JOURNAL OF APPLIED PHYSICS
VOLUME 83, NUMBER 11
1 JUNE 1998
Probing the magnetic microstructure of an amorphous GdFe system with magnetic anomalous small angle x-ray scattering P. Fischera) Institute for Physics, EP II, University of Augsburg, Memmingerstr. 6, D 86135 Augsburg, Germany
R. Zeller and G. Schu¨tz Institute for Experimental Physics IV, University of Wu¨rzburg, Am Hubland, D 97074 Wu¨rzburg, Germany
G. Goerigk and H.-G. Haubold Forschungszentrum Ju¨lich GmbH, IFF, D 52425 Ju¨lich, Germany
K. Pruegl and G. Bayreuther Institute for Experimental and Applied Physics, University of Regensburg, Universita¨tsstr. 31, D 93053 Regensburg, Germany
The combination of x-ray magnetic circular dichroism ~X-MCD! with anomalous small angle x-ray scattering ~ASAXS! allows to determine size distributions and correlations lengths in the nanometer range of magnetic precipitates in granular systems. Results on an amorphous GdFe system with a pronounced perpendicular magnetic anisotropy are reported. Standard ASAXS measurements taken at the Fe K edge provide information on the electronic structure yielding a correlation maximum at 75 Å and an average particle radius of 6 Å. The magnetic scattering curves ~MASAXS! were obtained at the corresponding Gd L 3,2 edges. Their intensities can be explained by magnetic contributions to the anomalous scattering factors f 8 and f 9 . A change of sign in the MASAXS is observed between profiles taken at the L 3 and the L 2 edge and with the change of circular polarization as expected from X-MCD. © 1998 American Institute of Physics. @S0021-8979~98!24911-5#
dd . u f ~ E,Z ! u 2 5 u f 0 1 f 8 ~ E ! 1i f 9 ~ E ! u 2 , dV
I. INTRODUCTION
A fundamental understanding of magnetic microstructures is an outstanding challenge both in current research of magnetism and its technological applications. Thereby reliable information on the electronic and magnetic structure on a typical length scale of 1–100 nm is mandatory. Among other recent observations of novel phenomena like the occurrence of the GMR, quantum oscillations or the magnetic interface anisotropy in magnetic thin films or multilayered systems, the origin of the perpendicular magnetic anisotropy in granular thin GdFe films is in particular still an open problem. An established technique to study size distributions and correlations of particles in the nm range is the small angle x-ray scattering ~SAXS!. Using tunable x rays with high brilliance being available at synchrotron sources the mode of contrast enhancement ~anomalous SAXS5ASAXS! can be engaged, i.e., involving the element-specific anomalous scattering amplitude f 8 (E), which varies with energy by about 20% in the vicinity of absorption edges, thus providing more detailed structural information on multicomponent systems. In a two-phase model the scattering contrast Dc in SAXS is given by (n 1 • f 1 2n 2 • f 2 ) with n i , f i being the density and atomic scattering amplitudes of phase i. The cross section d s /dV is proportional to Dc 2 which in the case of anomalous scattering can be related to (n 1 5n 2 )
with the atomic form factor f 0 5Z ~atomic number! and f 8 and f 9 being the additional anomalous contributions. f 8 and f 9 are connected to each other via a Kramers–Kronig relation, whence f 9 can be related to the absorption coefficient m (E) via the optical theorem f 9~ E ! 5
mc E m~ E !. 4pe2 h
~2!
The effect of x-ray magnetic circular dichroism ~XMCD!, i.e., the dependence of the absorption of circular polarized x rays on the projection of the magnetization onto the photon propagation direction (eˆ z ) in ferromagnetic samples1 occurs in the vicinity of inner-core absorption edges. Due to angular momentum conservation in the absorption process the photoelectron acquires both an expectation value of the spin ^ s z & and the orbital ^ l z & momentum projected onto eˆ z . It can therefore serve as a local probe for the spin and orbital polarization of the absorbing atom according to the principle of Pauli. ^ s z & amounts to 250% and 125% at the L 2 and L 3 edges, while ^ l z & 5175% at both L 2,3 edges. X-MCD has become a powerful tool for the element-specific and symmetry-selective investigation of the local magnetic structure on an atomic scale. Applying magneto-optical sum rules,2 it is possible to determine in certain cases spin and orbital moments separately. Beyond this local magnetic structure a spin-dependent contribution has been manifested in the extended x-ray absorption fine structure ~EXAFS!
a!
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0021-8979/98/83(11)/7088/3/$15.00
~1!
7088
© 1998 American Institute of Physics
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Fischer et al.
J. Appl. Phys., Vol. 83, No. 11, 1 June 1998
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FIG. 1. ASAXS ~d! and MASAXS ~L! scattering profiles of the amorphous GdFe system taken at the Fe K-edge and the Gd L 3 edge.
FIG. 2. MASAXS ~L! at the Gd L 3 edge with a Q 24 background subtracted for small Q values and results from a fit ~–! taking into account a log-normal distribution including correlation.
range ~magnetic EXAFS5MEXAFS!, too, which allows to study the magnetic short-range order in multicomponent systems even on a larger size scale up to 20 Å. The potential of X-MCD, however, is not restricted to the study of absorption profiles. In principle every method used in spectroscopy or crystallography, where the absorption coefficient is involved, can be extended to its magnetic counterpart. Thus the basic idea of magnetic anomalous small angle x-ray scattering ~MASAXS! is to achieve the contrast enhancement via the effect of X-MCD. As the dichroic signal depends on the projection of the local magnetization of the absorbing atoms onto eˆ z the magnetic scattering curves reflect the size distribution and correlation lengths of the magnetic scattering precipitates. Given the magnetic absorption coefficient for parallel/antiparallel alignment of magnetic electrons relative to eˆ z by m 6 (E)5 m 0 (E) 6 m c (E) the corresponding scattering amplitudes f 8 6 (E) and f 9 6 (E) both acquire magnetic contributions f 8c (E) and f 9c (E), namely,
magnetic flux densities up to 60 mT with its field direction pointing parallel/antiparallel to the photon beam direction sufficient to saturate the sample. The magnetic contrast scattering curve was then obtained according to Eq. ~5! by recording two scattering profiles with parallel/antiparallel orientation of the magnetization relative to eˆ z and fixed circular degree of polarization at an incident photon energy where the maximum dichroic effect is expected. The results reported here were obtained with a binary Gd28Fe72 system. The amorphous film was prepared by coevaporation from two electron-gun sources in a high vacuum system onto a 15 mm MylarR foil. For chemical protection, the Gd-Fe films of thickness h5105– 115 nm were covered with 20–22 nm Al layers on both sides of the Gd-Fe layer. A stack of 12 foils was enough to achieve a transmission of 0.5. A strong magnetic anisotropy perpendicular to the surface was verified by vibrating sample magnetometer ~VSM! measurements and Faraday effect results
f 8 6 ~ E ! 5 f 8 ~ E ! 6 f 8c ,
~3!
f 9 6 ~ E ! 5 f 9 ~ E ! 6 f 9c .
~4!
Inserting Eqs. ~3! and ~4! into Eq. ~1! the magnetic cross section, i.e., the difference in scattered intensities for parallel and antiparallel orientation is given by
S D S D ds dV
1
2
ds dV
2
.4 ~ f 0 1 f 8 ! f c8 14 f 9 f c9 .
~5!
II. EXPERIMENTAL DETAILS
The experiments were performed at the JUSIFA beamline at HASYLAB/Hamburg ~FRG!. The setup for the ASAXS measurements, described in detail in Ref. 3, was modified slightly for the magnetic measurements. In order to illuminate the sample with circular polarized x rays, the inclined view method was used. The beam position control monitor was set to an asymmetric position 2.5 mm above/ below the orbital plane with a slit height of 1.4 mm. The beam height position was checked by recording the beam profile after each scan. The calculated degree of circular polarization amounts to '70%. A small solenoid provided
FIG. 3. Anomalous scattering factors f 8 and f 9 ~--! and the corresponding magnetic contributions f c8 and f c9 ~–! calculated from highly accurate MEXAFS results at the Gd L 3 edge in Gd metal. The magnetic values are multiplied by a factor 100.
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Fischer et al.
J. Appl. Phys., Vol. 83, No. 11, 1 June 1998
FIG. 4. MASAXS obtained at the Gd L 3 ~d! and L 2 ~L! edge indicating the change of sign of the profile for the different edges.
exhibiting a rectangular hysteresis loop with a magnetic coercive field of '20 mT. III. RESULTS AND DISCUSSIONS
In Fig. 1 the magnetic scattering curve intensity obtained in that way versus momentum transfer Q measured at the Gd L 3 edge (E57243 eV) is presented in comparison with the ASAXS profile obtained at the corresponding Fe K edge indicating the gross similarity of the electronic and magnetic structure. The profile can be interpreted as due to two size distributions, where the Q 24 behavior at small Q values can be attributed to large particles. After a pronounced maximum at Q;0.06 Å 21 , which can be interpreted as a correlation maximum, the tail of a size distribution of smaller particles can be observed. Fit procedures taking into account a log-normal distribution to the experimental data including a correlation yielded a correlation length of 74.9 Å and size of the particle radius of 5.3 Å with slightly enhanced values for the magnetic case ~76.6 Å and 5.8 Å, respectively!. The results are shown in Fig. 2, where the Q 24 tail of the large particles had been subtracted. Corresponding EXAFS and MEXAFS studies indicate no wide range ordering compared to pure bcc Fe.4 This points to a rather complex structure of the system studied. Although the crystal structure seems to be amorphous, there is to some extent an ordered chemical structure, which is consistent with the assumption that column-like structures are formed in that magneto-optical films. Furthermore, the observed magnetic anisotropy could also be related to those columns. On the other hand, the magnetic correlation observed in the MASAXS would then originate from a chemical inhomogeneity. The intensity of the MASAXS profile can be related to accurate experimental measurements of MEXAFS in a wide range around the Gd L 3 edge with the help of the optical theorem @Eq. ~2!# and a Kramers–Kronig relation. The obtained results in a pure Gd system for f 8 , f c8 and f 9 , f c9 , respectively, as function of energy are shown in Fig. 3. From these data the contrast ratio between ASAXS and MASAXS observed in Fig. 1 can be directly deduced. It is interesting that this ratio is larger than the dichroic effect at E 57243 eV observed in absorption due to the large contribu-
FIG. 5. MASAXS obtained at the Gd L 3 edge above ~L! and below ~d! the orbital plane indicating the change of sign of the profile with circular degree of polarization.
tion of f 8c . However, similar enhanced effects have also been observed in magnetic resonant scattering in Ni.5 Characteristic features of X-MCD can be manifested by performing the MASAXS at the corresponding spin-orbit split L 2 edge of Gd. Taking into account the different values for ^ s z & at the L 3,2 edges their should be a change in sign of the scattering profile comparing the results at the L 3,2 edges. The MASAXS profiles shown in Fig. 4 exactly follow this feature as the direction of magnetization ~N and S! has to be reversed ~S–N! at the L 2 edge in order to yield the same sign of the profile compared to the L 3 edge ~N–S! and the scattering intensity at the L 2 edge is decreased compared to the L 3 edge as expected. As the dichroic signal depends on the relative orientation of the circular polarization photons and the magnetization of the sample MASAXS spectra taken with reversed photon helicity, i.e., above and below the orbital plane ~see Fig. 5! proof again a change of sign as expected. IV. OUTLOOK AND CONCLUSION
Magnetic small angle x-ray scattering is a new technique, which allows valuable insights into structural characteristics of magnetic particles in granular systems and diluted alloys on a nm scale. Additional support to establish reliable models of the magnetic structures will be provided by magnetic imaging techniques allowing a quantitative information on the local magnetization with high resolution.6 ACKNOWLEDGMENT
This work was supported by the German federal ministry of education, science, research and technology ~BMBF! Project No. 05-621-WAA-6. 1
G. Schu¨tz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G. Materlik, Phys. Rev. Lett. 58, 737 ~1987!. 2 B. T. Thole, P. Carra, F. Sette, and G. van der Laan, Phys. Rev. Lett. 68, 1943 ~1992!; P. Carra, B. T. Thole, M. Altarelli, and X. Wang, ibid. 70, 694 ~1993!. 3 H.-G. Haubold et al., Rev. Sci. Instrum. 60, 1943 ~1989!. 4 H. Nizam, diploma thesis, University of Augsburg, Germany ~1996!. 5 J. Hunecke, dipolma thesis, University of Munich, Germany ~1990!. 6 P. Fischer, G. Schu¨tz, G. Schmahl, P. Guttmann, and D. Raasch, Z. f. Phys. 101, 313 ~1996!.
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