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Soft X-ray magnetic scattering from striped magnetic domain structures
Physica B 283 (2000) 171}174
Soft X-ray magnetic scattering from striped magnetic domain structures G. van der Laan *, E. Dudzik , S.P. Collins , S.S. Dhesi , H.A. DuK rr , M. Belakhovsky, K. Chesnel, A. Marty, Y. Samson, B. Gilles Magnetic Spectroscopy Group, Daresbury Laboratory, Warrington WA4 4AD, UK CEA/Grenoble, Service de Physique des Mate& riaux et Microstructures, 17 Rue des Martyrs, 38054 Grenoble, France
Abstract We show that the magnetization pro"le of magnetic patterns in thin "lms can be obtained by using circular dichroism to recover the phase relation in X-ray resonant magnetic scattering. This is demonstrated for single-crystalline FePd layers with striped magnetic domain pattern where we obtain unambiguous evidence for the presence of magnetic #ux closure domains. 2000 Elsevier Science B.V. All rights reserved. PACS: 75.70.Ak; 78.70.Dm; 75.30.Pd Keywords: Magnetic domains; X-ray scattering; Thin-"lm technology; Circular dichroism; Phase relation
1. Introduction Magnetic domain structures have generated intense interest in the area of magneto-optical storage devices. Ordered magnetic domain patterns are a characteristic aspect of many low-dimensional systems with phases stabilized by competing interactions. The origin of stripe texture formation is due to the competition between exchange coupling which tends to align the moments on short-range scale and dipolar interaction which favors the antiparallel alignment on a long-range scale. In thin layers exhibiting a perpendicular magnetic anisotropy, the magnetization arranges in periodic up and down domains separated by domains walls. The line tension of the domain walls, originating from the interplay of exchange energy and anisotropy energy, favors the reduction of magnetic domain walls, however, magnetic dipole interaction tends to increase magnetic domain walls. In remanence, the ordered state is characterized by magnetic #ux lines which partially escape the sample. It was
* Corresponding author: Tel.: #44-1925-603448; fax: #441925-603124. E-mail address: [email protected] (G. van der Laan)
already predicted a long time ago that internal #ux closure could produce a high degree of order in the magnetic domains [1]. Despite the important fundamental and technological implications for ultrathin "lms and despite the advent of modern imaging techniques, such as magnetic force microscopy (MFM), Lorentz microscopy or scanning electron microscopy with polarization analysis (SEMPA), which monitor the magnetic stray "elds from the sample, there is so far inconclusive evidence for such closure domains with in-plane magnetization. In this paper we report on novel opportunities in magnetic domain pro"ling which are o!ered by the use of circular dichroism in X-ray resonant magnetic scattering. We utilize the strong magneto-optical signal at the L absorption edges of 3d transition metals which causes a Faraday rotation of the (linearly) polarized X-rays analogous to, but much stronger than, the Kerr ellipticity in the visible region [2]. The use of circularly polarized photons allows us to recover the phase relation which is otherwise lost in di!raction measurements. Therefore, the di!raction pattern gives additional information about the magnetization pro"le in the "lm. Element speci"city and sensitivity to the valence magnetic moment is established by tuning the X-ray energy to the 2p absorption edge of the 3d metal (e.g. j"17.5 As
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 9 2 5 - 0
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G. van der Laan et al. / Physica B 283 (2000) 171}174
for the Fe L ), where the core electrons are excited into unoccupied d states. Under Bragg condition, the wavelength of the X-ray excitation will match the magnetic domain periodicity and coherent resonance will cause an enhancement in the magnetic scattering of several orders of magnitude.
2. Experimental A 400 As thick FePd "lm was grown by molecular beam epitaxy onto a MgO(0 0 1) substrate and capped with a 20 As thick Pd layer to prevent contamination [3]. The codeposition of Fe and Pd at equiatomic composition was performed at 500 K, leading to a partial chemical ordering [4]. The MFM image in Fig. 1 shows well-ordered up and down stripes with a period of &1020 As . The perpendicular magnetic anisotropy can be quanti"ed by Q&0.8, which gives the ratio between the magnetic anisotropy and the square of the saturation magnetization. Magnetic scattering experiments were carried out using the Daresbury Laboratory two-circle di!ractometer [5] with 92% circularly polarized X-rays from beamline ID12B of the European Synchrotron Radiation Facility in Grenoble (France). The di!ractometer is under high vacuum to prevent X-ray absorption by air. Fig. 2 shows typical di!raction scans taken in two di!erent geometries. In geometry A the magnetic stripes are perpendicu-
Fig. 2. Magnetic satellite peaks around the central, specularly re#ected X-ray beam as observed in scattering geometry A (top) and B (bottom) with left (dotted line) and right (drawn line) circularly polarized X-rays. Circular dichroism is observed in the "rst-order satellites in geometry B but not in geometry A. The data for geometry A were taken at a detector angle of 403 (i.e. H"203 at the center of the scan) and for geometry B at an average detector angle of 28.53, so H"14.253. The detector angle is averaged because in geometry B the only de"ning slit in front of the photodiode is perpendicular, and the photodiode is quite large.
lar to the scattering plane. The scan is obtained by rocking the sample while keeping the detector (a photodiode mounted behind a rectangular aperture) at "xed scattering angle. The scan shows "rst-order magnetic satellites with a modulation vector, q, that agrees well with the domain periodicity, 2p/q, found with MFM. In geometry B the stripes are parallel to the scattering plane. The detector is mounted on a motorized arm which can be scanned perpendicular to the scattering plane. In geometry B the "rst-order di!raction peaks show circular dichroism with reversed sign for satellites at opposite sides of the specularly re#ected X-ray beam. Secondorder satellites are only observed in geometry B and have been discussed elsewhere [6].
3. Discussion Fig. 1. Magnetic force microscopy (MFM) image of a 2 lm; 2 lm area of a 400 As thick FePd "lm grown epitaxially on a MgO(0 0 1) substrate. The contrast in the image arises from magnetic domains with #ux lines directed up and downwards with respect to the "lm plane. The enlarged area shows schematically the magnetic layer pro"le expected in the presence of closure domains with in-plane magnetization.
The amplitude for the "rst-order resonant magnetic scattering at site j is f (u)"(e ;e) ) M F(u), H H
(1)
where k, e and k , e are the wave vectors and polarization vectors of the incident and scattered X-ray beam,
G. van der Laan et al. / Physica B 283 (2000) 171}174
173
respectively. M is the magnetization unit vector of jth H ion and F(u) is the magnetic sensitive part of the electricdipole resonance amplitude. The magnetic di!raction intensity is a function of both the photon energy, u, and the momentum transfer given by a scattering vector q"k !k. Within the "rst Born approximation one obtains
I(q, u)" f (u) exp(iq ) r ) , (2) H H H where the summation is over each of the magnetic ions at positions r . For a simple collinear structure, with all the H magnetization vectors parallel, the polarization dependence of the scattering is the same as for the single ion in Eq. (1). This makes that ferromagnetic materials are the hardest to study due to the overlap of magnetic and charge peaks. Fortunately, the interference between the two amplitudes leads to a change in the scattering signal when the sample magnetization is reversed [7,8]. Antiferromagnetically coupled layers or domains and spiral structures have the advantage that the magnetic di!raction peaks are separated from those of the chemical structure. Linearly polarized X-rays with components p and p which are perpendicular and parallel to the scattering plane, respectively, obey simple selection rules. To observe magnetic scattering a necessary condition is that in Eq. (1) the vector product (e ;e) ) M is non-zero. This H means, e.g. that for p polarization M must be parallel to the scattering plane, which has been used to determine the magnetic alignment of coupled layers in spin-valve and giant magnetoresistance materials [5]. In this paper we are interested in the presence of closure domains in magnetic domain structures. In a simpli"ed picture this leads to a magnetic ordering !P Q near the surface, cf. Fig. 1. When the ! and stripes are parallel to the scattering plane, we measure "rst-order magnetic satellites for both p and p polarization. There can be interference between these two channels both of which lead to p polarization of the outgoing beam. This phase relation is lost for linear polarization but can be retrieved by using circular polarization with components e Jp$ip. ! The `ideala ordering (!P Q) is invariant under simultaneous translation of the unit magnetization vectors by $p/2q and rotation by $p/2. The rotation is clockwise (anticlockwise) for a translation in the positive (negative) direction (cf. Fig. 1). This symmetry condition can be stated as M exp(iq ) r )"(M #iM )d(q!q ) H H X W W H #(M !iM )d(q#q ), (3) X W W where z and y refer to unit-vector components perpendicular to surface plane and scattering plane, respectively. Therefore, right-circularly polarized light gives
Fig. 3. Schematic picture of the resonant magnetic scattering for circularly polarized X-rays with an ideal magnetic ordering !P Q with periodicity 2p/q (c.f. Fig. 1). The sample magnetization vector is rotated clockwise (anticlockwise) under a translation in the positive (negative) direction. Due to angular momentum conservation right and left circularly polarized light result in "rst-order satellites at !q and #q, respectively, around the specularly re#ected beam.
a "rst-order scattering peak at !q and left-circularly polarized light gives a "rst-order scattering peak at #q. This e!ect is schematically illustrated in Fig. 3. For non-ideal ordering or elliptically polarized light the asymmetry will be accordingly reduced, but it should still hold that I(e , $q )"I(e , Gq ). From Eq. (3) it is > W \ W clear that to observe circular dichroism the magnetic modulation vector q must be perpendicular to the scattering plane. This explains why in Fig. 2 circular dichroism is observed in geometry B but not in geometry A.
4. Conclusions We have shown that the use of circular polarization in X-ray resonant magnetic scattering strongly enhances the possibilities to investigate magnetization pro"les of thin "lms. The interference between the scattering channels provides a direct tool to investigate closure domains and domain walls. This technique is not restricted to well-ordered domain structures but should also work for less regularly arranged patterns. The method can be applied in the presence of external magnetic "elds which o!ers the opportunity to study magnetic switching phenomena. Photon-energy-dependent measurements might also result in a site-speci"c determination of spin and orbital magnetic moments [9].
Acknowledgements We thank K. Larsson, O. Tjernberg, J.B. Goedkoop and N.B. Brookes for their help and technical assistance and the ESRF sta! for the excellent working conditions.
174
G. van der Laan et al. / Physica B 283 (2000) 171}174
References [1] C. Kittel, Phys. Rev. 70 (1946) 965. [2] C.-C. Kao, C.T. Chen, E.D. Johnson, D.P. Siddons, G.C. Smith, Phys. Rev. Lett. 65 (1990) 373. [3] V. Gehanno, A. Marty, B. Gilles, Y. Samson, Phys. Rev. B 55 (1997) 12 552. [4] P. Kamp, A. Marty, B. Gilles, R. Ho!mann, S. Marchesini, M. Belakhovsky, C. Boeglin, H.A. DuK rr, S.S. Dhesi, G. van der Laan, A. Rogalev, Phys. Rev. B 59 (1999) 1105. [5] G. van der Laan, H.A. DuK rr, E. Dudzik, M.D. Roper, S.P. Collins, T.P.A. Hase, I. Pape, Synch. Radiat. News 12 (3) (1999) 5.
[6] H.A. DuK rr, E. Dudzik, S.S. Dhesi, J.B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Mocuta, A. Marty, Y. Samson, Science 284 (1999) 2166. [7] J.M. Tonnerre, L. Se`ve, D. Raoux, G. SoullieH , B. Rodmacq, P. Wolfers, Phys. Rev. Lett. 75 (1995) 740. [8] M. Sacchi, C.F. Hague, L. Pasquali, A. Mirone, J.-M. Mariot, P. Isberg, E.M. Gullikson, J.H. Underwood, Phys. Rev. Lett. 81 (1998) 1521. [9] B.T. Thole, P. Carra, F. Sette, G. van der Laan, Phys. Rev. Lett. 68 (1992) 1943.
Soft X-ray magnetic scattering from striped magnetic domain structures G. van der Laan *, E. Dudzik , S.P. Collins , S.S. Dhesi , H.A. DuK rr , M. Belakhovsky, K. Chesnel, A. Marty, Y. Samson, B. Gilles Magnetic Spectroscopy Group, Daresbury Laboratory, Warrington WA4 4AD, UK CEA/Grenoble, Service de Physique des Mate& riaux et Microstructures, 17 Rue des Martyrs, 38054 Grenoble, France
Abstract We show that the magnetization pro"le of magnetic patterns in thin "lms can be obtained by using circular dichroism to recover the phase relation in X-ray resonant magnetic scattering. This is demonstrated for single-crystalline FePd layers with striped magnetic domain pattern where we obtain unambiguous evidence for the presence of magnetic #ux closure domains. 2000 Elsevier Science B.V. All rights reserved. PACS: 75.70.Ak; 78.70.Dm; 75.30.Pd Keywords: Magnetic domains; X-ray scattering; Thin-"lm technology; Circular dichroism; Phase relation
1. Introduction Magnetic domain structures have generated intense interest in the area of magneto-optical storage devices. Ordered magnetic domain patterns are a characteristic aspect of many low-dimensional systems with phases stabilized by competing interactions. The origin of stripe texture formation is due to the competition between exchange coupling which tends to align the moments on short-range scale and dipolar interaction which favors the antiparallel alignment on a long-range scale. In thin layers exhibiting a perpendicular magnetic anisotropy, the magnetization arranges in periodic up and down domains separated by domains walls. The line tension of the domain walls, originating from the interplay of exchange energy and anisotropy energy, favors the reduction of magnetic domain walls, however, magnetic dipole interaction tends to increase magnetic domain walls. In remanence, the ordered state is characterized by magnetic #ux lines which partially escape the sample. It was
* Corresponding author: Tel.: #44-1925-603448; fax: #441925-603124. E-mail address: [email protected] (G. van der Laan)
already predicted a long time ago that internal #ux closure could produce a high degree of order in the magnetic domains [1]. Despite the important fundamental and technological implications for ultrathin "lms and despite the advent of modern imaging techniques, such as magnetic force microscopy (MFM), Lorentz microscopy or scanning electron microscopy with polarization analysis (SEMPA), which monitor the magnetic stray "elds from the sample, there is so far inconclusive evidence for such closure domains with in-plane magnetization. In this paper we report on novel opportunities in magnetic domain pro"ling which are o!ered by the use of circular dichroism in X-ray resonant magnetic scattering. We utilize the strong magneto-optical signal at the L absorption edges of 3d transition metals which causes a Faraday rotation of the (linearly) polarized X-rays analogous to, but much stronger than, the Kerr ellipticity in the visible region [2]. The use of circularly polarized photons allows us to recover the phase relation which is otherwise lost in di!raction measurements. Therefore, the di!raction pattern gives additional information about the magnetization pro"le in the "lm. Element speci"city and sensitivity to the valence magnetic moment is established by tuning the X-ray energy to the 2p absorption edge of the 3d metal (e.g. j"17.5 As
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 9 2 5 - 0
172
G. van der Laan et al. / Physica B 283 (2000) 171}174
for the Fe L ), where the core electrons are excited into unoccupied d states. Under Bragg condition, the wavelength of the X-ray excitation will match the magnetic domain periodicity and coherent resonance will cause an enhancement in the magnetic scattering of several orders of magnitude.
2. Experimental A 400 As thick FePd "lm was grown by molecular beam epitaxy onto a MgO(0 0 1) substrate and capped with a 20 As thick Pd layer to prevent contamination [3]. The codeposition of Fe and Pd at equiatomic composition was performed at 500 K, leading to a partial chemical ordering [4]. The MFM image in Fig. 1 shows well-ordered up and down stripes with a period of &1020 As . The perpendicular magnetic anisotropy can be quanti"ed by Q&0.8, which gives the ratio between the magnetic anisotropy and the square of the saturation magnetization. Magnetic scattering experiments were carried out using the Daresbury Laboratory two-circle di!ractometer [5] with 92% circularly polarized X-rays from beamline ID12B of the European Synchrotron Radiation Facility in Grenoble (France). The di!ractometer is under high vacuum to prevent X-ray absorption by air. Fig. 2 shows typical di!raction scans taken in two di!erent geometries. In geometry A the magnetic stripes are perpendicu-
Fig. 2. Magnetic satellite peaks around the central, specularly re#ected X-ray beam as observed in scattering geometry A (top) and B (bottom) with left (dotted line) and right (drawn line) circularly polarized X-rays. Circular dichroism is observed in the "rst-order satellites in geometry B but not in geometry A. The data for geometry A were taken at a detector angle of 403 (i.e. H"203 at the center of the scan) and for geometry B at an average detector angle of 28.53, so H"14.253. The detector angle is averaged because in geometry B the only de"ning slit in front of the photodiode is perpendicular, and the photodiode is quite large.
lar to the scattering plane. The scan is obtained by rocking the sample while keeping the detector (a photodiode mounted behind a rectangular aperture) at "xed scattering angle. The scan shows "rst-order magnetic satellites with a modulation vector, q, that agrees well with the domain periodicity, 2p/q, found with MFM. In geometry B the stripes are parallel to the scattering plane. The detector is mounted on a motorized arm which can be scanned perpendicular to the scattering plane. In geometry B the "rst-order di!raction peaks show circular dichroism with reversed sign for satellites at opposite sides of the specularly re#ected X-ray beam. Secondorder satellites are only observed in geometry B and have been discussed elsewhere [6].
3. Discussion Fig. 1. Magnetic force microscopy (MFM) image of a 2 lm; 2 lm area of a 400 As thick FePd "lm grown epitaxially on a MgO(0 0 1) substrate. The contrast in the image arises from magnetic domains with #ux lines directed up and downwards with respect to the "lm plane. The enlarged area shows schematically the magnetic layer pro"le expected in the presence of closure domains with in-plane magnetization.
The amplitude for the "rst-order resonant magnetic scattering at site j is f (u)"(e ;e) ) M F(u), H H
(1)
where k, e and k , e are the wave vectors and polarization vectors of the incident and scattered X-ray beam,
G. van der Laan et al. / Physica B 283 (2000) 171}174
173
respectively. M is the magnetization unit vector of jth H ion and F(u) is the magnetic sensitive part of the electricdipole resonance amplitude. The magnetic di!raction intensity is a function of both the photon energy, u, and the momentum transfer given by a scattering vector q"k !k. Within the "rst Born approximation one obtains
I(q, u)" f (u) exp(iq ) r ) , (2) H H H where the summation is over each of the magnetic ions at positions r . For a simple collinear structure, with all the H magnetization vectors parallel, the polarization dependence of the scattering is the same as for the single ion in Eq. (1). This makes that ferromagnetic materials are the hardest to study due to the overlap of magnetic and charge peaks. Fortunately, the interference between the two amplitudes leads to a change in the scattering signal when the sample magnetization is reversed [7,8]. Antiferromagnetically coupled layers or domains and spiral structures have the advantage that the magnetic di!raction peaks are separated from those of the chemical structure. Linearly polarized X-rays with components p and p which are perpendicular and parallel to the scattering plane, respectively, obey simple selection rules. To observe magnetic scattering a necessary condition is that in Eq. (1) the vector product (e ;e) ) M is non-zero. This H means, e.g. that for p polarization M must be parallel to the scattering plane, which has been used to determine the magnetic alignment of coupled layers in spin-valve and giant magnetoresistance materials [5]. In this paper we are interested in the presence of closure domains in magnetic domain structures. In a simpli"ed picture this leads to a magnetic ordering !P Q near the surface, cf. Fig. 1. When the ! and stripes are parallel to the scattering plane, we measure "rst-order magnetic satellites for both p and p polarization. There can be interference between these two channels both of which lead to p polarization of the outgoing beam. This phase relation is lost for linear polarization but can be retrieved by using circular polarization with components e Jp$ip. ! The `ideala ordering (!P Q) is invariant under simultaneous translation of the unit magnetization vectors by $p/2q and rotation by $p/2. The rotation is clockwise (anticlockwise) for a translation in the positive (negative) direction (cf. Fig. 1). This symmetry condition can be stated as M exp(iq ) r )"(M #iM )d(q!q ) H H X W W H #(M !iM )d(q#q ), (3) X W W where z and y refer to unit-vector components perpendicular to surface plane and scattering plane, respectively. Therefore, right-circularly polarized light gives
Fig. 3. Schematic picture of the resonant magnetic scattering for circularly polarized X-rays with an ideal magnetic ordering !P Q with periodicity 2p/q (c.f. Fig. 1). The sample magnetization vector is rotated clockwise (anticlockwise) under a translation in the positive (negative) direction. Due to angular momentum conservation right and left circularly polarized light result in "rst-order satellites at !q and #q, respectively, around the specularly re#ected beam.
a "rst-order scattering peak at !q and left-circularly polarized light gives a "rst-order scattering peak at #q. This e!ect is schematically illustrated in Fig. 3. For non-ideal ordering or elliptically polarized light the asymmetry will be accordingly reduced, but it should still hold that I(e , $q )"I(e , Gq ). From Eq. (3) it is > W \ W clear that to observe circular dichroism the magnetic modulation vector q must be perpendicular to the scattering plane. This explains why in Fig. 2 circular dichroism is observed in geometry B but not in geometry A.
4. Conclusions We have shown that the use of circular polarization in X-ray resonant magnetic scattering strongly enhances the possibilities to investigate magnetization pro"les of thin "lms. The interference between the scattering channels provides a direct tool to investigate closure domains and domain walls. This technique is not restricted to well-ordered domain structures but should also work for less regularly arranged patterns. The method can be applied in the presence of external magnetic "elds which o!ers the opportunity to study magnetic switching phenomena. Photon-energy-dependent measurements might also result in a site-speci"c determination of spin and orbital magnetic moments [9].
Acknowledgements We thank K. Larsson, O. Tjernberg, J.B. Goedkoop and N.B. Brookes for their help and technical assistance and the ESRF sta! for the excellent working conditions.
174
G. van der Laan et al. / Physica B 283 (2000) 171}174
References [1] C. Kittel, Phys. Rev. 70 (1946) 965. [2] C.-C. Kao, C.T. Chen, E.D. Johnson, D.P. Siddons, G.C. Smith, Phys. Rev. Lett. 65 (1990) 373. [3] V. Gehanno, A. Marty, B. Gilles, Y. Samson, Phys. Rev. B 55 (1997) 12 552. [4] P. Kamp, A. Marty, B. Gilles, R. Ho!mann, S. Marchesini, M. Belakhovsky, C. Boeglin, H.A. DuK rr, S.S. Dhesi, G. van der Laan, A. Rogalev, Phys. Rev. B 59 (1999) 1105. [5] G. van der Laan, H.A. DuK rr, E. Dudzik, M.D. Roper, S.P. Collins, T.P.A. Hase, I. Pape, Synch. Radiat. News 12 (3) (1999) 5.
[6] H.A. DuK rr, E. Dudzik, S.S. Dhesi, J.B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Mocuta, A. Marty, Y. Samson, Science 284 (1999) 2166. [7] J.M. Tonnerre, L. Se`ve, D. Raoux, G. SoullieH , B. Rodmacq, P. Wolfers, Phys. Rev. Lett. 75 (1995) 740. [8] M. Sacchi, C.F. Hague, L. Pasquali, A. Mirone, J.-M. Mariot, P. Isberg, E.M. Gullikson, J.H. Underwood, Phys. Rev. Lett. 81 (1998) 1521. [9] B.T. Thole, P. Carra, F. Sette, G. van der Laan, Phys. Rev. Lett. 68 (1992) 1943.