The sample was a 4 4 2 mm3 crystal, with the surface a cleaved (0 0 1) plane, and mounted in a displex cryostat with the (1 1 0) and (0 0 1) directions in the vertical scattering plane when all angles were set to zero. The whole study was performed at 12 K, the lowest reachable temperature. At this temperature, the magnetic structure was frozen in the AFP3 antiferro-para-magnetic phase [1], with a propagation vector tm =(0 0 4/7) corresponding to a (mmkkm0kmmkkm0k) stacking sequence. The associated lattice modulation has a propagation vector tc =(0 0 2/7) [3]. With these propagation vectors, first-order magnetic satellites sit at the same position as the second-order lattice distortion ðtm ¼ 2tc Þ; while first-order charge satellites are located at the third-order magnetic satellites positions ðtc ¼ 2 3tm Þ:
At the Ce L2 and L3 edges, we used a LiF(2 2 0) crystal to analyze the polarization. The results at both edges are qualitatively similar and we show here only the results at the L2 edge, where the intensities strongest, due to reduced absorption by the kapton and beryllium windows along the beam path. We present here only the data at the L2 edge. Fig. 1 shows the data obtained at the (0 4/7 4) and (0 2/7 4) positions in both the s–s and s–p polarization channels. s and p represent the components of the X-ray beam polarization perpendicular and parallel to the scattering plane, respectively. Strong resonances of similar line shape are observed at both positions in the s–p channel, with a maximum 2.5 eV above the edge. The position relatively to the absorption edge shows that this resonance is mainly dipole (2p–5d) [5]. The intensity reaches 11 000 counts/s at the (0 4/7 4) reflection, and is about 10 times weaker at the (0 2/7 4), which mainly reflects the ratio of the magnetic structure factors. In the s–s channel, at the (0 4/7 4) position, the resonance peaks at an energy 3 eV below the edge and is of purely quadrupole origin (2p–4f), as expected from the resonant scattering cross sections [6]. The non-zero background is the nonresonant lattice modulation intensity. At the (0 2/7 4) in s–s; the signal is dominated by the lattice modulation, with a dip reflecting the variation of the absorption through the edge. Similar measurements performed at positions corresponding to the other two domains (along a and c), show weaker intensities, especially along c, as a signature of less populated domains.
3. Non-resonant scattering At a photon energy of 7.84 keV, away from all Ce and Sb absorption edges, a scan along c shows satellites at positions (0 0 472/7), and (0 0 474/7), similarly to the results in [2]. Polarization analysis of the scattered beam, using the (0 0 6) reflection of a pyrolitic graphite crystal shows that the polarization is un-rotated and confirms that these satellites arise from charge scattering and reflect lattice modulations. We could not observe satellites from the other two domains propagating in the [a, b] plane (surface of the crystal) although these domains, with moments in the plane, are expected to be more populated. This can be explained by the direction of the lattice modulation: the scattering amplitude is given by Q . u, where Q is the scattering wave vector and u represents the direction of the lattice modulation.
5. Antimony L edges At the Sb L edges, the polarization was analyzed using an Al(2 0 0) crystal. By analogy with
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
76 12000
(0 4/7 4) σ−π
10000 8000 6000 4000 2000 0 (0 4/7 4) σ−σ
160 140 120 100 80
Intensity (cts/s/200mA)
60 1200
(0 2/7 4) σ−π
1000 800 600 400 200 0 (0 2/7 4) σ−σ
550 500 450 400 350 300
10000 9000 8000 7000 6000 5000 4000 3000 6.150
6.155
6.160 6.165 Energy (keV)
6.170
6.175
Fig. 1. (0 2/7 4) and (0 4/7 4) satellites at the Ce L2 edge. The data are obtained by scanning the energy while keeping the scattering vector constant (fixed Q scans). The bottom panel shows the measured fluorescence. The vertical line marks the position of the absorption edge.
Fig. 2. Fixed Q energy scans at the (0 2/7 4) and (0 4/7 4) satellites at the Sb L1 edge. The vertical line marks the position of the absorption edge. The scale for the integrated intensities has been chosen to reflect approximately to the measured peak intensities in counts/second.
observations in the 5f compounds UAs and UGa3, where a strong dipole resonance was observed at the K edge (1s–4p) [7], we first concentrated on the L1 edge (Fig. 2).
ARTICLE IN PRESS A. Stunault et al. / Physica B 345 (2004) 74–77
In the s–p channel, a double dipole (2s–5p) resonance is observed for both the (0 2/7 2) and (0 4/7 2) reflections, with two maxima, at the edge and 2.5 eV above the edge, respectively. However, the intensity is only seven times weaker at the (0 2/7 2) reflection than at the (0 4/7 2), which is less than expected from the magnetic structure factors. In s–s dipole resonant intensities are observed above the non-resonant charge. Leakage only from the s–p channel (E3% due to the imperfect selection of the polarization by the analyzer) cannot account for the observed resonance. Moreover, the resonant intensity is higher at the (0 2/7 2). The dipole resonance in the s–s channel cannot be of magnetic origin [6] but must be rather related to anisotropy in the 4p Sb charge distribution, leading to Templeton scattering [8]. In s–p; the stronger intensity at (0 4/7 2) points to a magnetic origin, although contribution from the charge distribution is not excluded. Only careful evaluation of the absorption and study of other satellites and of the azimuthal dependence will allow the separation of both effects. We checked that the resonant intensities vanish at the same temperature as either the non-resonant signal, or the Ce L edge resonances, confirming the connection to the Ce long-range magnetic order. Finally, we observed a much weaker resonance in s–p (E1 count/s at the (0 4/7 2) position) at the L3 edge, but not at the L2 edge.
77
6. Conclusion The present experimental results show that, in compounds where the cerium moment is saturated, resonant X-ray scattering experiments may be easily feasible, with strong resonant intensities. The main result however is the observation of a resonance at the antimony L1 edge, both in s–s and s–p: The s–p dipole resonance can be at least partially attributed to the induced spin polarization of the Sb p-electrons, like UAs and UGa3 [7], which supports the model of strong p–f hybridization in CeSb. The s–s resonance unambiguously reflects the anisotropy of the 4p charge distribution.
References [1] J. Rossat-Mignod, et al., J. Magn. Magn. Mat. 31–34 (1983) 398. [2] D.F. McMorrow, et al., J. Phys.: Condens. Matter 9 (1997) 1133; Iwasa, et al., Physica B 281–282 (2000) 437. [3] K. Iwasa, et al., Phys. Rev. Lett. 88 (2002) 207201. [4] H. Takahashi, et al., J. Phys. C 18 (1985) 2697; H. Kitazawa, et al., J. Magn. Magn. Mat. 31–34 (1983) 421. [5] A. Stunault, et al., Phys. Rev. B 65 (2002) 064436. [6] J.P. Hannon, et al., Phys. Rev. Lett. 61 (1988) 1245. [7] D. Mannix, et al., Phys. Rev. Lett. 86 (2001) 4128. [8] D.H. Templeton, et al., Acta Crystallogr. A 36 (1980) 237.