RAPID COMMUNICATIONS PHYSICAL REVIEW B VOLUME 58, NUMBER 8 15 AUGUST 1998-II X-ray magnetic linear dichroism in absorption at the L edge of metallic Co, Fe, Cr, and V M. M. Schwickert Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 G. Y. Guo Daresbury Laboratory, Warrington, Cheshire WA4 4AD, United Kingdom M. A. Tomaz Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 W. L. O'Brien Synchrotron Radiation Center, University of Wisconsin-Madison, 3731 Schneider Drive, Stoughton, Wisconsin 53589 G. R. Harp Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 Received 17 February 1998; revised manuscript received 26 May 1998 It is demonstrated that x-ray magnetic linear dichroism XMLD in absorption spectroscopy is a viable technique for element-specific magnetic characterization of metallic thin films and multilayers. XMLD is measured at the Fe, Co, Cr, and V L2,3 edges, and varies from 1­11% of the edge jump in the absorption coefficient, with a magnitude that scales with the square of the magnetic moment. The XMLD spectra show satisfactory agreement with first principles calculations of this effect. S0163-1829 98 50832-6 Because of its element specific nature, synchrotron based than the XMLD fraction (n n )/(n n ) 2 here x-ray magnetic dichroism1­3 has become an important tool n ( ) is the hole occupation number of the spin up down for the study of magnetic moments in alloys and multilayers. bands . For example, in bulk Fe the peak XMCD at the 2p The most common dichroism variants magnetic circular di- edge is 150% normalized to the edge jump , while we chroism in photoemission MCD ,4 x-ray magnetic circular show here that the peak XMLD is only 8%. dichroism in x-ray absorption XMCD ,1,3 and magnetic lin- Another subtle difference between XMCD and XMLD is ear dichroism in the angular distribution of electrons elucidated by Ref. 12. There dichroism spectra are decom- MLDAD ,5 are sensitive to the average magnetization M posed into components arising from Sz labeled w011), of a particular species and are useful for the study of ferro- Lz (w101), and so forth. At the L2 edge of Fe, both 2p1/2 magnetic or ferrimagnetic systems. A second class of dichro- multiplets contribute positively to the Sz component of the ism techniques are sensitive to M2 specifically, magnetic XMCD. Comparatively, these multiplets have equal and op- linear dichroism in photoemission MLD ,6 the transverse posite contributions to the Sz component of the XMLD. magnetooptic Kerr effect T-MOKE Ref. 7 and its x-ray Therefore to measure Sz with XMCD, one needs only to absorption analog,8 and x-ray magnetic linear dichroism in distinguish the L3 and L2 edges separated by 13 eV in Fe . x-ray absorption XMLD Refs. 2 and 9 . These provide The same measurement by XMLD is more difficult, since it greater opportunity for the study of antiferromagnetic AF requires resolution of the individual multiplet states sepa- systems. rated by 1 eV). Here we focus on XMLD, which measures changes in the To make matters worse, each multiplet has an intrinsic x-ray absorption coefficient. As such, it does not require an broadening that is inversely proportional to the core-hole electron spectrometer, and is experimentally less demanding lifetime. In the solid state the atomic multiplets are further than photoemission techniques such as MCD, MLDAD, and broadened into bands. Thus, if the core-hole lifetime is short MLD. Furthermore, XMCD and XMLD spectra are now or the hybridization strong, the Sz component of the well understood in terms of sum rules10­13 which permit their XMLD spectrum is strongly suppressed. This is exactly the decomposition into components arising from Sz , Lz , etc. situation in transition metal TM systems, hence XMLD As compared with XMCD, XMLD has the additional advan- may not be measurable in a metal.16 Indeed, the two extant tage that it uses linearly polarized radiation, since the most studies reporting nonzero TM XMLD have focused on metal commonly used synchrotron radiation sources are linearly oxides,2,9,17,18 where the multiplet peaks are narrow and well polarized, and the extraction of circularly polarized radiation separated.20 from such sources usually incurs a significant loss of Here we present the first XMLD spectra taken at the L intensity.14 edge of Co, Fe, Cr, and V metallic thin films and However, until now there have been only two reports us- multilayers.19 These are shown to be in satisfactory agree- ing XMLD2,9 as compared with dozens using XMCD, partly ment with first principles calculations of this effect. We because most work has focused on ferromagnetic systems. In verify the XMLD equivalent of the ``transferability a ferromagnetic transition metal15 the XMCD fraction of the approximation'' 22 in XMCD, wherein the magnitude of the absorption coefficient (n n )/(n n ) is larger XMLD when normalized to the edge jump is proportional 0163-1829/98/58 8 /4289 4 /$15.00 PRB 58 R4289 © 1998 The American Physical Society RAPID COMMUNICATIONS R4290 SCHWICKERT, GUO, TOMAZ, O'BRIEN, AND HARP PRB 58 FIG. 1. The x rays strike the sample surface at normal incidence. The easy (e) and hard (h) axes are perpendicular and parallel, respectively, to the in-plane component of the applied magnetic field Ref. 28 . X-ray absorption spectra are taken with M parallel and perpendicular to the polarization axis . to M2 . Also presented is an approach for the measurement of XMLD spectra that simplifies experimental requirements by taking advantage of magnetocrystalline anisotropy in ep- itaxial thin films. This paper focuses on four samples prepared by sputter deposition as described elsewhere23 with structures: A, 25 Å Fe/200 Å Fe/50 Å FeCo/50 Å Co @ 250° C; B, 25 Å Fe/200 Å Fe @ 300 °C; C, 25 Å Cr/15 Å Cr/ 1.5 Å Cr/7.5 Å Fe 40@100 °C; D, 25 Å Cr/15 Å Cr/ 1.5 Å V/7.5 Å Fe 40@100 °C; MgO 110 substrates were used. The first 25 Å layer of ei- ther Fe or Cr was grown at 600 °C to enhance pseudo- FIG. 2. X-ray absorption spectra for Co sample A), Fe B, C, epitaxial growth and each film was capped with 20-Å Al to and D), Cr (C), and V (D) at the 2p absorption edges. In each prevent oxidation. Specular x-ray diffraction showed that the case, the lower curve shows the XMLD spectrum obtained from the films were epitaxial, with a bcc 112 orientation see Refs. absorption spectra, scaled as indicated. 23 and 24 , except for the topmost Co layer of sample A, which had an hcp 100 texture.25 All samples showed a a bending magnet source with a total electron yield tech- strong uniaxial magnetic anisotropy. Easy and hard magnetic nique. Data were taken in applied magnetic fields sufficient axes were determined by magneto-optical Kerr effect to saturate the magnetization along the hard axis M * MOKE magnetometry see, e.g., Refs. 23 and 24 and hard 1, H axis saturation fields were all 1000 Oe. Each sample x 1000 Oe), and in zero applied field with the mag- showed negligible remanence along its hard axis, indicating netization relaxed to the easy axis ( M * 0). To neutralize circular dichroism effects due to sample a 90° change in magnetization direction between saturation misalignment, or any other potential asymmetry in the appa- and zero applied field.26 ratus, measurements were taken in the sequence of Since XMLD is maximized when the magnetization is switched by 90° between parallel and perpendicular to the H ,0 ,H ,0 , . . . , applied field. Here H refer to H x ap- plied along the positive or negative x axis, while 0 indi- photon polarization, , it usually requires two electromag- cates the remanent state following saturation in the direc- nets. Here we eliminate one electromagnet by exploiting the tions. Magnetization directions were switched at each photon magneto-crystalline anisotropy27 in our epitaxial films, as shown in Fig. 1. Samples are mounted with the magnetic energy. The absorption spectra H and H or 0 and 0 ) were averaged to give the absorption spectra ( ) or hard axis, (h), parallel to the polarization axis, , which is ( ) .30 also parallel to the x component of the applied magnetic Figure 2 displays the absorption curves at the Co, Fe, Cr, field,28 H x (h H x x ). The sample easy axis, (e), is and V 2p edges. The linear dichroism, defined as ( aligned along y . The synchrotron radiation strikes the sample ), is clearly measurable in all cases. To obtain a quan- with normal incidence. This nullifies any signal arising from titative measure of the XMLD, we define circular dichroism or T-MOKE.29 Since the sample is fixed relative to the incident beam and the magnetization is rotated XMLD max max , 1 XMLD of the first kind , these measurements have no con- tribution from the crystal field.9,21 where is the step height far above the L edges see ex- The measurements were made at the Synchrotron Radia- ample in Fig. 2 as described in Refs. 31 and 22 dichroism tion Center in Madison, Wisconsin. Photoabsorption experi- signal scaled to a per-atom basis . This particular but arbi- ments were made using 90% linearly polarized light from trary choice was made since an integral of the XMLD over RAPID COMMUNICATIONS PRB 58 X-RAY MAGNETIC LINEAR DICHROISM IN . . . R4291 FIG. 4. XMLDmax Eq. 1 is compared with M2 for the elements studied here. The two kinds of symbols represent two sets of measurements taken on different beamlines with different photon energy resolutions. The line fit indicates XMLDmax 1.88*M2( 2B) with correlation coefficient R2 0.96. While Cr and V are not normally magnetic at room temperature, they have previously been shown to acquire the stated magnetic moments in multilayers with Fe Refs. 23 and 24 . 0.87 B V for Fe5 /V1. The calculated magnetic anisot- ropy energies show that both multilayers have a uniaxial in-plane anisotropy with the easy axis along 11¯0 and the hard axis along 111¯ in agreement with experiment. The theoretical absorption and XMLD spectra plotted in Fig. 3 have been Lorentzian broadened to take the finite core-hole lifetime into account. The broadening used here is slightly smaller than that used in previous calculations,21 which re- flects the high photon energy resolution of the experimental measurements. FIG. 3. Theoretical x-ray absorption and XMLD spectra solid lines from the structures discussed in the text. For comparison, the The overall magnitude and shape of the theoretical Fe and respective experimental XMLD spectra are plotted on the same V spectra Fig. 3 agree reasonably well with the measured scale markers . ones. Further calculations showed that the shapes of the Cr and V XMLD spectra are sensitive to the Fe-Cr or Fe-V any edge would identically cancel out the contribution from interlayer spacing. Thus, the differences in the shapes of the the spin or orbital moments.12 Furthermore, we found experi- experimental and theoretical Cr or V XMLD spectra may mentally that because of the difficulty of getting a perfectly reflect the structural differences between the experimental flat baseline with in-field measurements, XMLD integrals and theoretical multilayers. could not be reliably distinguished from zero to within ex- The sum rules for XMLD provide no information regard- perimental error. ing the spin or orbital moment.12 To quantify M2 measure- Theoretical XMLD spectra Fig. 3 were calculated within ments, we propose an approach analogous to the determina- the itinerant one-electron model from the spin-polarized rela- tion of M from XMCD in Refs. 23, 24, and 33. First, the tivistic band structures of bcc Fe5Cr1 and Fe5V1 112 absorption curve from a sample is compared with that of a multilayers.20,25 The band structures were calculated self- standard, and they are put on the same scale. Then the consistently using the relativistic linear muffin-tin orbital sample XMLD magnitude is compared with that of the stan- method based on the first principles local spin-density func- dard, resulting in a measure of M2 . For this process to tional theory LSDA see Refs. 20 and 21 and references succeed it is important that the XMLD spectrum does not therein . The orbital polarization as implemented in Ref. 32 change in shape but only in magnitude between the sample which corrects the errors in the orbital magnetic moments and standard. In Fig. 2 it is seen that the three Fe spectra given by the standard LSDA calculations, was included. studied here have the same shape, which bodes well for this Ideal bcc 112 superlattices were assumed and the experi- approach. mental bcc Fe lattice constant was used for the in-plane lat- Another useful analysis of XMCD spectra uses the tice constants. ``transferability approximation'' 22 whereby it is possible to For the Fe5 /V1 multilayer, the Fe-V interlayer spacing compare magnetic moments in different elements by compar- was expanded by 8.3% to take into account the larger V ing suitably scaled XMCD spectra. This method is especially atomic volume. The calculated total magnetic moments are helpful in systems where the number of valence band holes 2.27 B Fe , 0.70 B Cr for Fe5 /Cr1, and 2.20 B Fe , is not known. In Fig. 4 we test the analogous approximation RAPID COMMUNICATIONS R4292 SCHWICKERT, GUO, TOMAZ, O'BRIEN, AND HARP PRB 58 for XMLD. The experimental XMLD a more difficult test for theory, and the combination of high max for each element is plotted versus M2 , as determined by XMCD. XMLDmax is quality experiment and theory promises to reveal more infor- shown to be highly correlated to M2 , in agreement with mation regarding the spin-polarized band structure in the in- expectation. vestigated metals. For the first time, XMLD is measured in metallic transi- tion metals. Signal levels up to 11% of the absorption step The authors gratefully acknowledge support by the Na- height are obtained. A comparison with theory shows favor- tional Science Foundation CAREER Award No. DMR- able agreement. Since XMLD measures M2 it is especially 9623246. The Synchrotron Radiation Center is supported by favorable for antiferromagnetically coupled systems. As the NSF under Award No. DMR-9212658. M.M.S. was noted above, XMLD spectra have much more fine structure partly supported by the Condensed Matter and Surface Sci- than analogous XMCD spectra. Thus XMLD spectra provide ence Program of Ohio University. 1 J. L. Erskine and E. A. Stern, Phys. Rev. B 12, 5016 1975 . 22 M. G. Samant et al., Phys. Rev. Lett. 72, 1112 1994 . 2 G. van der Laan et al., Phys. Rev. B 34, 6529 1986 . 23 M. A. Tomaz et al., Phys. Rev. B 55, 3716 1997 . 3 G. Schu¨tz et al., Phys. Rev. Lett. 58, 737 1987 . 24 M. A. Tomaz et al., J. Phys.: Condens. Matter 9, L179 1997 . 4 L. Baumgarten et al., Phys. Rev. Lett. 58, 737 1987 . 25 The crystal structure of the cobalt film was not sufficiently well 5 Ch. Roth et al., Phys. Rev. Lett. 70, 3479 1993 . characterized to undertake a calculation of the XMLD to com- 6 Ch. Roth et al., Solid State Commun. 86, 647 1993 . pare with this sample. Since preliminary calculations Refs. 20 7 J. Voss et al., J. Electron Spectrosc. Relat. Phenom. 80, 329 and 21 have already shown that the XMLD effect can depend 1996 . on the crystal structure, we don't expect the present experiment 8 F. U. Hillebrecht et al., Phys. Rev. Lett. 58, 2224 1995 . to agree with previous results. 9 P. Kuiper et al., Phys. Rev. Lett. 70, 1549 1993 . 26 10 Although remanence in these films may not be a single domain B. T. Thole, Paolo Carra, F. Sette, and G. van der Laan, Phys. state, the predominant orientation of the magnetization is along Rev. Lett. 68, 1943 1992 . 11 the easy axis apart from the rather small volume in the domain Paolo Carra et al., Phys. Rev. Lett. 70, 694 1993 . 12 G. van der Laan, Phys. Rev. B 55, 8086 1997 . boundaries . Since XMLD is sensitive only to M2 , the multi- 13 G. van der Laan, Phys. Rev. B 57, 112 1998 . domain nature of the film is unimportant. 27 14 Elliptical or helical undulators, on the other hand, are very effec- We point out that while the uniaxial magnetic anisotropy was tive sources of circularly polarized light. employed to rotate the magnetization, it is not a necessary re- 15 Note that this statement is not necessarily true for rare earth ma- quirement for XMLD. We have recently observed the XMLD terials, see, e.g., J. B. Goedkoop, B. T. Thole, G. van der Laan, effect in fourfold symmetric Fe 100 and Ni 100 samples when G. A. Sawatzky, F. M. F. de Groot, and J. C. Fuggle, Phys. Rev. magnetized along their easy axes M. M. Schwickert et al. to be B 37, 2086 1988 . published . Furthermore, we emphasize that XMLD is readily 16 By comparison, XMLD effects are much larger in the gas phase, observed in thick films ( 1000 Å) hence is a ``bulk'' effect, where the orbital moment is not quenched. See, e.g., A. von dem and is not predicated on the symmetry breaking of a surface or Borne et al., Phys. Rev. Lett. 78, 4019 1997 . interface. 17 One previous study of bulk Ni found negligible XMLD J. Vogel 28 The apparatus was originally designed for XMCD, hence the and M. Sacchi, Phys. Rev. B 53, 3409 1995 . This was prob- magnetic field was actually applied at 45° with respect to the ably due to the small Ni magnetic moment and the relatively surface normal when the sample is aligned perpendicular to the high noise levels in that experiment. incident x-ray beam. However, due to large demagnetization 18 Several studies have reported XMLD in rare earth systems, see, fields in these samples, the magnetization never departed from e.g., J. Vogel and M. Sacchi, J. Magn. Magn. Mater. 150, 293 the sample plane by more than 4°. 1995 ; Surf. Sci. 365, 831 1996 . 29 Recall that T-MOKE is the change in the reflection coefficient of 19 XMLD has two realizations.20,21 XMLD of the ``first kind'' em- p-polarized x rays depending on the magnetization direction ployed here measures the change in absorption coefficient while Ref. 8 . the magnetization direction is alternated between parallel and 30 Due to a difference in detection efficiency for in-field and rema- perpendicular to the photon polarization. This is a purely mag- nent measurements, ( ) were multiplied by a constant fac- netic effect, and is directly proportional to M2 . XMLD of the tor to put them on the same scale as ( ). Additionally, a ``second kind'' holds the magnetization fixed while the photon polarization is alternated. XMLD of the second kind contains quadratic polynomial curve was sometimes subtracted from the contributions from nonmagnetic sources, such as of the quadru- dichroism spectrum, whenever the difference between and pole moment of the electron charge distribution. spectra deviated in the region before the L3 or far beyond the 20 G. Y. Guo, H. Ebert, W. M. Temmerman, and P. J. Durham, L2 edges. Such corrections were usually small, and the resulting Phys. Rev. B 50, 3861 1994 . spectra were highly reproducible, even on different beamlines. 21 31 G. Y. Guo, H. Ebert, W. M. Temmerman, and P. J. Durham, in J. Sto¨hr, NEXAFS Spectroscopy, Springer Series in Surface Sci- Metallic Alloys: Experimental and Theoretical Perspectives, ed- ences Vol. 25 Springer, Heidelberg, 1992 . ited by J. S. Faulkner and R. G. Jordan Kluwer Academic, 32 G. Y. Guo, Phys. Rev. B 55, 11 619 1997 . Dordrecht, 1994 . 33 M. A. Tomaz et al., Phys. Rev. B 56, 5474 1997 .