- Email: [email protected]
Synchrotron X-ray magnetic scattering
Nuclear Instruments and Methods in Physics Research B 199 (2003) 295–300 www.elsevier.com/locate/nimb
Synchrotron X-ray magnetic scattering W.G. Stirling
*
European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble Cedex 09, France
Abstract Research on magnetic materials constitutes an increasingly important part of the programmes of most major synchrotron radiation centres. The extremely high brilliance and small spot size of advanced synchrotron beamlines, combined with element-specific resonant effects at certain absorption edges, provide a powerful probe of magnetic structures and phase transitions, with excellent wavevector resolution. Over the last decade a variety of experimental techniques have been developed, exploiting these effects for the study of thin film, multilayer and bulk magnetic materials. In this paper the basic concepts of X-ray magnetic scattering will be introduced, followed by recent examples taken from work at Daresbury Laboratory (UK), the European Synchrotron Radiation Facility (Grenoble, France) and the National Synchrotron Light Source (Brookhaven National Laboratory, USA). Investigations of domain patterns in thin magnetic films employing X-ray resonant magnetic scattering (XRMS) will be described, followed by a series of examples of XRMS studies of actinide (U, Np, Pu) magnetic materials. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 75.25.+z; 75.50.Ee; 75.60.Ch; 78.70.Ck Keywords: Magnetic materials; Resonant scattering; Actinides
1. Introduction Over the last 20 years synchrotron X-ray magnetic scattering has grown from a scientific curiosity to become a routine technique for the investigation of magnetism and magnetic materials. A number of experimental techniques have been developed. These can be grouped broadly into two classes – those based on spin-dependent absorption and those exploiting the spin-dependent X-ray scattering cross-section. Of course, the underlying physics of the two processes is very closely related; while the former is a wavevector Q ¼ 0 method, the latter also provides information as a *
Tel.: +33-476-88-20-30; fax: +33-476-88-24-18. E-mail address: [email protected] (W.G. Stirling).
function of Q. Lovesey and Collins have summarised both theory and practice in their book published in 1996 [1]. For recent reviews see [2,3]. It is worth noting the form of the spin-dependent scattering cross-section, following Blume and Gibbs [4,5]: d2 r ¼ dX0 dE0 k!k0 ;a!b + 2 2 * X e iK:rj b e a ^e:^e0 mc2 j * +2 ihx X iK:rj iK pj 2 b e :A þ sj :B a j mc hk 2 o Ea Eb ðhx0k hxÞ ; ð1Þ
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 5 8 9 - 6
296
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
where the symbols have their usual meanings, viz: 0
k, k e, e0 hx, hx 0 K j pj , s j a, b A, B
incident, scattered photon wavevectors incident, scattered photon polarizations incident, scattered photon energies momentum transfer ðk k0 Þ labels electrons electron momentum, electron spin initial and final states of the scatterer matrices depending on the incident and scattered polarizations
From Eq. (1), where the first term describes the Thomson charge scattering, it can be seen that by judicious choice of the experimental conditions (polarizations, geometry), the spin (S) and orbital (L) contributions to the total magnetization density can be separated and isolated. This is a particular strength of magnetic photon scattering; the separation of S and L is not possible by neutron scattering. It is also evident from Eq. (1) that the magnetic component of X-ray scattering will normally be very weak since the pre-factor ( hx=mc2 ) of the 2 second term is only of order 10 (for hx ¼ 10 keV), resulting in a 104 factor for the magnetic intensity compared to the charge scattering intensity. However, the discovery of resonant effects at particular absorption edges, by Gibbs and colleagues [6,7], has revolutionised the use of synchrotron X-rays in the study of magnetic structures and phase transitions. X-ray resonant magnetic scattering (XRMS) enhancements are particularly marked at the L edges of lanthanides ( 102 ) and the M edges of actinides (enhancements of up to 106 –107 ). XRMS is now a routine experimental technique for the investigation of magnetic materials (particularly antiferromagnets (AF) where magnetic and charge scattering are separated in reciprocal space) and has several distinguishing features, notably that it provides an element specific probe, with excellent wavevector resolution, of very small (mg ! lg) samples. In Sections 2 and 3 we describe recent examples of the use of XRMS. 2. Perpendicular magnetic anisotropy and closure domains of FePd thin flims As well as studies of fundamental magnetism (such as spin arrangements at the atomic level, to
be dealt with below), XRMS has important applications to more ‘‘applied’’ magnetism. The development and understanding of thin films and multilayers displaying perpendicular magnetic anisotropy (PMA) is one such field. Dudzik et al. [8] have investigated FePd thin films exhibiting different degrees of PMA. These samples, consisting of FePd on a MgO subof approximately 400 A ) Pd layer, were strate, capped with a thin ( 20 A grown by MBE. Striped domains of width 0.09 lm (magnetisation "#"#"# perpendicular to the film plane) arise from the competition between the PMA and the shape anisotropy. In order to reduce the strong magnetic flux at the surface, then, closure domains form, resulting in a "!# "!# " magnetisation configuration of closed magnetic loops. These closure domains are not simple to observe and study by conventional techniques. However, XRMS can be used to investigate such magnetic structures and Dudzik et al. have used this method to make magnetic depth profiling measurements of their FePd films. The measurements were made at the Daresbury Laboratory (SRS stations 5U1 and 1.1) and at the ESRF (beamlines ID12A and B). Throughout, relatively ‘‘soft’’ X-ray energies were employed to exploit the resonances at the Fe and Pd L3 edges (0.709 and 3.17 keV, respectively). The existence of closure domains in the samples with low degrees of PMA was demonstrated in two ways. First, as shown by D€ urr et al. [9], magnetic satellites which show circular dichroism (with a change of sign from one side of the specular peak to the other) arise from chiral magnetic structures. This effect was observed for the low-PMA samples [8] as shown by the transverse ðqx; qyÞ scans of Fig. 1 (geometry B). ‘‘Geometry A’’ is the conventional h–2h reflectivity mode with the striped domains (in-sample-plane) perpendicular to the scattering plane, whereas the stripes were parallel to the scattering plane in geometry B. The lack of dichroism in geometry A is in accord with considerations of the scattering cross-section. The second evidence of closure domains was obtained from (geometry A) scans along the qz direction (‘‘magnetic rod’’ scans). The intensity profiles exhibited ‘‘shoulders’’, consistent with calculated lineshapes including closure domains.
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
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3.1. U(AsSe) solid solutions The rock-salt structure UX compounds, where X is a pnictide or chalcogenide, assume a fascinating range of magnetic structures (ferromagnetic, antiferromagnetic, incommensurate), with examples of single k, 2k and 3k structures [10]. Longfield et al. [11,12] have used XRMS at the U MIV edge (3.73 keV) to investigate the U(As1x Sex ) series of solid solutions, using beamlines ID20 and BM28 at the ESRF. UAs is a type I 1k antiferromagnet (TN ¼ 127 K), exhibiting a second phase transition to a type Ia 2k structure at 64 K. USe is
Fig. 1. Scans transverse to the specular peak for two different FePd film [8]. geometries (described in the text) for a 400 A Magnetic satellite peaks are seen, with X-ray circular dichroism in geometry B. Solid (dotted) line: right (left) circularly polarized radiation.
However, for the high-PMA sample no such feature was observed. The work of Dudzik et al. [8] has shown that the degree of PMA strongly influences the formation of closure domains at the surface of magnetic thin films. In addition, XRMS has been shown to be a powerful tool for studies of these effects.
3. Actinide magnetic structures and phase transitions Actinide (U, Np, Pu) magnetism has been a particularly lively area of XRMS research due to the very large M-edge resonances (see Section 1) and the sustained interest in the great variety of magnetic configurations arising from the 5f interactions. Here we describe briefly three recent investigations exemplifying the use of XRMS techniques.
Fig. 2. XRMS data [11] at the incommensurate to commensurate phase transition of UAs0:8 Se0:2 .
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W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
a [1 1 1] easy-axis ferromagnet with Tc ¼ 160 K. Doping UAs with Se produces a series of commensurate and incommensurate magnetic structures [13]. Fig. 2 exemplifies the structural information that can be obtained using XRMS. Close to TN (125 K for UAs0:8 Se0:2 ), the magnetic structure is AF incommensurate, with a transition to a commensurate (k ¼ 0:5) state at lower temperatures. At even lower temperatures in the commensurate phase, a further change is observed. Fig. 3 shows the variation with temperature of the magnetic intensity at specular ð0; 0; 2 þ kÞ and off-specular ðk; 0; 2Þ wavevectors. The X-ray cross-section is such that different AF domains are sampled at these two wavevectors. The change observed at and below 60 K may be understood as a change from a 3k to a 2k commensurate structure. Thus XRMS can provide very detailed information on subtle changes of magnetic structure and domain population. In parallel with magnetic diffraction measurements it is often instructive to consider corresponding changes to the lattice structure. Fig. 4 shows how the ð0; 0; 6Þ lattice reflection changes with temperature. In the paramagnetic phase and the AF phase down to 60 K there is a single charge peak. This splits along the c direction, reflecting the onset of a cubic to tetragonal distor-
Fig. 3. Integrated intensity as a function of temperature of specular (closed circles) ð0; 0; 2 þ kÞ and off-specular (opencircles) magnetic satellites ðk; 0; 2Þ of UAs0:8 Se0:2 [11].
tion of magnitude ðc aÞ=c 2:3 104 . This lattice distortion accompanies the magnetic transition discussed above (cf. Fig. 3); this ‘‘new’’ magnetic phase for T < 60 K and x 0:2 had not been observed in previous neutron diffraction measurements [13]. 3.2. (UNp)Ru2 Si2 solid solutions Other interesting studies of solid solutions have been made in which the magnetic cations are substituted, changing the 5f electron count. Here, we
Fig. 4. (a) Temperature variation of the ð0; 0; 6Þ lattice Bragg peak of UAs0:82 Se0:18 [11]. (b) Contour map of ð0; 0; 6Þ at 12 K [11].
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
consider two recent investigations involving substitution of U by Np and Pu. The heavy fermion superconductor URu2 Si2 orders antiferromagnetically at 17.5 K with the moments lying along the c-axis and with propagation wavevector ð0; 0; 1Þ [14]. While normal uranium materials have moments of typically 1 lB , URu2 Si2 exhibits an ordered moment of only 0.02 lB , giving rise to speculation as to the true nature of the ordering process. Since Np and U have about the same ionic radius it is possible to substitute the U with
299
Np to produce the U1x Npx Ru2 Si2 series of solid solutions. These materials have TN 20–25 K with an almost constant moment of 1.5–1.6 lB . XRMS has been used by Lidstr€ om et al. [15] to study the development of the U and Np moments separately in members of this series. As Fig. 5 demonstrates, the X-ray technique permits this separation by working with the X-ray energy appropriate for the particular element being considered. It is by no means simple to relate the resonance intensities to the corresponding magnetic moments. Nevertheless, Lidstr€ om et al. [15] have extracted the moments for the x ¼ 0:5 sample, assuming U4þ and Np3þ ground states, and estimate a U moment of about 0.3 lB , at least an order of magnitude larger than that of URu2 Si2 . 3.3. (PuU)Sb solid solutions A combination of neutron and X-ray diffraction has been used very recently to probe the structures of (Pux U1x )Sb solid solutions [16]. The former
Fig. 5. XRMS spectra for NpRu2 Si2 and Np0:5 U0:5 Ru2 Si2 [15]. The full line is a model fit involving a superposition of Lorentzian functions at the different resonances.
Fig. 6. XRMS data for Pu0:75 U0:25 Sb [16] at the Pu (closed symbols) and U (open symbols) MIV edges. (a) Magnetic satellite ð0; 0:25; 2Þ; note the logarithmic intensity scale. (b) Integrated intensities, normalized at 20 K.
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technique has established the ordering wavevector (e.g. k ¼ 1 for x ¼ 0:25 and k ¼ 0:25 for x ¼ 0:75), the average moment, and the temperature dependence of the moment. XRMS was used to examine the range of the ordering process and to follow the ordering separately at the two magnetic ion sites. Fig. 6(a) presents magnetic satellite data for Pu0:75 U0:25 Sb (x ¼ 0:75). These peaks have widths much larger than that of the instrumental resolution and correspond to correlation lengths of 400– . So, even at 0.1 TN , the ordering is not 500 A truly long-range. The development of the magnetic ordering (magnetic moment) is shown in Fig. 6(b). There is a discontinuity at about 55 K ðT 0 Þ which was identified as a 3k to 1k transition, also seen in susceptibility measurements. Note also the slower development of the Pu ordered moment. 4. Conclusions In this brief and limited review some examples of recent XRMS work have been summarised. The technique has many possible applications to ‘‘pure’’ and ‘‘applied’’ magnetic materials, often together with other magnetic measurement techniques (susceptibility, neutron scattering, etc.). With the continued expansion of the number of synchrotron sources world-wide, we can confidently expect a steady increase in the range of applications of X-ray techniques to the study of magnetic materials. Acknowledgements Many colleagues contributed to the work described in this article. In particular, I wish to thank Profs. G.H. Lander and M.J. Cooper for their collaboration over many years of investigation of magnetic materials. I am grateful to Drs. Longfield, Mannix, Normile and Dhesi for their advice
and support. The support and advice of staff at SRS, ESRF and NSLS is gratefully acknowledged.
References [1] S.W. Lovesey, S.P. Collins, X-ray Scattering and Absorption by Magnetic Materials, Oxford Science Publications, 1996. [2] W.G. Stirling, M.J. Cooper, J. Magn. Magn. Mater. 200 (1999) 755. [3] Synchrotron Radiation News, 14 (5) (2001). [4] M. Blume, J. Appl. Phys. 57 (1985) 3615. [5] M. Blume, D. Gibbs, Phys. Rev. B 37 (1988) 1779. [6] D. Gibbs, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. Lett. 61 (1988) 1241. [7] D. Gibbs, G. Gr€ ubel, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. B 43 (1991) 5663. [8] E. Dudzik, S.S. Dhesi, H.A. D€ urr, S.P. Collins, M.D. Roper, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, Phys. Rev. B 62 (2000) 5779. [9] H.A. D€ urr, E. Dudzik, S.S. Dhesi, J.B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Mocuta, A. Marty, Y. Samson, Science 284 (1999) 2166. [10] J. Rossat-Mignod, G.H. Lander, P. Burlet, Handbook on the Physics and Chemistry of the Actinides, NorthHolland, Amsterdam, Vol. 1, 1984, p. 415. [11] M.J. Longfield, W.G. Stirling, E. Lidstr€ om, D. Mannix, G.H. Lander, A. Stunault, G.J. McIntyre, K. Mattenberger, O. Vogt, Phys. Rev. B 63 (2001) 134401-1. [12] M.J. Longfield, W.G. Stirling, G.H. Lander, Phys. Rev. B 63 (2001) 134402-1. [13] M. Kuznietz, P. Burlet, J. Rossat-Mignod, O. Vogt, J. Magn. Magn. Mater. 69 (1987) 12. [14] B. F ak, C. Vettier, J. Flouquet, F. Bourdarot, S. Raymond, A. Verniere, P. Lejay, P. Boutouille, N.R. Bernhoeft, S.T. Bramwell, R.A. Fischer, N.E. Phillips, J. Magn. Magn. Mater. 154 (1996) 339. [15] E. Lidstr€ om, D. Mannix, A. Hiess, J. Rebizant, F. Wastin, G.H. Lander, I. Marri, P. Carra, C. Vettier, M.J. Longfield, Phys. Rev. B 61 (2000) 1375. [16] P.S. Normile, W.G. Stirling, D. Mannix, G.H. Lander, F. Wastin, J. Rebizant, F. Bourdarot, P. Burlet, B. Lebech, S. Coburn, Phys. Rev. B 66 (2002) 014405; P.S. Normile, W.G. Stirling, D. Mannix, G.H. Lander, F. Wastin, J. Rebizant, S. Coburn, Phys. Rev. B 66 (2002) 014406.
Synchrotron X-ray magnetic scattering W.G. Stirling
*
European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble Cedex 09, France
Abstract Research on magnetic materials constitutes an increasingly important part of the programmes of most major synchrotron radiation centres. The extremely high brilliance and small spot size of advanced synchrotron beamlines, combined with element-specific resonant effects at certain absorption edges, provide a powerful probe of magnetic structures and phase transitions, with excellent wavevector resolution. Over the last decade a variety of experimental techniques have been developed, exploiting these effects for the study of thin film, multilayer and bulk magnetic materials. In this paper the basic concepts of X-ray magnetic scattering will be introduced, followed by recent examples taken from work at Daresbury Laboratory (UK), the European Synchrotron Radiation Facility (Grenoble, France) and the National Synchrotron Light Source (Brookhaven National Laboratory, USA). Investigations of domain patterns in thin magnetic films employing X-ray resonant magnetic scattering (XRMS) will be described, followed by a series of examples of XRMS studies of actinide (U, Np, Pu) magnetic materials. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 75.25.+z; 75.50.Ee; 75.60.Ch; 78.70.Ck Keywords: Magnetic materials; Resonant scattering; Actinides
1. Introduction Over the last 20 years synchrotron X-ray magnetic scattering has grown from a scientific curiosity to become a routine technique for the investigation of magnetism and magnetic materials. A number of experimental techniques have been developed. These can be grouped broadly into two classes – those based on spin-dependent absorption and those exploiting the spin-dependent X-ray scattering cross-section. Of course, the underlying physics of the two processes is very closely related; while the former is a wavevector Q ¼ 0 method, the latter also provides information as a *
Tel.: +33-476-88-20-30; fax: +33-476-88-24-18. E-mail address: [email protected] (W.G. Stirling).
function of Q. Lovesey and Collins have summarised both theory and practice in their book published in 1996 [1]. For recent reviews see [2,3]. It is worth noting the form of the spin-dependent scattering cross-section, following Blume and Gibbs [4,5]: d2 r ¼ dX0 dE0 k!k0 ;a!b + 2 2 * X e iK:rj b e a ^e:^e0 mc2 j * +2 ihx X iK:rj iK pj 2 b e :A þ sj :B a j mc hk 2 o Ea Eb ðhx0k hxÞ ; ð1Þ
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 5 8 9 - 6
296
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
where the symbols have their usual meanings, viz: 0
k, k e, e0 hx, hx 0 K j pj , s j a, b A, B
incident, scattered photon wavevectors incident, scattered photon polarizations incident, scattered photon energies momentum transfer ðk k0 Þ labels electrons electron momentum, electron spin initial and final states of the scatterer matrices depending on the incident and scattered polarizations
From Eq. (1), where the first term describes the Thomson charge scattering, it can be seen that by judicious choice of the experimental conditions (polarizations, geometry), the spin (S) and orbital (L) contributions to the total magnetization density can be separated and isolated. This is a particular strength of magnetic photon scattering; the separation of S and L is not possible by neutron scattering. It is also evident from Eq. (1) that the magnetic component of X-ray scattering will normally be very weak since the pre-factor ( hx=mc2 ) of the 2 second term is only of order 10 (for hx ¼ 10 keV), resulting in a 104 factor for the magnetic intensity compared to the charge scattering intensity. However, the discovery of resonant effects at particular absorption edges, by Gibbs and colleagues [6,7], has revolutionised the use of synchrotron X-rays in the study of magnetic structures and phase transitions. X-ray resonant magnetic scattering (XRMS) enhancements are particularly marked at the L edges of lanthanides ( 102 ) and the M edges of actinides (enhancements of up to 106 –107 ). XRMS is now a routine experimental technique for the investigation of magnetic materials (particularly antiferromagnets (AF) where magnetic and charge scattering are separated in reciprocal space) and has several distinguishing features, notably that it provides an element specific probe, with excellent wavevector resolution, of very small (mg ! lg) samples. In Sections 2 and 3 we describe recent examples of the use of XRMS. 2. Perpendicular magnetic anisotropy and closure domains of FePd thin flims As well as studies of fundamental magnetism (such as spin arrangements at the atomic level, to
be dealt with below), XRMS has important applications to more ‘‘applied’’ magnetism. The development and understanding of thin films and multilayers displaying perpendicular magnetic anisotropy (PMA) is one such field. Dudzik et al. [8] have investigated FePd thin films exhibiting different degrees of PMA. These samples, consisting of FePd on a MgO subof approximately 400 A ) Pd layer, were strate, capped with a thin ( 20 A grown by MBE. Striped domains of width 0.09 lm (magnetisation "#"#"# perpendicular to the film plane) arise from the competition between the PMA and the shape anisotropy. In order to reduce the strong magnetic flux at the surface, then, closure domains form, resulting in a "!# "!# " magnetisation configuration of closed magnetic loops. These closure domains are not simple to observe and study by conventional techniques. However, XRMS can be used to investigate such magnetic structures and Dudzik et al. have used this method to make magnetic depth profiling measurements of their FePd films. The measurements were made at the Daresbury Laboratory (SRS stations 5U1 and 1.1) and at the ESRF (beamlines ID12A and B). Throughout, relatively ‘‘soft’’ X-ray energies were employed to exploit the resonances at the Fe and Pd L3 edges (0.709 and 3.17 keV, respectively). The existence of closure domains in the samples with low degrees of PMA was demonstrated in two ways. First, as shown by D€ urr et al. [9], magnetic satellites which show circular dichroism (with a change of sign from one side of the specular peak to the other) arise from chiral magnetic structures. This effect was observed for the low-PMA samples [8] as shown by the transverse ðqx; qyÞ scans of Fig. 1 (geometry B). ‘‘Geometry A’’ is the conventional h–2h reflectivity mode with the striped domains (in-sample-plane) perpendicular to the scattering plane, whereas the stripes were parallel to the scattering plane in geometry B. The lack of dichroism in geometry A is in accord with considerations of the scattering cross-section. The second evidence of closure domains was obtained from (geometry A) scans along the qz direction (‘‘magnetic rod’’ scans). The intensity profiles exhibited ‘‘shoulders’’, consistent with calculated lineshapes including closure domains.
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
297
3.1. U(AsSe) solid solutions The rock-salt structure UX compounds, where X is a pnictide or chalcogenide, assume a fascinating range of magnetic structures (ferromagnetic, antiferromagnetic, incommensurate), with examples of single k, 2k and 3k structures [10]. Longfield et al. [11,12] have used XRMS at the U MIV edge (3.73 keV) to investigate the U(As1x Sex ) series of solid solutions, using beamlines ID20 and BM28 at the ESRF. UAs is a type I 1k antiferromagnet (TN ¼ 127 K), exhibiting a second phase transition to a type Ia 2k structure at 64 K. USe is
Fig. 1. Scans transverse to the specular peak for two different FePd film [8]. geometries (described in the text) for a 400 A Magnetic satellite peaks are seen, with X-ray circular dichroism in geometry B. Solid (dotted) line: right (left) circularly polarized radiation.
However, for the high-PMA sample no such feature was observed. The work of Dudzik et al. [8] has shown that the degree of PMA strongly influences the formation of closure domains at the surface of magnetic thin films. In addition, XRMS has been shown to be a powerful tool for studies of these effects.
3. Actinide magnetic structures and phase transitions Actinide (U, Np, Pu) magnetism has been a particularly lively area of XRMS research due to the very large M-edge resonances (see Section 1) and the sustained interest in the great variety of magnetic configurations arising from the 5f interactions. Here we describe briefly three recent investigations exemplifying the use of XRMS techniques.
Fig. 2. XRMS data [11] at the incommensurate to commensurate phase transition of UAs0:8 Se0:2 .
298
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
a [1 1 1] easy-axis ferromagnet with Tc ¼ 160 K. Doping UAs with Se produces a series of commensurate and incommensurate magnetic structures [13]. Fig. 2 exemplifies the structural information that can be obtained using XRMS. Close to TN (125 K for UAs0:8 Se0:2 ), the magnetic structure is AF incommensurate, with a transition to a commensurate (k ¼ 0:5) state at lower temperatures. At even lower temperatures in the commensurate phase, a further change is observed. Fig. 3 shows the variation with temperature of the magnetic intensity at specular ð0; 0; 2 þ kÞ and off-specular ðk; 0; 2Þ wavevectors. The X-ray cross-section is such that different AF domains are sampled at these two wavevectors. The change observed at and below 60 K may be understood as a change from a 3k to a 2k commensurate structure. Thus XRMS can provide very detailed information on subtle changes of magnetic structure and domain population. In parallel with magnetic diffraction measurements it is often instructive to consider corresponding changes to the lattice structure. Fig. 4 shows how the ð0; 0; 6Þ lattice reflection changes with temperature. In the paramagnetic phase and the AF phase down to 60 K there is a single charge peak. This splits along the c direction, reflecting the onset of a cubic to tetragonal distor-
Fig. 3. Integrated intensity as a function of temperature of specular (closed circles) ð0; 0; 2 þ kÞ and off-specular (opencircles) magnetic satellites ðk; 0; 2Þ of UAs0:8 Se0:2 [11].
tion of magnitude ðc aÞ=c 2:3 104 . This lattice distortion accompanies the magnetic transition discussed above (cf. Fig. 3); this ‘‘new’’ magnetic phase for T < 60 K and x 0:2 had not been observed in previous neutron diffraction measurements [13]. 3.2. (UNp)Ru2 Si2 solid solutions Other interesting studies of solid solutions have been made in which the magnetic cations are substituted, changing the 5f electron count. Here, we
Fig. 4. (a) Temperature variation of the ð0; 0; 6Þ lattice Bragg peak of UAs0:82 Se0:18 [11]. (b) Contour map of ð0; 0; 6Þ at 12 K [11].
W.G. Stirling / Nucl. Instr. and Meth. in Phys. Res. B 199 (2003) 295–300
consider two recent investigations involving substitution of U by Np and Pu. The heavy fermion superconductor URu2 Si2 orders antiferromagnetically at 17.5 K with the moments lying along the c-axis and with propagation wavevector ð0; 0; 1Þ [14]. While normal uranium materials have moments of typically 1 lB , URu2 Si2 exhibits an ordered moment of only 0.02 lB , giving rise to speculation as to the true nature of the ordering process. Since Np and U have about the same ionic radius it is possible to substitute the U with
299
Np to produce the U1x Npx Ru2 Si2 series of solid solutions. These materials have TN 20–25 K with an almost constant moment of 1.5–1.6 lB . XRMS has been used by Lidstr€ om et al. [15] to study the development of the U and Np moments separately in members of this series. As Fig. 5 demonstrates, the X-ray technique permits this separation by working with the X-ray energy appropriate for the particular element being considered. It is by no means simple to relate the resonance intensities to the corresponding magnetic moments. Nevertheless, Lidstr€ om et al. [15] have extracted the moments for the x ¼ 0:5 sample, assuming U4þ and Np3þ ground states, and estimate a U moment of about 0.3 lB , at least an order of magnitude larger than that of URu2 Si2 . 3.3. (PuU)Sb solid solutions A combination of neutron and X-ray diffraction has been used very recently to probe the structures of (Pux U1x )Sb solid solutions [16]. The former
Fig. 5. XRMS spectra for NpRu2 Si2 and Np0:5 U0:5 Ru2 Si2 [15]. The full line is a model fit involving a superposition of Lorentzian functions at the different resonances.
Fig. 6. XRMS data for Pu0:75 U0:25 Sb [16] at the Pu (closed symbols) and U (open symbols) MIV edges. (a) Magnetic satellite ð0; 0:25; 2Þ; note the logarithmic intensity scale. (b) Integrated intensities, normalized at 20 K.
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technique has established the ordering wavevector (e.g. k ¼ 1 for x ¼ 0:25 and k ¼ 0:25 for x ¼ 0:75), the average moment, and the temperature dependence of the moment. XRMS was used to examine the range of the ordering process and to follow the ordering separately at the two magnetic ion sites. Fig. 6(a) presents magnetic satellite data for Pu0:75 U0:25 Sb (x ¼ 0:75). These peaks have widths much larger than that of the instrumental resolution and correspond to correlation lengths of 400– . So, even at 0.1 TN , the ordering is not 500 A truly long-range. The development of the magnetic ordering (magnetic moment) is shown in Fig. 6(b). There is a discontinuity at about 55 K ðT 0 Þ which was identified as a 3k to 1k transition, also seen in susceptibility measurements. Note also the slower development of the Pu ordered moment. 4. Conclusions In this brief and limited review some examples of recent XRMS work have been summarised. The technique has many possible applications to ‘‘pure’’ and ‘‘applied’’ magnetic materials, often together with other magnetic measurement techniques (susceptibility, neutron scattering, etc.). With the continued expansion of the number of synchrotron sources world-wide, we can confidently expect a steady increase in the range of applications of X-ray techniques to the study of magnetic materials. Acknowledgements Many colleagues contributed to the work described in this article. In particular, I wish to thank Profs. G.H. Lander and M.J. Cooper for their collaboration over many years of investigation of magnetic materials. I am grateful to Drs. Longfield, Mannix, Normile and Dhesi for their advice
and support. The support and advice of staff at SRS, ESRF and NSLS is gratefully acknowledged.
References [1] S.W. Lovesey, S.P. Collins, X-ray Scattering and Absorption by Magnetic Materials, Oxford Science Publications, 1996. [2] W.G. Stirling, M.J. Cooper, J. Magn. Magn. Mater. 200 (1999) 755. [3] Synchrotron Radiation News, 14 (5) (2001). [4] M. Blume, J. Appl. Phys. 57 (1985) 3615. [5] M. Blume, D. Gibbs, Phys. Rev. B 37 (1988) 1779. [6] D. Gibbs, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. Lett. 61 (1988) 1241. [7] D. Gibbs, G. Gr€ ubel, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. B 43 (1991) 5663. [8] E. Dudzik, S.S. Dhesi, H.A. D€ urr, S.P. Collins, M.D. Roper, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, Phys. Rev. B 62 (2000) 5779. [9] H.A. D€ urr, E. Dudzik, S.S. Dhesi, J.B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Mocuta, A. Marty, Y. Samson, Science 284 (1999) 2166. [10] J. Rossat-Mignod, G.H. Lander, P. Burlet, Handbook on the Physics and Chemistry of the Actinides, NorthHolland, Amsterdam, Vol. 1, 1984, p. 415. [11] M.J. Longfield, W.G. Stirling, E. Lidstr€ om, D. Mannix, G.H. Lander, A. Stunault, G.J. McIntyre, K. Mattenberger, O. Vogt, Phys. Rev. B 63 (2001) 134401-1. [12] M.J. Longfield, W.G. Stirling, G.H. Lander, Phys. Rev. B 63 (2001) 134402-1. [13] M. Kuznietz, P. Burlet, J. Rossat-Mignod, O. Vogt, J. Magn. Magn. Mater. 69 (1987) 12. [14] B. F ak, C. Vettier, J. Flouquet, F. Bourdarot, S. Raymond, A. Verniere, P. Lejay, P. Boutouille, N.R. Bernhoeft, S.T. Bramwell, R.A. Fischer, N.E. Phillips, J. Magn. Magn. Mater. 154 (1996) 339. [15] E. Lidstr€ om, D. Mannix, A. Hiess, J. Rebizant, F. Wastin, G.H. Lander, I. Marri, P. Carra, C. Vettier, M.J. Longfield, Phys. Rev. B 61 (2000) 1375. [16] P.S. Normile, W.G. Stirling, D. Mannix, G.H. Lander, F. Wastin, J. Rebizant, F. Bourdarot, P. Burlet, B. Lebech, S. Coburn, Phys. Rev. B 66 (2002) 014405; P.S. Normile, W.G. Stirling, D. Mannix, G.H. Lander, F. Wastin, J. Rebizant, S. Coburn, Phys. Rev. B 66 (2002) 014406.