Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 Polarized-neutron re#ectometry J.F. Ankner , G.P. Felcher * Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Material Science Division, Argonne National Laboratory, Building 223, Argonne, IL 60439, USA Received 25 February 1999; received in revised form 7 April 1999 Abstract Polarized-neutron specular re#ectometry (PNR) was developed in the 1980s as a means of measuring depth-resolved magnetization in #at "lms with characteristic thicknesses from 2 to 5000 As. PNR has been widely used to study homogeneous and heterogeneous magnetic "lms, as well as superconductors. Starting from simple pro"les, and gradually solving structures of greater complexity, PNR has been used to observe or clarify phenomena as diverse as the magnetism of very thin "lms, the penetration of #uxoids in superconductors, and the magnetic coupling across non-magnetic spacers. Although PNR is considered to be a probe of depth-dependent magnetic structure, laterally averaged in the plane of the "lm, the development of new scattering techniques promises to enable the characterization of lateral magnetic structures. Retaining the depth-sensitivity of specular re#ectivity, o!-specular re#ectivity can resolve in-plane structures over nanometer to micron length scales. Presently limited by the neutron #uxes available, neutron re#ectivity is expected to blossom in the next century, thanks to the increased brightness of the neutron beams, due not only to continuing improvements in neutron optics, but especially to the advent of second-generation spallation neutron sources. 1999 Elsevier Science B.V. All rights reserved. PACS: 61.12.He; 78.70.!i Keywords: Re#ectometry; Polarized neutron; Magnetic thin "lms 1. Principles angles of incidence, permits an evaluation of the chemical and magnetic depth pro"le. If the surface The wave properties of the neutron make pos- is corrugated, or if the material under the surface is sible the optical study of matter by means of neu- not laterally homogeneous, the angle of the exiting tron beams [1,2]. As shown in Fig. 1, a beam of neutrons may be di!erent from that of the incom- neutrons is re#ected from a #at, laterally homo- ing beam, either in the re#ection plane ( geneous object. The intensity of the re#ected beam, O ), or out of it ( O0), depending on the geometry of the recorded at di!erent neutron wavelengths and inhomogeneities. The case of specular re#ection is the simplest to treat. The momentum of the neutron, "k""2 / * Corresponding author. Tel.: #1-630-252-5516; fax: #1- (where is the neutron wavelength), can be separ- 630-252-7777. ated into two components, parallel and perpen- E-mail address: felcher@anl.gov (G.P. Felcher) dicular to the surface. Only the perpendicular (z() 0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 3 9 2 - 3 742 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 "le) is more complex, and will be discussed later. However, some simple rules give a #avor of the link between the two quantities. In general, the re#ectivity is unitary for most materials up to a value of QA"(16 Nb of order 0.01 As\. Beyond this limit, the re#ectivity de- creases rapidly with a mean asymptotic Q\ X de- Fig. 1. Glancing angles of incidence ( pendence. For Q ) and exit ( ) characterize X>, R\\, R>\, and R\>. 4 sin The spin-dependent SchroKdinger equation takes QX"kX !kX " (2) a very simple form when all of the magnetic induc- tion in the neutron path is collinear. In this case, provides a convenient metric for characterizing the neutrons remain polarized in the original state specular re#ection process in which incident- and (R>\"R\>"0). Neutrons polarized parallel re#ected-beam wave vectors (k , k ) enter and exit (#) [antiparallel (!)] to H the surface at the same glancing angle [5]. Since  see a potential ;!"( /2m)Nb$ B, where is the neutron momentum QX is the quantum mechanical conju- magnetic moment. The magnetic medium is, in gate to position z, one can transform the depth e!ect, birefringent. Since the strength of the mag- pro"le of scattering material b(z) into re#ectivity netic scattering in ferromagnetic materials is com- R(QX). The inverse process (from re#ectivity to pro- parable to that of the nuclear, an analysis of the J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 743 scattering (Fig. 2a). However, the orientation of an in-plane ferromagnetic layer (Fig. 2b) can be deter- mined by measuring the intensity of spin-#ip rela- tive to non-spin-#ip scattering. When the magnetization is perpendicular to the surface (Fig. 2c), there is no di!erence in refractive index be- tween neutrons polarized parallel and anti-parallel to H. In the specularly re#ected beam, such a sample is indistinguishable from one with no magnetization. The presence of domains and their size distribution strongly a!ects the specularly re- #ected intensity (Fig. 2d). The coherence length of the neutron beam on the surface is about 100 m, larger than the lateral domain size in many sam- ples. These small domains produce signi"cant scat- tering o! the specular beam, which also becomes depolarized. Currently, except in select instances, o!-specular scattering cannot be quantitatively in- terpreted. Obtaining this in-plane structural in- formation is one of the most signi"cant motivations to develop o!-specular scattering techniques and data analysis. Fig. 2. The orientation and magnitude of the sample magneti- zation M(z) relative to the applied "eld H determines the relative proportions of spin-#ip (SF) and non-spin-#ip (NSF) scattering. 2. Instruments (a) M(z) in the plane of the surface, parallel to H produces no SF scattering, but creates di!erent spin-dependent refractive indices A re#ectometer is a simple instrument (Fig. 3) for neutrons polarized parallel and anti-parallel to H. (b) M(z) [8,9]. A neutron beam of wavelength strikes canted at an arbitrary angle in the surface plane produces both SF and NSF intensity. (c) M(z) components normal to the a sample surface at an angle and is re#ected from surface have no e!ect on neutron specular intensity. (d) The the surface at angle . The instrument functions as presence of domains complicates interpretation of SF and NSF a di!ractometer with resolution su$cient to separ- intensities. O!-specular methods o!er a means of characterizing ate transmitted and re#ected beams at values of these domains. QX near where the re#ectivity becomes unitary. Specular re#ectivity ( " ) is solely a function of the momentum transfer along the z(-direction, re#ectivities R>> and R\\ makes possible hence in practice a range of Q a quantitative determination of B(z). Components X is spanned either by changing the wavelength, and keeping "xed the of B perpendicular to a sample surface are not angle of incidence, or by changing the angle of directly detected by specular neutron re#ectivity. incidence at "xed wavelength. Appropriate devices, By analogy with Eq. (3), neutrons are re#ected by such as polarizing mirrors and #at-coil spin #ip- potential gradients across interfaces. Since pers, polarize the incoming neutrons along an ap- e ) B"0, perpendicular components of B are con- plied magnetic "eld or analyze the polarization of stant across a re#ecting interface and therefore do the re#ected beam. Conventionally, the direction of not produce specularly re#ected intensity [7]. initial polarization is "xed. The sample may change Fig. 2 summarizes the phenomenology of the polarization of the neutron and an analyzer magnetic re#ection. A polarized neutron beam chooses, among the re#ected neutrons, those alig- incident on a ferromagnetic layer aligned parallel ned with the polarizer. Reversal of the neutron spin to an external "eld exhibits no specular spin-#ip is obtained by energizing #ippers placed before and 744 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 Fig. 3. Neutron re#ectometers at both "xed-wavelength and broadband sources consist of the same general components: a reactor or spallation neutron source, two slits s and s to de"ne the incident-beam collimation, incident-beam polarizing and spin-#ipping elements, a #at sample on a positioning table, exit-beam polarization analysis, and a position-sensitive or single detector. after the sample. The re#ectivities are then charac- 3. Data modeling terized by the sign of the neutron polarization be- fore and after re#ection with respect to the As outlined above, calculating the specular re- reference "eld: R>>, R\\, R>\, and R\>. #ectivity of polarized neutrons from a sequence of As an example, Fig. 4 plots the spin-dependent homogeneous refracting slabs entails a straightfor- re#ectivity of a multilayer of Fe/Cr in which the ward application of the solution of the one-dimen- magnetization of successive Fe layers is non-col- sional SchroKdinger equation. By selecting "ne linear [10]. The presence of R!8 specular intensity enough depth increments, one can model arbitrar- is a signature of magnetic order perpendicular to ily complex b(z) and B(z). After collecting re#ectiv- the applied "eld. In some circumstances, the inter- ity in the four spin states R>>, R\\, R>\, and pretation of this scattering is straightforward. For R\>, and accounting for such e!ects as back- instance, Fig. 4b exhibits a Bragg re#ection at ground scattering and polarization e$ciency, one QX"0.045 As\, entirely of magnetic origin. The begins with a model of the sample based on prior peak arises from a series of magnetic layers, alter- knowledge of its growth conditions [11,12]. The nately magnetized in opposite directions (AF). The nuclear and magnetic structure of the "lm can then non-spin-#ip (R!!) and spin-#ip (R!8) re#ectivi- be determined by adjusting the parameters of this ties are, respectively, proportional to M, and M,, model to "t the data. the projections of the staggered magnetization par- As an example of this process, consider the allel and perpendicular to the neutron polarization specular re#ectivity of a sputtered (59 As Fe/49 As axis. After making a similar analysis of the fer- Si) romagnetic peak (at Q / glass multilayer shown in Fig. 5. These data X"0.09 As\), one can deter- [13] were taken in saturation, with Fe layer mo- mine the angle between the two sublattice ments aligned parallel to the applied "eld, and magnetizations. For other values of QX, the rela- therefore exhibit no spin-#ip scattering. Fig. 5a tionship between spin-dependent re#ectivities and shows the data from the (##) spin state and Fig. spin structure is not transparent and details of the 5b the (!!). The gray lines result from a model non-collinear structure are obtained by model "t- in which the iron layers exhibit uniform magneti- ting. zation. Note in particular how poorly this model J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 745 Fig. 4. Spin-polarized neutron specular re#ectivity data mea- sured in remanence (H"30 Oe) from two superlattices featur- ing the same layer thicknesses, 52 As Fe/17 As Cr, prepared at two di!erent growth temperatures ¹%. (a) The sample grown at room temperature produces no spin-#ip (SF) scattering and its non-spin-#ip (NSF) intensity is consistent with a model in which successive Fe layers are aligned with the applied "eld. (b) The sample prepared at ¹%"2503C exhibits strong SF scattering which, when modeled with the NSF intensity, reveals that suc- cessive Fe layers align symmetrically with respect to the sample Fig. 5. Spin-polarized re#ectivity data from a [59 As Fe/49 As anisotropy axes (inset) at an unusual angle (from Ref. [10]). Si]/glass multilayer. The Fe layers are aligned with the 300-Oe applied "eld, so there is no spin-#ip scattering. (a) The data taken with neutron polarization parallel to H for a simple model with uniform Fe layer magnetization (gray) and one including layer thickness disorder and 6.2-As thick interfacial magnetic "ts the (!!) data in the vicinity of the second dead layers. (b) The data with the neutron polarization anti- (Q parallel to H are very sensitive to the presence of the magnetic X"0.115 As\) and fourth (QX"0.23 As\) su- perlattice peaks. However, by postulating 6-As- dead layer, particularly the second and fourth superlattice har- thick magnetically dead (or disordered, recall Fig. monics (from Ref. [13]). 2d) layers in the Fe at the Si interface, one achieves a much better "t to the data (black lines). As can be seen from the scattering density pro"les in the in- tion of sample structure. Consequently, very di!er- sets, the presence of the dead layers has little e!ect ent scattering density pro"les may produce specu- on the (##) superlattice intensities, but lar re#ectivities that are statistically similar. There profoundly changes the (!!), e!ectively halving have been a number of recent advances in direct the multilayer periodicity and thereby enhancing inversion of re#ectivity data that, in principle, re- the intensities of even-order superlattice re#ections. tain the phase of r, by means of the addition of two A relatively subtle interfacial e!ect produces a dis- or three reference layers [14}17]. Even if the sample tinct signature in the polarized-neutron re#ectivity to be examined is non-magnetic, it may be conve- data. nient to add a reference layer that is ferromagnetic. As with other scattering techniques, measure- In such a system, the reference layer has di!erent ments of the re#ected intensity R""r" lose the re#ectance when analyzed with neutrons of oppo- phase information required for a unique determina- site polarization state. The practical applicability of 746 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 this approach, to eliminate ambiguities stemming from the non-uniqueness of "tting procedures, is presently the object of intensive research. A brief review will be given in the following sections of the scienti"c themes that have been pursued up to now. There will also be a presenta- tion of those for which the quest has not yet been successful, but which show promise of being solved in the near future. 4. Superconducting 5lms Historically, the "rst published polarized-neu- tron specular re#ectometry (PNR) experiment mea- sured the London penetration depth in a superconductor. The penetration depth charac- terizes completely the diamagnetism of a "lm for applied magnetic "elds below HA, the "eld at which magnetic #ux is expelled from the bulk. Values of the penetration depth determined at dif- ferent laboratories have converged satisfactorily. This is not only true of conventional superconduc- tors, like niobium [18,19], but also of the high-¹ superconductor YBaCuO\V, where measure- ments point to a penetration depth of the order of 1000 As (see Fig. 6) [20,21]. In this respect, PNR now rivals other techniques, such as muon spin resonance. At the same time, analysis of the data allows a veri"cation of the detailed depth depend- ence of the magnetic "eld penetration into the sur- face, up to now assumed to have (with the exception of pure type-I superconductors) ex- ponential form. Above HA, an inhomogeneous state is created in type-II superconductors, with the magnetic "eld penetrating along lines of #uxoids. Arrays of #uxoids have been observed with surface-sensitive techniques when the magnetic "eld is applied per- pendicular to the surface. With the "eld parallel to Fig. 6. The London penetration depth ( the surface, the #uxoids may remain entirely within *"1350$150 As) of a YBaCuO "lm is determined to high precision by consistent the material. Under these circumstances, a pen- modeling of non-spin-#ip specular intensity taken with the beam etrating probe such as neutron re#ection should be incident both from vacuum and from within the SrTiOsubstrate. (a) The re#ectivity measured incident from the substrate (1) and the tool of choice. from vacuum (2). (b) Spin asymmetry [(R>>!R\\)/ The nature of magnetic con"gurations above (R>>#R\\)] plotted with beam incident from vacuum and HA is still under discussion. From transport (c) from substrate. (d) Neutron scattering density plotted as measurements, it appears that the con"guration of a function of depth for the two spin states, showing sensitivity to #uxoids is not universal, but depends strongly on small refractive index di!erences (from Ref. [21]). J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 747 the anisotropy of the coherence lengths, the thick- bulk in magnitude, direction, and type of magnetic ness of the superconducting layers, and the density order. These new properties result from a complex of pinning centers. The only anisotropy present in set of circumstances, such as incomplete quenching a single "lm of niobium is shape anisotropy. Mater- of the orbital moments, tension or compression of ial anisotropy can be introduced by layering thin the lattice on the substrate, and transfer of electrons "lms of superconductor with metallic spacers (epi- between magnetic "lm and substrate. Polarized taxially grown high-¹ materials represent an ex- neutron re#ection has been used to determine the treme case). In all cases, pinning centers may give absolute value of the magnetic moment per atom rise to a disordered distribution of #uxoids not (notably in Fe and Co) in very thin "lms (see Fig. 7) aligned with the "eld but straggling through the [27}31]. The results are in good agreement with "lm. The magnetic response is then well described those theoretically predicted, as well as those ob- by the Bean model [22]. In the absence of pinning tained by alternative techniques [32,33]. centers, #uxoids should order into a lattice. When the anisotropy is extreme, the #uxoid currents are located principally within the supercon- ducting layers, minimizing the tunneling through the non-superconducting layers (Josephson vor- tices). For less anisotropic media, a di!erent organ- ization of #uxoids has been suggested [23]: above HA, a single line of #ux forms at the center of the "lm to minimize the repulsion from either surface. In practice, geometrical conditions severely re- strict the range of observable #uxoid lattice spac- ings, and the intensity of the di!raction line is expected to be very weak. Up to now, the presence of a #uxoid lattice has been inferred only from the spin dependence of the specular re#ectivity. The e!ect of #uxoids on the specular re#ectivities de- pends on their concentration as a function of z. If pinned at random, their e!ect would only be seen close to the total re#ection wave vector (QX+QA). However, a line of #uxoids located at the center of a superconducting "lm of thickness d gives rise to a maximal spin dependence of the re#ectivity at QX+2 /(d/2). This solution has been found to be consistent with re#ectivity measurements on YBaCuO [24,25]. On the other hand, an array of Josephson #uxoids in a multilayer is expected to exhibit a maximal spin dependence of the re#ectiv- ity at the Bragg re#ections of the multilayer. A re- sponse of this kind has been observed in Nb/Si multilayers [26]. Fig. 7. Enhanced magnetic moment is observed in thin buried Fe layers. The dashed lines plot the neutron spin asymmetry 5. Magnetization in single 5lms [(R>>!R\\)/(R>>#R\\)] expected for Fe exhibiting the bulk moment. Fitted curves (solid lines) are consistent with In "lms less than a few nanometers thick, mag- enhanced moments that become more pronounced for thinner netic materials are signi"cantly altered from the "lms (from Ref. [28]). 748 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 Fig. 8. Re#ectivity from a 1000-As thick "lm of Co on Si. A magnetic "eld H"13 kOe was applied perpendicular to the surface. This "eld was insu$cient to overcome shape anisotropy. The in-plane component of the magnetization therefore induces neutron spin-#ip scattering in the re#ected beam. The change in re#ected exit angle ( , in the "gure) for the spin-#ipped neutrons depends on the square of wavelength times applied "eld normal to the surface H. (a) Shows R>> as vertical and R>\ as wavelength-dispersed contours; (b) vertical R\\ with wavelength-dispersed R\> contours (from Ref. [34]). J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 749 O!-specular spin-#ip magnetic scattering has been observed in large external magnetic "elds. The prototype experiments were carried out on a "lm of ferromagnetic cobalt. The natural magnetization of this "lm lies in the plane of the surface. A magnetic "eld H, applied perpendicular to the surface, was insu$cient to overcome this shape anisotropy. However, some of the re#ected neutrons #ipped their spin, thereby exchanging potential energy (by the amount of the Zeeman splitting) with kinetic energy. From the laws of conservation of energy and momentum for the spin-#ipped neutrons, one can derive the condition  "  $1.47; 10\ H ( and are the incident and re#ected angles in radians, H is expressed in kOe, and in As) [34}36]. Spin-#ipped neutrons are re#ected at angles signi"cantly di!erent from the angle of inci- dence (Fig. 8) even in "elds of a few kOe. The Zeeman splitting physically separates neutrons of opposite spin. In addition to measuring layer-averaged magnet- ization as a function of depth via specular re#ectiv- ity, one can also study surface magnetic structure on atomic length scales by means of grazing-angle di!raction. If incident and exit angles ( and in Fig. 1) are kept below the critical angle for total re#ection, then the penetration depth of the neu- tron evanescent wave below the sample surface is limited to 50}100 As for most materials [37]. Inten- sity measured by scanning through a surface- plane Bragg re#ection then arises solely from atoms con"ned to this thin surface layer. Fig. 9a shows the intensity of the (1 1 0) surface Bragg peak of an Fe(1 0 0) "lm as a function of and ; Fig. 9b the results of a model calculation [38]. The neutrons are initially unpolarized, yet the di!racted inten- sities I>>, I\\, I>\, and I\> appear at di!erent spots. Within the ferromagnetic material, neutrons Fig. 9. Grazing-angle di!raction measurement of the (1 1 0) surface Bragg re#ection from an Fe(1 0 0) "lm. (a) Intensity of opposite spin e!ectively have a di!erent contours measured as a function of incident ( wavelength (as a result of refraction). The novel ) and exit ( ) re#ection angles basically con"rm a simple model based on result of this experiment is the presence of non- uniformly magnetized Fe, according to which I\\ has a max- negligible I>\ and I\>. A layer of iron fully mag- imum when " " A\+0.193, while I>> has a maximum at netized parallel to the surface should exhibit no " " A>+0.323. The presence of auxiliary maxima near ( spin-#ip intensity. Its presence is the signature of , )"( A!, A8) reveals the presence of spin-#ip scattering, caused by perpendicular moment components in the oxide layer magnetic moments directed perpendicular to the (from Ref. [38]). surface, possibly due to scattering from a disordered native oxide layer. Sensitivity to surface- normal magnetic components and to atomic order 750 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 (inaccessible to specular re#ectivity measurements), population changed with the direction of the mag- as well as depth resolution, are compelling advant- netization in F. AF domains with a sublattice mag- ages of grazing-angle di!raction which may out- netization perpendicular to that of the F layer were weigh the di$culties of the technique. statistically slightly favored. More de"nite 903 coupling has been found in FeO/CoO superlatti- ces [45] between ferrimagnetic Fe 6. Coupling between magnetic layers O and antifer- romagnetic CoO layers. In perhaps the most intriguing model proposed Exchange anisotropy, a phenomenon discovered [39], AF consists of domains of very limited lateral almost 50 years ago, remains unexplained today. extent (of the order of a few tens of Angstroms). The requirements for observing exchange anisot- With a "nite number of spins in a domain at the ropy are satis"ed when a ferromagnetic (F) and an interface, it becomes statistically possible to induce anti-ferromagnetic material (AF) are in contact, exchange bias as a residual e!ect. If this were the and F orders magnetically at a temperature higher case, the AF layers would not contribute to specu- than that of AF. Upon cooling the F/AF couple in lar re#ectivity but would give rise instead to a dif- a magnetic "eld to below the NeHel temperature of fuse distribution of intensity either in the forward AF, the sample's magnetization loop remains per- direction or in wide-angle di!raction at grazing manently biased in the direction of the cooling "eld. incidence. Experiments of this kind require more All models hitherto proposed explain this magnetic powerful neutron sources. behavior in terms of a con"guration of spins at the The interaction between two ferromagnetic F/AF interface in which AF spins do not fully layers interleaved with a metallic spacer that is switch when the F layer's magnetization reverses either non-magnetic or weakly AF, depends strong- [39]. Unfortunately, none of these models fully ly on the nature and thickness of the spacer. PNR explains the e!ect. studies have been conducted on Fe/Cr/Fe [47] and In the simplest model, the AF layer is composed Co/Cu/Co [46] sandwiches. If the two magnetic of atomic planes with uncompensated spins. Inter- layers are unequal in either thickness, chemistry, or facial AF atoms align with the bias "eld and do not because one is anchored to an antiferromagnet, the #ip when the magnetization is reversed. To study system may behave as a spin-valve. PNR has been the magnetic depth pro"le in the proximity of used to measure the magnetization of each layer of a buried interface, PNR is, in principle, an excellent such sandwiches [48,49], con"rming the results in- probe, provided that the F/AF pairs are prepared ferred by magnetization measurements. as thin "lms on #at surfaces. Yet, in experiments on Co/CoO and Permalloy/FeMn pairs [40,41], the measured re#ectivities for the two neutron spin 7. Magnetic multilayers states were identical, even when re#ectivities cal- culated on the basis of the models above were First for a few selected pairs, then for a host of signi"cantly di!erent. In contrast, measurements combinations of Fe, Co, Ni interleaved by most of [42] on an FeO/NiO multilayer revealed mag- the 3, 4, and 5d transition metals, it was found that netic di!erences in the two saturated states of the the coupling between successive ferromagnetic magnetic hysteresis loop, due possibly to interfacial layers oscillates from ferromagnetic (F) to antifer- domain wall formation in the ferrimagnetic FeO romagnetic (AF) as the thickness of the non-mag- layers. netic spacers varies. Magnetic "elds ranging from In an alternative model [43], the AF atomic several to a few thousand Oersted saturate the planes parallel to the interface are compensated, magnetization of AF-coupled multilayers, with a and the AF moments align at 903 (spin #op) with corresponding large change of magnetoresistance. respect to F. Some features of this model have been The magnetic structure predicted for the AF state is tested in a recent experiment [44] on Co/CoO. The of type #!#!, a simple doubling of the chemical AF CoO layer was composed of domains whose periodicity d. This structure has been con"rmed J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 751 directly by PNR. In this case, the basic PNR experi- ment consists of measuring the intensity of Bragg re#ections at values of 2 sin / equal to 1/d and 1/2d: the "rst gives information on the ferromag- netic contribution of the average bilayer, the sec- ond on the AF contribution. A number of authors have observed this magnetic con"guration in di!er- ent systems, studied the pattern of antiferromag- netic domains, their evolution with the application of a magnetic "eld, and the correlation with mag- netoresistance [50}55]. However, PNR measure- ments have been applied to perform a considerably more sophisticated analysis in certain of these sys- tems. In the course of studying Fe/Cr superlattices, it was sought to correlate the magnetization of Fe with the spin density wave (SDW) in Cr. The SDW gives rise to magnetic satellites around the Cr(0 0 1) di!raction line [56,57]. From the relative inten- sities of these di!raction lines, it has been found that the period of the SDW and even its phase vary systematically with Cr layer thickness. In general, to determine the details of the mag- Fig. 10. Antiferromagnetic di!use scattering measured in a [30 As Fe/10 As Cr] superlattice. (a) Prior to annealing, the "lm netic pro"le of the repeat unit of a superlattice, exhibits strong di!use scattering along a ridge of Q a large Q V centered on X region needs to be explored. Bragg re#ec- Q tions appear, for a typical bilayer thickness of a few X"0.078 As\+2 /(2;40 As). In contrast, the peak at QX"0.16 As\+2 /40 As, indicative of the chemical modula- tens of Angstroms, at intervals Q tion, is purely specular. The prominent half-order ridge of inten- X&0.1}0.2 As\. An even more detailed description can be obtained sity is caused by 0.7 m in-plane domains antiferromagnetically coupled to underlying layers. (b) After annealing at 3503C, for epitaxially grown superlattices, by measuring a specular peak is visible, revealing a partial coalescence of small the intensities of the di!raction lines due to the domains into domains larger than the coherence length of the mean atomic spacings (QX&2 As\) and their su- neutrons (from Ref. [65]). perlattice satellites. For Gd/Y superlattices [58], Bragg di!raction was used to infer the existence of magnetic dead layers at the interface. Analysis of the polarization state of re#ected neutrons has been used to determine depth- and magnetism is no longer uniform in the plane direction-dependent magnetization. By this means, of the "lm, and the "nite size of the domains it was con"rmed that in coupled multilayers with gives rise to scattering around the direction of the weak interlayer interactions, magnetic con"gura- re#ected beam. This has been repeatedly observed tions forming 903 or other angles exist, as justi"ed if (Fig. 10) [63}66]. From the width of this di!use biquadratric terms in the magnetic exchange be- scattering domain sizes have been deduced. A rig- come important [10,56,59}62]. orous theoretical framework for interpreting the The study of o!-specular magnetic scattering has data would make these measurements far more attracted increasing attention in recent years. In- useful. homogeneities in the plane of the "lm give rise to Less studied, but of growing interest, are multi- scattering which, in general, appears at re#ected layers involving rare earths interleaved with angles O and O0 (recall Fig. 1). If an FM or transition elements [67}70]. In multilayers of rare- an AF multilayer consists of in-plane domains, its earth/Fe or rare-earth/Co, both components are 752 J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 magnetically ordered. For example, in Gd/Fe multilayers, the magnetization vectors of the Gd and Fe layers are oppositely directed, but in general are not compensated. A weak magnetic "eld is su$cient to orient the resulting ferrimagnetic mo- ment, but not to disrupt the magnetic con"gura- tion. Increasing the "eld is predicted to cause a phase transition from the ferrimagnetic to a twisted con"guration, sensitive to the atoms in the outermost interfacial layers [71]. If the excess interfacial magnetization is due to Fe, the magne- tization of the Fe-terminated face should be more readily directed toward the applied magnetic "eld than that of the Gd layer that terminates the opposite face. PNR measurements are indeed con- sistent with this overall model and eventually should be able to provide a detailed picture of the orientation of the magnetization throughout the multilayer. In a single Fe/Gd bilayer, it has been found that the soft Gd}Gd exchange interaction Fig. 11. The change in magnetic coupling induced by charging an Fe/Nb superlattice with hydrogen. AF coupling strength causes a twist of the magnetization within the Gd passes through a peak and then abruptly declines with increas- layer [72,73]. ing hydrogen pressure (from Ref. [75]). Recently, La/Fe multilayers were constructed that exhibit a fragile helical magnetic structure, stable in time, but permanently destroyed after application of a "eld of 100 Oe. This e!ect turned the crystal lattices. Here the reversibility is between out to result from imprinting during "lm depos- the rare earth RH ition, rather than by interlayer coupling [74]. Each  and RH states. layer was 30 As thick, and during deposition the sample was rotated in an external "eld of 3 Oe, 8. The future strong enough to magnetize the Fe layer being deposited but not su$cient to perturb the magnet- The exercise of predicting future development is ization of the Fe layers already grown. As revealed challenging and, when viewed in retrospect, amus- by PNR, adjacent Fe layers formed a helical struc- ing. However, it is fair to say that the next decade ture with a chirality and periodicity determined by will see important technical developments. PNR is the rotational direction and speed of the substrate sorely limited by the brightness of current neutron and the rate of deposition. sources. A new generation of high-#ux pulsed neu- Hydrogenation changes reversibly the band tron sources being designed and built in the United structure and metallic character of the components States, and planned for Europe and Japan, will of a multilayer in a selective way, and by an amount increase the available neutron #ux by an order of controllable with the hydrogen pressure. In Nb/Fe magnitude. At the same time, e!orts are underway and V/Fe superlattices, it has been shown [75,76] to utilize these #uxes more e$ciently. In the 1990s, that hydrogen enters solely in the Nb and V latti- the development of supermirrors has allowed better ces. Magnetically, the e!ect of hydrogenation is to piping of neutrons to the sample position, but gains switch reversibly between the AF- and FM-coupled hitherto have been due to #at mirrors. The next states (Fig. 11). In rare earth/transition element several years should see developments of focusing multilayers, the formation of rare-earth hydrides optics based on curved mirrors or (a "eld yet large- greatly reduces the structural mismatch between ly untouched) magnetic lenses. Finally, ongoing J.F. Ankner, G.P. Felcher / Journal of Magnetism and Magnetic Materials 200 (1999) 741}754 753 developments in spin-polarized He devices [77] Acknowledgements for the polarization analysis of polychromatic, di- vergent beams should revolutionize o!-specular This work was supported by US-DOE DE-AC05- magnetic re#ectivity research and other areas of 960R22464 and US-DOE, BES-MS contract 31- neutron scattering. 109-ENG-38. The authors would like to thank J.A.C. Concurrently with the development of hardware, Bland, W. Donner, F. Klose, V. Lauter-Pasyuk, and a robust e!ort is underway to develop more power- A. Schreyer for providing "gures used in the text. ful and transparent methods of data analysis. 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