- Email: [email protected]
Cr (1 0 0) superlattices using spin polarized neutron reflectivity
PHYSlCA ELSEVIER
Physica B 198 (1994) 173 176
Direct observation of non-collinear spin structures in Fe/Cr (1 0 0) superlattices using spin polarized neutron reflectivity A. S c h r e y e r a'*, J.F. A n k n e r b, H. Z a b e l a, M . S c h a f e r c, C . F . M a j k r z a k b, P. G r f i n b e r g c "Experimentalphysik IV, Ruhr-Universitiit Bochum, 44780 Bochum, Germany bNational Institute of Standards and Technology, Gaithersburg, MD 20899, USA CForschungszentrum Jiilich, 52425 Jiilich, German),
Abstract
Using the sensitivity of spin polarized neutron reflectivity with exit beam polarization analysis to the orientation of the in-plane magnetic moment, we have directly observed a non-collinear magnetization profile in Fe/Cr (100) superlattices which results from biquadratic coupling. A new approach is presented which allows the quantitative understanding of the data and which leads to detailed conclusions about the magnetization profile and magnetic domain structure in the sample. These conclusions are fully validated by domain observations with Kerr microscopy.
The system Fe/Cr has served as the point of discovery for many now widely studied effects in thin layered magnetic materials. After the observation of the oscillatory exchange coupling between the Fe layers and the related giant magnetoresistance effect [1, 2], the discovery of a biquadratic exchange coupling was a major new landmark [3]. This biquadratic coupling favours a non-collinear (90 °) orientation of adjacent Fe layer magnetizations for certain interlayer thicknesses instead of the collinear antiferromagnetic (AF) (180 °) alignment which occurs in the case of bilinear coupling. Whereas the AF spin structure in Fe/Cr and other systems has been directly confirmed by neutron scattering methods (see e.g. Ref. [4]), no neutron studies of transition metal systems exhibiting these non-collinear spin structures exist so far. Very recently, we have demonstrated our ability to distinguish uniquely between collinear AF and noncollinearly coupled spin structures using SPNR with exit beam polarization analysis [5]. This
method is ideally suited for this task since it is sensitive to both orientation and magnitude of the in-plane magnetic moment. In the present paper we want to present a quantitative data analysis which allows detailed conclusions about the magnetization profile and the domain structure and briefly discuss field-dependent SPNR data. As described in more detail elsewhere in this volume [6], the sensitivity of the method to magnitude and orientation of the magnetic moment is a direct consequence of the interaction of the neutron's magnetic moment with the magnetic field caused by any unpaired electrons in the sample [7]. This interaction can be described in terms of an effective scattering length bteff (incident polarization, exit polarization) for each layer l of a superlattice. For the typical scattering geometry of a reflectivity measurement with the scattering vector Q perpendicular to the film plane and for the case of the neutron polarization axis P lying in the film plane (e.g. see Ref. [6], Fig. 1) the b~ff are b~rr(+
* Corresponding author.
+)
b'+A
t
b~fr( + , - ) = b ~ r f ( - , + ) = A/~_,
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 3 ) E 0 5 3 1 - K
(1) (2)
174
A. Schreyer et al./Physica B 198 (1994) 173 176
with the average nuclear scattering length b~of the atoms in layer l, the components of the in-plane magnetic moment /t I in layer 1 parallel (Ih) and perpendicular (±) to P, a constant A --0.2695 × 10 -4 ~/PB, the Bohr magneton #B and the neutron polarization parallel ( + ) (antiparallel ( - )) to an applied field HIJP. Whereas the non-spin-flip (NSF) cross-sections ( + , ___) are sensitive to both nuclear and magnetic structure, the spin flip (SF) crosssections ( + , -T-)contain purely magnetic information. From both equations it is immediately clear that the orientation of the magnetic in-plane moments relative to P and their magnitude can be extracted by simultaneously fitting the calculated NSF and SF reflectivities to measured data. In the small angle reflectivity regime this calculation is performed in analogy to optical reflectivity I-7]. The refractive index of each layer 1 for neutrons depends, apart from the incident wavelength, solely on the product of the effective scattering length bteff and the average number density N t of the scatterers. For the case of Fe/Cr both N ~turn out to be equal, making b~ff the only important parameter. Since b~ff sensitively depends on the orientation of the in-plane magnetic moment, a birefringence, i.e. a splitting of the critical scattering vector QcNsv of total external reflection, is induced for the NSF cross-sections in the case of the existence of a magnetic in-plane component /~I]P (see Eq. (1)). A comparative discussion of the SPNR from superlattices with various types of magnetization profiles including this birefringence effect is provided in Ref. [6]. The sample used in this study was grown by molecular beam epitaxy methods on the same GaAs/Fe/Ag substrate-buffer system described e.g. in Ref. [3]. Instead of a wedged trilayer, a Fe/Cr (1 00) superlattice with 9(53 ,~ Fe/17 ,~ Cr) double layers having a surface area of 1 × 1 cm 2 was grown epitaxially at 250°C starting with Fe and finishing with a protective ZnS layer on top of the last Fe layer [5]. The SPNR measurements were performed on the angle dispersive reflectometer BT-7 [7] at the National Institute of Standards and Technology at a fixed wavelength of 2.367 ~. All four crosssections were measured with an Fe/Si supermirror and a spin flipper mounted before and behind the
sample. The magnetic field at the sample position was varied between 0.5 (minimum neutron guide field) and 230 mT using an electromagnet. In this whole field range flipping ratios I + / I - ~ 25, defined as the ratio of the primary beam intensities of the + and - neutron spin states, were achieved for the front and back pairs of supermirror and spin flipper, respectively. Using an inversion formalism [8] the data were corrected for the efficiencies of the polarizing elements. To correct for background and the diffuse scattering component, the true specular reflectivity was obtained by subtracting an independently measured off-specular reflectivity. In Fig. 1 SPNR data of the superlattice measured in a field of 1.7 mT is shown together with a fit to the data (solid lines). The SF cross-sections were measured to be equal and were added to improve counting statistics. As indicated in the inset in the upper right corner, the field H was applied along one of the sample's easy axes (dashed lines), i.e. a sample diagonal. Also defined in the inset are the NSF and SF axes, which are sensitive to the parallel and perpendicular components of the in-plane magnetization relative to P, respectively (see Eqs. (1) and (2)). The data exhibit a large splitting in the NSF cross-sections at low Q around QNsv and around the first-order superlattice peaks which appear at Ql = 2 n / A ~ 0.9 ~ - I ( A = (dye + dcr)) in all cross-sections. Furthermore, half-order peaks at about Q a/2 = 2 n / 2 A occur in all cross-sections. The fact that all peaks exhibit the same width shows that the nuclear and magnetic coherence lengths are equal, indicating a well-defined and coherent magnetic order throughout the whole film thickness. From the discussion above the magnetization profile of the sample can be immediately qualitatively inferred. The splitting of the Q~SV and of the NSF first-order superlattice peak intensities (Eq. (1)) and the existence of the SF peak at Q1 (Eq. (2)) indicates a significant resulting magnetization with components parallel to the NSF and the SF axis. The strong half-order peak in all cross-sections, on the other hand, is direct proof of a doubling of the magnetic as compared to the nuclear superlattice period for magnetization components along both the NSF and SF axes. These two observations require a magnetization profile which, on the one hand oscillates in the plane between two angles to
A. Schreyer et al./Physica B 198 (1994) 173-176
NIq~
II P II 1.4
-1 ~-2
0
Y. 9-3 ¢=
-1
,,---4
-2 -3 I
!
--,
e
2A
o
\
-4
F
L 0
0.02
0.04
0.06
0.08
0.1
q / ~.-1
Fig. 1. SPNR NSF (top) and SF (bottom) data ofa biquadratically coupled Fe/Cr superlattice plotted as a function of scattering vector together with a theoretical calculation (solid lines). The NSF cross-sections are split into ( + , +) (circles) and ( - , - ) (squares). The SF cross-sections are equal and have been shifted downwards by two orders of magnitude. They are plotted against the scale on the right axis. In the inset in the upper right corner, a top view of the sample showing the orientation of the sample's easy axes relative to the applied field H and the neutron polarization vector P is depicted together with the two types of layer magnetizations occurring in the system due to biquadratic coupling. The dashed arrow indicates the resulting magnetization which causes the observed splitting of the NSF data and the SF peak at the first-order superlattice peak position. In the inset in the lower left corner the stacking sequence of the layer magnetizations which cause the half-order superlattice peaks is depicted in a schematic side view of the sample along the NSF axis. Also shown are the two domain types which had to be assumed to explain the data quantitatively (solid lines). provide the doubling of the magnetic superlattice period, and on the other hand forms a resulting m o m e n t along the N S F and the SF axes. Consequently, the angle between neighbouring Fe layers cannot be 180 ° (collinear, AF coupling) since in this case no resulting m o m e n t would exist [5]. A noncollinear magnetization profile is required instead, as indicated in the insets of Fig. 1. Due to the two easy axes 90 ° apart and the small applied field it is tempting to assume a coupling angle of 90 °. This coincides with d o m a i n observations on the similarly prepared wedged trilayers [3] by Kerr microscopy.
175
These conclusions were confirmed by measuring the reflectivity with the sample turned clockwise by 45 ° a r o u n d an axis perpendicular to the sample plane, making sure that the applied field is smaller than the sample's coercive field. As expected from the anticipated magnetization profile, a half-order peak is observed only in the SF cross-sections due to the doubling of the magnetic periodicity now being visible only in the SF c o m p o n e n t (see Ref. [6], Fig. 2(c) in this volume). Furthermore, because of the whole resulting m o m e n t now pointing along the N S F axis, a larger splitting of the N S F crosssections is observed. These results clearly are consistent with the expected 90 ° s y m m e t r y of the magnetization profile. Also shown in Fig. 1 is a reflectivity calculation (for methodical details, see Ref. [9]) assuming bulk N l, sharp interfaces and a mixed incoherent and coherent superposition of two different d o m a i n structures. All features of the data are quite well reproduced. The difference between incoherent and coherent superposition lies in the domain averaging process. In the case of incoherent superposition the reflected intensity from an ensemble of domains is calculated by adding the squared amplitudes, i.e. the intensities, of the individual domains. This procedure corresponds to a simple averaging of the intensities. In the case of coherent superposition, on the other hand, first the amplitudes from all domains are added and then this sum is squared to obtain the reflected intensity from the d o m a i n ensemble. Therefore, only an averaged magnetization per layer enters the calculated reflectivity in the coherent case, whereas in the case of incoherent superposition all contributions are s u m m e d up without the possibility of, e.g. a cancelling effect of the magnetization c o m p o n e n t s in each layer. A good fit of the half-order peak intensities was achieved only with a superposition of the reflection amplitudes of two 90 ° coupled domains of the type shown in the lower left inset of Fig. 1, with opposite stacking sequences of the respective magnetization directions in each layer (i.e. (90 °, 0 °, 90 °, . . . ) and (0 °, 90 °, 0 °, . . .)). Assuming only a single magnetic d o m a i n of either type, i.e. the same stacking sequence in the whole sample, significantly overestimates the half-order intensities in all four crosssections. Furthermore, an incoherent superposition
176
A. Schreyer et al. / Physica B 198 (1994) 173-176
of these two types of domains does not change this result since in this case only the intensities are averaged. On the other hand, in the case of coherent superposition the assumption of an equal occupancy of both domain types leads to the extreme case of the absence of any half-order peak intensity. Since in this case the average magnetization per layer enters the calculation (dashed arrow in Fig. 1), no doubling of the magnetic periodicity over the nuclear one occurs, leaving the NSF splitting around Q~SVand the first-order peaks unchanged. In order to explain the measured half-order peak intensities, we therefore have to combine both, the incoherent and coherent superposition approach. The best fit shown in Fig. 1 was obtained by incoherently adding the (90 °, 0 °, 9 0 ° , . . . ) and (0 ~', 90 °, 0 ° , . . . ) reflectivities to the coherently added ((90 c, 0 °, 9 0 ° , . . . ) x 0 . 5 + ( 0 °, 90 °, 0 °, . . . ) x 0 . 5 ) spectrum with fractions of 0.125, 0.125 and 0.75, respectively. The large fraction of the coherently added reflectivity without any half-order intensity is needed to correct for the overestimated halforder intensity from the other spectra. According to this result both domain types are present in the system with equal occupancy. The assumption of a larger contribution of one domain type leads to a worse fit in the low Q region. The presence of any other domain type, consistent with the known easy axes and coupling angle, can be excluded since it would lead to a different orientation of the resulting moment. This would contradict the measured data. All results of this analysis, i.e. the existence of only two domain types which differ in their stacking sequence and the equal occupancy of these two domain types are fully confirmed by direct observation of the lateral domain structure with Kerr microscopy on the same sample under equal
conditions. We have also measured the half- and first-order peak intensities as a function of applied field up to 230 mT. The most important result of this measurement is, that the sample is not fully saturated at 230 mT. The saturation field, which is a direct measure of the strength of the biquadratic coupling, therefore is much larger than anticipated before. A more detailed account of such measurements and of the Kerr microscopy results together with
a test of the proposed domain model will be given in a forthcoming paper [10]. In conclusion, we have presented a quantitative analysis of four cross-section SPNR data from a biquadratically coupled F e / C r superlattice, indicating the existence of a 90 ° coupled magnetization profile in this' system. The information obtained about the domain structure is fully validated by domain observations using Kerr microscopy. We want to thank R. Sch/ifer for the Kerr microscopy and R. Schreiber for technical help with the sample preparation. Furthermore, we gratefully acknowledge partial financial support from the Bundesministerium ffir Forschung und Technologie through Grant No. 03-ZA3BOC and from NATO through Grant No. CRG 901064.
References [1] P. Griinberg, R. Schreiber, Y. Pang, M.B. Brodsky and H. Sowers, Phys. Rev. Lett. 57 (1986) 2442; S. Demokritov, J.A. Wolf and P. Griinberg, Europhys. Lett. 15 (1991) 881. [2] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [3] M. Rfihrig, R. Sch/ifer, A. Hubert, R. Mosler, J.A. Wolf, S. Demokritov and P. Grtinberg, Phys. Star. Sol. A 125 (1991) 635. [4] S.S.P. Parkin, A. Mansour and G.P. Felcher, Appl. Phys. Lett. 58 (1991) 1473. [5] J.F. Ankner, A. Schreyer, Th. Zeidler, C.F, Majkrzak, H. Zabel, J.A. Wolf and P. Griinberg, in: Magnetic Ultrathin Films, Multilayers and Surfaces, eds. C. Chappert, R. Clarke, R.F.C. Farrow, P. Griinberg, W.J.M. de Jonge, B.T. Jonker, Kannan M. Krishnan and Shigeru Tsunashima, MRS Symposia Proc. Vol. 313 (Materials Research Society, Pittsburgh) p. 761. [6] H. Zabel, Physica B 198 (1994) 156. [7] C.F. Majkrzak, Physica B 173 (1991) 75, and references therein; G.P. Felcher, Physica B 192 (1993) 137. [8] C.F. Majkrzak, in: Handbook of Neutrons, ed. W. Gl/iser (Springer, Berlin, Heidelberg), to appear. [9] J.F. Ankner, to be published; for applications, see: A. Schreyer, Th. Zeidler, Ch. Morawe, N. Metoki, H. Zabel, J.F. Ankner and C.F. Majkrzak, J. Appl. Phys. 73 (1993) 7616; J.F. Ankner, A. Schreyer, C.F. Majkrzak, K. Br6hl, Th. Zeidler, P. B6deker and H. Zabel, in: Magnetic Ultrathin Films, Multilayers and Surfaces, see Ref. [5]. [10] A. Schreyer et al., to be published.
Physica B 198 (1994) 173 176
Direct observation of non-collinear spin structures in Fe/Cr (1 0 0) superlattices using spin polarized neutron reflectivity A. S c h r e y e r a'*, J.F. A n k n e r b, H. Z a b e l a, M . S c h a f e r c, C . F . M a j k r z a k b, P. G r f i n b e r g c "Experimentalphysik IV, Ruhr-Universitiit Bochum, 44780 Bochum, Germany bNational Institute of Standards and Technology, Gaithersburg, MD 20899, USA CForschungszentrum Jiilich, 52425 Jiilich, German),
Abstract
Using the sensitivity of spin polarized neutron reflectivity with exit beam polarization analysis to the orientation of the in-plane magnetic moment, we have directly observed a non-collinear magnetization profile in Fe/Cr (100) superlattices which results from biquadratic coupling. A new approach is presented which allows the quantitative understanding of the data and which leads to detailed conclusions about the magnetization profile and magnetic domain structure in the sample. These conclusions are fully validated by domain observations with Kerr microscopy.
The system Fe/Cr has served as the point of discovery for many now widely studied effects in thin layered magnetic materials. After the observation of the oscillatory exchange coupling between the Fe layers and the related giant magnetoresistance effect [1, 2], the discovery of a biquadratic exchange coupling was a major new landmark [3]. This biquadratic coupling favours a non-collinear (90 °) orientation of adjacent Fe layer magnetizations for certain interlayer thicknesses instead of the collinear antiferromagnetic (AF) (180 °) alignment which occurs in the case of bilinear coupling. Whereas the AF spin structure in Fe/Cr and other systems has been directly confirmed by neutron scattering methods (see e.g. Ref. [4]), no neutron studies of transition metal systems exhibiting these non-collinear spin structures exist so far. Very recently, we have demonstrated our ability to distinguish uniquely between collinear AF and noncollinearly coupled spin structures using SPNR with exit beam polarization analysis [5]. This
method is ideally suited for this task since it is sensitive to both orientation and magnitude of the in-plane magnetic moment. In the present paper we want to present a quantitative data analysis which allows detailed conclusions about the magnetization profile and the domain structure and briefly discuss field-dependent SPNR data. As described in more detail elsewhere in this volume [6], the sensitivity of the method to magnitude and orientation of the magnetic moment is a direct consequence of the interaction of the neutron's magnetic moment with the magnetic field caused by any unpaired electrons in the sample [7]. This interaction can be described in terms of an effective scattering length bteff (incident polarization, exit polarization) for each layer l of a superlattice. For the typical scattering geometry of a reflectivity measurement with the scattering vector Q perpendicular to the film plane and for the case of the neutron polarization axis P lying in the film plane (e.g. see Ref. [6], Fig. 1) the b~ff are b~rr(+
* Corresponding author.
+)
b'+A
t
b~fr( + , - ) = b ~ r f ( - , + ) = A/~_,
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 3 ) E 0 5 3 1 - K
(1) (2)
174
A. Schreyer et al./Physica B 198 (1994) 173 176
with the average nuclear scattering length b~of the atoms in layer l, the components of the in-plane magnetic moment /t I in layer 1 parallel (Ih) and perpendicular (±) to P, a constant A --0.2695 × 10 -4 ~/PB, the Bohr magneton #B and the neutron polarization parallel ( + ) (antiparallel ( - )) to an applied field HIJP. Whereas the non-spin-flip (NSF) cross-sections ( + , ___) are sensitive to both nuclear and magnetic structure, the spin flip (SF) crosssections ( + , -T-)contain purely magnetic information. From both equations it is immediately clear that the orientation of the magnetic in-plane moments relative to P and their magnitude can be extracted by simultaneously fitting the calculated NSF and SF reflectivities to measured data. In the small angle reflectivity regime this calculation is performed in analogy to optical reflectivity I-7]. The refractive index of each layer 1 for neutrons depends, apart from the incident wavelength, solely on the product of the effective scattering length bteff and the average number density N t of the scatterers. For the case of Fe/Cr both N ~turn out to be equal, making b~ff the only important parameter. Since b~ff sensitively depends on the orientation of the in-plane magnetic moment, a birefringence, i.e. a splitting of the critical scattering vector QcNsv of total external reflection, is induced for the NSF cross-sections in the case of the existence of a magnetic in-plane component /~I]P (see Eq. (1)). A comparative discussion of the SPNR from superlattices with various types of magnetization profiles including this birefringence effect is provided in Ref. [6]. The sample used in this study was grown by molecular beam epitaxy methods on the same GaAs/Fe/Ag substrate-buffer system described e.g. in Ref. [3]. Instead of a wedged trilayer, a Fe/Cr (1 00) superlattice with 9(53 ,~ Fe/17 ,~ Cr) double layers having a surface area of 1 × 1 cm 2 was grown epitaxially at 250°C starting with Fe and finishing with a protective ZnS layer on top of the last Fe layer [5]. The SPNR measurements were performed on the angle dispersive reflectometer BT-7 [7] at the National Institute of Standards and Technology at a fixed wavelength of 2.367 ~. All four crosssections were measured with an Fe/Si supermirror and a spin flipper mounted before and behind the
sample. The magnetic field at the sample position was varied between 0.5 (minimum neutron guide field) and 230 mT using an electromagnet. In this whole field range flipping ratios I + / I - ~ 25, defined as the ratio of the primary beam intensities of the + and - neutron spin states, were achieved for the front and back pairs of supermirror and spin flipper, respectively. Using an inversion formalism [8] the data were corrected for the efficiencies of the polarizing elements. To correct for background and the diffuse scattering component, the true specular reflectivity was obtained by subtracting an independently measured off-specular reflectivity. In Fig. 1 SPNR data of the superlattice measured in a field of 1.7 mT is shown together with a fit to the data (solid lines). The SF cross-sections were measured to be equal and were added to improve counting statistics. As indicated in the inset in the upper right corner, the field H was applied along one of the sample's easy axes (dashed lines), i.e. a sample diagonal. Also defined in the inset are the NSF and SF axes, which are sensitive to the parallel and perpendicular components of the in-plane magnetization relative to P, respectively (see Eqs. (1) and (2)). The data exhibit a large splitting in the NSF cross-sections at low Q around QNsv and around the first-order superlattice peaks which appear at Ql = 2 n / A ~ 0.9 ~ - I ( A = (dye + dcr)) in all cross-sections. Furthermore, half-order peaks at about Q a/2 = 2 n / 2 A occur in all cross-sections. The fact that all peaks exhibit the same width shows that the nuclear and magnetic coherence lengths are equal, indicating a well-defined and coherent magnetic order throughout the whole film thickness. From the discussion above the magnetization profile of the sample can be immediately qualitatively inferred. The splitting of the Q~SV and of the NSF first-order superlattice peak intensities (Eq. (1)) and the existence of the SF peak at Q1 (Eq. (2)) indicates a significant resulting magnetization with components parallel to the NSF and the SF axis. The strong half-order peak in all cross-sections, on the other hand, is direct proof of a doubling of the magnetic as compared to the nuclear superlattice period for magnetization components along both the NSF and SF axes. These two observations require a magnetization profile which, on the one hand oscillates in the plane between two angles to
A. Schreyer et al./Physica B 198 (1994) 173-176
NIq~
II P II 1.4
-1 ~-2
0
Y. 9-3 ¢=
-1
,,---4
-2 -3 I
!
--,
e
2A
o
\
-4
F
L 0
0.02
0.04
0.06
0.08
0.1
q / ~.-1
Fig. 1. SPNR NSF (top) and SF (bottom) data ofa biquadratically coupled Fe/Cr superlattice plotted as a function of scattering vector together with a theoretical calculation (solid lines). The NSF cross-sections are split into ( + , +) (circles) and ( - , - ) (squares). The SF cross-sections are equal and have been shifted downwards by two orders of magnitude. They are plotted against the scale on the right axis. In the inset in the upper right corner, a top view of the sample showing the orientation of the sample's easy axes relative to the applied field H and the neutron polarization vector P is depicted together with the two types of layer magnetizations occurring in the system due to biquadratic coupling. The dashed arrow indicates the resulting magnetization which causes the observed splitting of the NSF data and the SF peak at the first-order superlattice peak position. In the inset in the lower left corner the stacking sequence of the layer magnetizations which cause the half-order superlattice peaks is depicted in a schematic side view of the sample along the NSF axis. Also shown are the two domain types which had to be assumed to explain the data quantitatively (solid lines). provide the doubling of the magnetic superlattice period, and on the other hand forms a resulting m o m e n t along the N S F and the SF axes. Consequently, the angle between neighbouring Fe layers cannot be 180 ° (collinear, AF coupling) since in this case no resulting m o m e n t would exist [5]. A noncollinear magnetization profile is required instead, as indicated in the insets of Fig. 1. Due to the two easy axes 90 ° apart and the small applied field it is tempting to assume a coupling angle of 90 °. This coincides with d o m a i n observations on the similarly prepared wedged trilayers [3] by Kerr microscopy.
175
These conclusions were confirmed by measuring the reflectivity with the sample turned clockwise by 45 ° a r o u n d an axis perpendicular to the sample plane, making sure that the applied field is smaller than the sample's coercive field. As expected from the anticipated magnetization profile, a half-order peak is observed only in the SF cross-sections due to the doubling of the magnetic periodicity now being visible only in the SF c o m p o n e n t (see Ref. [6], Fig. 2(c) in this volume). Furthermore, because of the whole resulting m o m e n t now pointing along the N S F axis, a larger splitting of the N S F crosssections is observed. These results clearly are consistent with the expected 90 ° s y m m e t r y of the magnetization profile. Also shown in Fig. 1 is a reflectivity calculation (for methodical details, see Ref. [9]) assuming bulk N l, sharp interfaces and a mixed incoherent and coherent superposition of two different d o m a i n structures. All features of the data are quite well reproduced. The difference between incoherent and coherent superposition lies in the domain averaging process. In the case of incoherent superposition the reflected intensity from an ensemble of domains is calculated by adding the squared amplitudes, i.e. the intensities, of the individual domains. This procedure corresponds to a simple averaging of the intensities. In the case of coherent superposition, on the other hand, first the amplitudes from all domains are added and then this sum is squared to obtain the reflected intensity from the d o m a i n ensemble. Therefore, only an averaged magnetization per layer enters the calculated reflectivity in the coherent case, whereas in the case of incoherent superposition all contributions are s u m m e d up without the possibility of, e.g. a cancelling effect of the magnetization c o m p o n e n t s in each layer. A good fit of the half-order peak intensities was achieved only with a superposition of the reflection amplitudes of two 90 ° coupled domains of the type shown in the lower left inset of Fig. 1, with opposite stacking sequences of the respective magnetization directions in each layer (i.e. (90 °, 0 °, 90 °, . . . ) and (0 °, 90 °, 0 °, . . .)). Assuming only a single magnetic d o m a i n of either type, i.e. the same stacking sequence in the whole sample, significantly overestimates the half-order intensities in all four crosssections. Furthermore, an incoherent superposition
176
A. Schreyer et al. / Physica B 198 (1994) 173-176
of these two types of domains does not change this result since in this case only the intensities are averaged. On the other hand, in the case of coherent superposition the assumption of an equal occupancy of both domain types leads to the extreme case of the absence of any half-order peak intensity. Since in this case the average magnetization per layer enters the calculation (dashed arrow in Fig. 1), no doubling of the magnetic periodicity over the nuclear one occurs, leaving the NSF splitting around Q~SVand the first-order peaks unchanged. In order to explain the measured half-order peak intensities, we therefore have to combine both, the incoherent and coherent superposition approach. The best fit shown in Fig. 1 was obtained by incoherently adding the (90 °, 0 °, 9 0 ° , . . . ) and (0 ~', 90 °, 0 ° , . . . ) reflectivities to the coherently added ((90 c, 0 °, 9 0 ° , . . . ) x 0 . 5 + ( 0 °, 90 °, 0 °, . . . ) x 0 . 5 ) spectrum with fractions of 0.125, 0.125 and 0.75, respectively. The large fraction of the coherently added reflectivity without any half-order intensity is needed to correct for the overestimated halforder intensity from the other spectra. According to this result both domain types are present in the system with equal occupancy. The assumption of a larger contribution of one domain type leads to a worse fit in the low Q region. The presence of any other domain type, consistent with the known easy axes and coupling angle, can be excluded since it would lead to a different orientation of the resulting moment. This would contradict the measured data. All results of this analysis, i.e. the existence of only two domain types which differ in their stacking sequence and the equal occupancy of these two domain types are fully confirmed by direct observation of the lateral domain structure with Kerr microscopy on the same sample under equal
conditions. We have also measured the half- and first-order peak intensities as a function of applied field up to 230 mT. The most important result of this measurement is, that the sample is not fully saturated at 230 mT. The saturation field, which is a direct measure of the strength of the biquadratic coupling, therefore is much larger than anticipated before. A more detailed account of such measurements and of the Kerr microscopy results together with
a test of the proposed domain model will be given in a forthcoming paper [10]. In conclusion, we have presented a quantitative analysis of four cross-section SPNR data from a biquadratically coupled F e / C r superlattice, indicating the existence of a 90 ° coupled magnetization profile in this' system. The information obtained about the domain structure is fully validated by domain observations using Kerr microscopy. We want to thank R. Sch/ifer for the Kerr microscopy and R. Schreiber for technical help with the sample preparation. Furthermore, we gratefully acknowledge partial financial support from the Bundesministerium ffir Forschung und Technologie through Grant No. 03-ZA3BOC and from NATO through Grant No. CRG 901064.
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