VOLUME 198, Nos. 1-3 ISSN 0921-4526 APRIL I 1994 held in Dubna, Russia 24-29 June 1993 Guest Editors: H.J. Lauter V.V. Pasyuk PHYBE3 198 (1-3) 1-266 (,1994) ~ ELSEVIER Physica B 198 (1994) 150-155 Forward scattering of neutrons from polymeric and magnetic m ul tila yers G.P. Felcher Ar,f(fl/IIIl' Nutill1/a/ Lahll/,atllr!, Ar,f(III/I/l', JL 6(14-~9, USA Abstract Grazing incidence neutrons are not only reflected and refracted from imperfect layers. but also partially scattered by lateral dishomogeneities. In general. scattering may take place both in the reflection plane ("forward scattering") and out of it. The forward scattering from multilayers is highly structured in ridges. whose maxima can be indexed in terms of the multilayer spacings. In experiments on diverse diblock copolymers, two kinds of ridges were found. either at constant-k: loci or else at constant-q: loci. The relative intensity of the ridges appears to be related to the type and size of imperfections of the lamellar structure. Constant-q: streaks of magnetic nature were also found in the forward scattering of metallic superlattices (Fe/Cr. Co/Ru, Fe/Nb) in the antiferromagnetic state. Here the diffuse scattering appears around the antiferromagnetic peaks while they are absent from the structural peaks. as if the crystalline superlattice were to partition into antiferromagnetic domains of limited lateral extension and columnar character. Introduction several microns can be observed. These objects are two orders of magnitude larger than those observ- In grazing incidence geometry neutrons are able in other small angle scattering geometries. The either refracted or specularly reflected from an present note is concerned with the phenomenology exactly planar sample. At an angle of incidence ();, of this kind of scattering -which shall be named and for a neutron wavelength ;., the component of f()r"'ard scatteri/1?J -from imperfect multilayers. the incident wave vector perpendicular to their The data presented here were collected at two surface is k=; = 27tsin fJ;/;.. Similarly, for the exit POSY reflectometers [5] at the Intense Pulsed beam kzr = 27t sin Or/;.. The scattering vector is sim- Neutron Source at Argonne National Laboratory. ply q= = k=i + k=r. From the intensity reflected as In both instruments a pulsed beam of neutrons, of a function of q= the depth profile of the material all wavelengths in the thermal range, are brought may be obtained with great accuracy [I, 2]. When onto the sample at an angle Oj. Position-sensitive the sample's planes are not perfect (because the detectors record the neutrons reflected at ()r = 0; (as surface or some interfaces are rough, or the layers well as the scattered neutrons at Or :;C Oj) as a are undulated, or the layers are marred by im- function of their time-of-flight from the source, purities), neutrons are also scattered: the scattering and thus of their wavelength. The detectors are may take place in the plane of reflection (defined by position-sensitive only along one direction (increas- the angle of incidence fJ; and reflection Or ), or else at ing 0) and in practice integrate over A.910 ...;;- "0 * -IIJ 0,0 .. Fig 3. Contour plot of the neutron intensities forwardly scattered from a sputtered multilayer of Fe/Cr. The thickness of the Fe layers is 30 A, that of Cr is 10 A. The magnetic structure is antiferromagnetic, and it gives rise to the intensity scattered at q= -0.075 A I. At twice this value the Bragg reflection due to the modulation in material composition is visible. surface layer. In the absence of an external mag- (but the angle of incidence (}j remains constant) the netic field, these moments are likely to point along maximum of J: occurs always for the same value of one of the equivalent crystallographic axes. q:. Under this condition the exit beam makes an The lateral dimensions of the domains observed angle (}r ¥ ()j with the surface and qx becomes finite. for Fe/Cr can be calculated with the help of At the onset of qx, J x rapidly decreases; Lx may be chosen by finding the value of q., at which J x = 0. a simple formula. In the kinematic approximation the diffuse intensity around the antiferromagnetic For instance, for the sample of Fe/Cr giving rise to peak is [16] the scattering of Fig. 3, Lx -0.4 I.1m. (3) 4. Discussion Fluctuations along y were omitted. In Eq. (3), a is The diffuse scattering of magnetic multilayers is the anti ferromagnetic spacing and N z is the number characterized by a constant-q= ridge and yet is not of layers composing the film. ax is a dummy para- due to conformal roughness. Drawing an analogy meter and what is of interest in the .x direction is the with conventional crystallography, conformal total length Lo' = N x ax. At the Bragg reflection roughness merely distorts a single crystal; instead, qx = O and the arguments in J: are multiples of 27t. the antiferromagnet is composed of a collage of When the incident wave vector k = 27t/;, is changed crystallites. It would be interesting to ascertain the G.P. Fell"h('r/Physil"(1 B 11)8111)1)4) I.)() I.).) 155 legitimacy of the multidomain model from the de- tailed q., dependence of the scattered intensity. [4J M. Tolan. G. K6nig. L. Briigemann. W. Press. F.B Brink- op and J.P. Kotthaus. Europhys. Lett. 20 (1992) 223 However, such an analysis would require magnetic [5J A. Karim. B.H. Arendt. R. Goyette. Y.Y. Huang. R. Kleb multilayers in which the distribution of domains and G.P. Felcher, Physica B 173 (1991) 17. was more uniform than in the present sample. [6J G. Coulon. T.P. Russell. V.R. Deline and P.F. Green. In summary, some aspects were shown of the Macromolecules 22 (1989) 2581. [7J S.H. Anastasiadis. T.P. Russell. S.K. Satija and C.F. Maj- forward scattering of imperfect multilayers. From krzak. Phys. Rev. Lett. 62 ( 1989) 1852; J. Chem Phys. 92 the time of Y oneda 's observations a robust work of (1990) 5677. development has taken place [19-21] to explain [8J G.P. Felcher. R.J. Goyette. S. Anastasiadis. T.P. Russell. the features of forward scattering in terms of M. Foster and F. Bates. Phys. Rev. Lett.. submitted. the distorted wave Born approximation. For multi- [9J Y. Yoneda. Phys. Rev. 131 (1963) 2010. [10J D.G. Stearns. J. Appl. Phys. 71 (1992) 4286. layers such an approach might be unwieldy [IIJ D. Bahr. W. Press. R. 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