VOLUME 85, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 4 DECEMBER 2000 Quantification of Magnetic Domain Disorder and Correlations in Antiferromagnetically Coupled Multilayers by Neutron Reflectometry Sean Langridge and Jörg Schmalian* Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom C. H. Marrows, D. T. Dekadjevi, and B. J. Hickey Department of Physics and Astronomy, E. C. Stoner Laboratory, University of Leeds, Leeds LS2 9JT, United Kingdom (Received 20 May 1999) The in-plane correlation lengths and angular dispersion of magnetic domains in a transition metal multilayer have been studied using off-specular neutron reflectometry techniques. A theoretical frame- work considering both structural and magnetic disorder has been developed, quantitatively connecting the observed scattering to the in-plane correlation length and the dispersion of the local magnetization vector about the mean macroscopic direction. The antiferromagnetic domain structure is highly verti- cally correlated throughout the multilayer. We are easily able to relate the neutron determined magnetic domain dispersion to magnetization and magnetoresistance experiments. PACS numbers: 75.70.Cn, 75.25.+z, 75.70.Pa It has become commonplace that magnetic multilayers typically 1 mm [19]). Since the neutrons are highly comprising 3d ferromagnetic layers interleaved with non- penetrative the measurements also sample the whole mul- magnetic spacers exhibit giant magnetoresistance (GMR) tilayer vertically, unlike, for example, the transition metal for appropriate thicknesses of spacer layer [1]. These are LIII x-ray measurements [20], which sample primarily the the regimes of the oscillatory interlayer coupling [2] where uppermost interfaces because of the high x-ray absorption the ground state is an antiferromagnetic (AF) alignment of coefficient. neighboring layer magnetizations. The change in resistiv- A further complication is that magnetization is a vec- ity arises from the spin dependent scattering of the con- tor quantity and so is able to display a greater variety of duction electrons which depends not only on the magnetic different types of disorder than a structural surface, repre- moment alignment but also on the interfacial disorder [3] sented mathematically by a scalar function. A uniformly and the details of the magnetic domain structure. For magnetized layer having a structurally rough interface will example, it is clear that a vertically incoherent magnetic also have a magnetic surface which deviates from an ideal domain structure will have the effect of lowering the GMR plane, and is said to possess magnetic roughness [21]. On by preventing perfect AF alignment in adjacent layers [4]. the other hand, a nonuniform distribution of magnetization The determination of the properties of buried layers and direction is termed a domain structure and is also a form interfaces is a long-standing experimental problem in the of magnetic disorder. Both these types of disorder will study of heterostructures such as these multilayers. The give rise to off-specular magnetic scatter, and care must be investigation of structurally rough interfaces is now well taken to distinguish these experimentally. established and makes use of diffuse x-ray scattering tech- Co Cu multilayers of 50 bilayer repeats, with Cu spacer niques. The theoretical tools for analyzing various in- thicknesses corresponding to both of the first two AF re- terface morphologies are well advanced [5­8]. Recent gions of the coupling oscillation [2], were deposited by advances in x-ray techniques have applied this structural dc magnetron sputtering at 3 Å s in 3 mTorr of Ar. The formalism to the study of "magnetically rough" systems reflectivity measurements were performed on the time-of- [9­15]. Nevertheless, the problem of quantifying mag- flight polarized neutron reflectometer CRISP at the ISIS netic disorder by this method remains difficult, primarily facility [22,23]. To maximize the flux the reflectometer due to the indirect and complicated nature of the spin- was run in the nonpolarized mode with an incident wave- photon interaction [16,17]. Using neutron techniques, for length range of 0.5­6.5 Å. An electromagnet at the sample which the interaction between the neutron's dipole mo- position provides an in-plane reversible field of 67 kOe. ment and the sample magnetization is simple and direct, The scattered neutrons are detected by a one-dimensional this problem can be resolved. 3He detector. The combination of the time-of-flight tech- In this Letter we report on neutron scattering mea- nique and the multidetector ensure that both the parallel surements on magnetically coupled multilayers and the (QZ) and perpendicular (QX) (to the surface normal) com- quantitatively determined field dependence of the domain ponents of the neutron wave-vector transfer (see Fig. 1) distribution. The large lateral coherence length of the are obtained in a single measurement. Typical acquisi- neutron beam, .30 mm [18], ensures that the measure- tion times are of the order of 2 h for an entire reciprocal ments sample many magnetic domains, often not the case space map, which compares favorably with resonant x-ray with even advanced synchrotron sources (coherence length techniques [20]. 4964 0031-9007 00 85(23) 4964(4)$15.00 © 2000 The American Physical Society VOLUME 85, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 4 DECEMBER 2000 Figure 1(a) shows the observed reciprocal space inten- The narrow width in QZ (see inset) implies that the AF sity map for the nominal Co 20 Å Cu 20 Å 3 50 mul- order is coherent throughout the whole multilayer. tilayer at remanence. This Cu thickness corresponds to the A major conclusion of this paper results from the com- second AF peak in the oscillatory exchange coupling. Al- parison of the QX distribution of the two peaks. The though we have similar data for other layer thicknesses nuclear Bragg peak is sharp but the AF peak, entirely mag- we concentrate on this sample in this Letter. Three fea- netic in origin, is diffuse. The low structural roughness tures are apparent in the data: the specularly reflected is consistent with the results of conventional x-ray stud- ridge (QX 0 Å21), the first order nuclear Bragg peak ies of similar samples, where rms roughnesses as low as (QZ 0.15 Å21), and the 1 1 Å were found [24]. When at saturation [Fig. 1(b)] the 2 order Bragg peak correspond- ing to the AF periodicity (QZ 0.075 Å21). The nuclear diffuse scatter is very weak over the entire QZ range in Bragg peak indicates that the bilayer thickness is 42 Å. question, and so we associate the diffuse scatter around the magnetic peak in Fig. 1(a) with the existence of AF cou- pled domains. In contrast, in a study of Fe Cr multilayers the magnetic diffuse scatter moved from around the AF 12 order peak into diffuse scatter around the first order peak on application of a saturating field [25]. Sinha has shown that this is due to the presence of magnetic roughness, not domains, as domain disorder is swept out by a saturating field [26]. The diffuse scattering is strongly peaked in QZ, giving evidence for the coherent coupling of the magnetic do- mains vertically through the multilayer. No evidence for diffuse scattering from uncorrelated regions was observed which would be uniformly distributed in QZ [27]. Ap- plying a saturating field [Fig. 1(b)] destroys the AF cor- relations resulting in a ferromagnetic alignment of adja- cent Co layer moments. Figure 2 details sections in QX through the AF Bragg peak as the field is applied. At low fields (,100 Oe) the diffuse scatter dominates. As the field is increased to saturation only the specular ridge re- mains. Equivalent sections through the nuclear Bragg peak reveal no evidence of diffuse scattering at any field. In order to quantitatively analyze our data a theo- retical framework for diffuse magnetic scattering in systems with both structural and magnetic disorder is required. Considering a system where the magnetization profile m r is constrained to lie in the sample plane due to the shape anisotropy, we can write m r MCo cosf r , sinf r , 0 , with f r being the local di- rection of the magnetization, which is of magnitude MCo. Thus, we consider solely directional variations of m r which describe the different orientations of the magnetic domains. We treat f r as a random variable, charac- terized by the correlation function M jrj f r f 0 . f r plays a role reminiscent of the local height variation in the structural model of Sinha [5], and we parametrize M r as FIG. 1 (color). (a) The observed scattering from the Co 20 Å Cu 20 Å 3 50 multilayer in zero applied field. M r s2 The intensity centered at Q me 2r jm . (1) Z 0.075 Å21 corresponds to the AF ordering wave vector and arises purely from the magnetic sm f2 is the width of the angular distribution and ordering. The intensity at twice this wave vector is the first order therefore characterizes the magnetic domain disorder. jm multilayer structural Bragg peak. The dark areas represent the is the lateral correlation length, i.e., a measure of a typical kinematical limits of the measurement. (b) The corresponding domain size. Structural roughness is included following measurement in a saturation field of H 700 Oe. The nuclear the formalism of Sinha [5]. We consider the magnetic peak appears wider than the specular ridge at low QZ since the instrumental resolution in Q scattering function within the Born approximation, S Q ~ X degrades as the reciprocal of the P R neutron wavelength. The inset shows the specular reflectivity ab d3r eiQ?r dab 2 Qa Qb ma r mb 0 , where Qa for the low (open symbol) and high (closed symbol) field data. is a unit vector component of the transferred momentum, 4965 VOLUME 85, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 4 DECEMBER 2000 distribution, as the neutron spin-magnetization interaction is explicitly included. This was not possible in previous work [25,28,29], where straightforward adaptations of structural models [27,30] were used. In our experimental geometry the detector aperture is set up such that the neu- tron intensity is integrated out over QY, which is parallel to the applied field. Finally, when evaluated at the AF ordering vector, it holds that m0 ~ sin u 2 , where u is the angle between Co moments in adjacent layers. In the kinematic picture, the intensity of the 12 order Bragg peak is proportional to m20. We remark in passing that, within the Gaussian approximation, we treat the angle f r , normally restricted to between 6p, as an unrestricted variable. Therefore, the model will only approximately describe a system with equally distributed angles. The results of numerically convoluting the specular and diffuse [Eq. (2)] contributions with the instrumental resolution function and of performing a least-squares fit to the data are shown in Fig. 2 as the solid lines. To extract the structural - and hence implicitly the magnetic - FIG. 2. The diffuse scattering observed at the AF peak (QZ correlated roughness parameter we have fitted the specular 0.075 Å21) as a function of applied field. Each scan is offset reflectivity at saturation, where the sample is in a single for clarity. The lines are fits to the data. The lowest scan (solid domain state, i.e., s symbols) is an equivalent section through the nuclear peak at m 0 and jm . The structural saturation (Q roughness ss 3 6 1 Å extracted is consistent with Z 0.15 Å21), the width of which is independent of field. previous x-ray results [31]. At this level no diffuse scattering from the structural roughness is observable in Q. Performing the average with respect to the different our experimental data -the width of the specular ridge domain orientations by assuming a Gaussian distribution is determined by instrumental resolution. This structural for f r , we find in addition to the specular scattering, parameter has been used in all the fits at lower fields to S ensure we are varying only the domain structure within spec Q 4p2Dd Qk , the diffusive scattering function our model. We have found that the domain disorder is by Z far the main contribution to the diffuse scatter at all fields Sdiff Q D d2r eiQk?r s 1 m 1 sm , (2) below total saturation. In Fig. 3 we show various magnetic quantities for our where the terms in square brackets correspond to three dif- sample as a function of applied field. Panels (a) and (b) dis- ferent diffuse scatter contributions, arising from structural play the magnetization loop as measured by magneto-optic inhomogeneities, magnetic inhomogeneities, and the inter- Kerr effect (MOKE) and the normalized change in resistiv- ference between them. The joint Debye-Waller factor, D, ity (GMR), respectively. The large GMR indicates a high is expressed as m20e2 Q2Zs2s1s2m ; m0 is the antiferromag- degree of AF alignment around the coercive field. The netic order parameter, discussed below. The amplitudes final three panels indicate quantities derived from our fits of the structural and magnetic inhomogeneities are given to the neutron diffuse scatter. For fields close to rema- by s2s C 0 and s2m M 0 , with the usual structural nence the Co layers have a global antiparallel alignment correlation function C r s2se 2r js . Qk is the in-plane (c) with a wide distribution of domain directions (d) and a component of Q. characteristic domain size of 1 mm (e). As the field is The terms in square brackets in (2) correspond to the applied three effects occur in order, but with considerable three diffuse scatter contributions, with the structural and overlap: the antiparallel alignment across the nonmagnetic magnetic parts expressed as spacer is diminished, the orientational domain distribution s e Q2 within a given layer focuses around the applied field di- Z C r , (3) rection, and at field higher than the coercivity the domains m 1 2 Q2X sinh M r enlarge to 7 mm. Above 200 Oe there still remains 1 1 2 Q2 a substantial domain distribution, although the orientation Y cosh M r 2 1 . (4) of adjacent layers is nearly ferromagnetic (m0 ! 0). At The first of these three diffuse scattering terms is entirely these fields the diffuse scattering approaches the experi- equivalent to that derived by Sinha. The second corre- mental background (primarily from incoherent scattering) sponds to domain distributions, while the final cross term and represents the limits of the current measurements. For contains the magnetic roughness. The use of this formula this reason we cannot measure values of sm close to zero allows us to quantify the diffuse scatter due to a domain as saturation is approached. The data clearly show the 4966 VOLUME 85, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 4 DECEMBER 2000 tionship between domain disorder, domain size, interlayer coupling, and the GMR effect itself. The authors gratefully acknowledge fruitful discussions with M. Sferrazza, J. R. P. Webster, J. Penfold, S. W. Lovesey, A. I. Goldman, and S. K. Sinha. C. H. M. thanks the Royal Commission for the Exhibition of 1851 for financial support. 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