Physica B 192 (1993) 137-149 North-Holland ~ SDI: 0921-4526(93)EO120-6 G.P. Felcher Argonne Nationa[ Laboratory, Argonne. IL, USA A review is given of the role of polarized neutron reflectivity (PNR) in measuring the magnetic profile close to the surface and in thin films of superconductors and magnetic materials. For type I and type II superconductors PNR provided a new and direct determination of the penetration depth. For very thin ferromagnetic films PNR was able to determine the absolute value of the magnetic moments. In magnetic superlattices, formed by the alternation of ferromagnetic layers and nonmagnetic spacers, PNR was used to confirm the basic magnetic structure as well as to determine the direction of the magnetic moments of the individual layers. In addition to reflectivity, forward magnetic scattering may very well extend the usefulness of PNR to the case of laterally dishomogeneous systems. I. Reflectivity from magnetic layers er equation for the neutron may be separated in cartesian coordinates. Practically only the z Polarized neutron reflectivity (PNR) has blos- component of the motion needs to be consid- somed in recent years, because it is a simple ered: in the plane (x, y) (parallel to the surface) method to measure the magnetic depth profile of the motion is that of a free particle and the thin films and in proximity of the surface and of corresponding components of the wavevector interfaces. Neutron reflectivity is an optical tech- are constant. The two spinor components nique: thus the interaction of neutrons with 1/I+(z), 1/I-(z) of the neutron wave function obey, matter, which gives rise to reflection, is ap- at a depth z in the medium, the Schrodinger proached in a form slightly different from the equations r2,31: conventional treatment of neutron scattering. When neutrons propagate through a medium in which the scattering centers are small compared ~ )(~ + (Vn + 2ILnBII)I/J with the neutron wavelength, the effect of the 2m dz medium may be represented by a smooth pseu- h2k; dopotential whose magnitude is related simply to + 2J.Ln B i 1/1 1/1 2m the scattering density and the magnetic induction (2 in the material [11 as ( n2 )(d21/l- 2m d:;-z- ) + (Vn,- 2J.LnBII )1/1- 27rfl~ nzkz Vcff V +v =-bN+B.s n m m + 2f.Ln B -L 1/1 + = -zrr:-1/l- where b is the sum of all the scattering lengths where k z = 27r(sin (}j / A ) is the component of the over the N atoms occupying a unit volume. If the momentum of the incident neutron normal to the potential is a function only of the depth from the surface (as in a stratified medium) the Schroding- surface, (}j the angle of incidence, A the neutron wavelength and ILn its magnetic moment. The z-axis is chosen to point from the vacuum toward the surface which is placed at z = 0. The Correspondence to: G.P. Felcher, MSD-223, Argonne Na. tional Laboratory, Argonne, IL 60439, USA. wavefunction in the halfspace z < 0 is 0921-4526/93/$06.00 @ 1993- Elsevier Science Publishers B.V. All rights reserved 138 G.P. Felcher I Magnetic depth profiling studies by polarized neutron reflection 1/1+ = exp(ikz .z) + R++ exp(-ikz .z) , , , .. 10v (3) 1/1- = R exp( ik z) , ," ;>, 10.' for an incoming wavefunction fully polarized in ..-; ~ the + state. If at depths greater than ZF the > .;jU refractive index becomes constant and nonmag- 4) 10. \ 1;: netic the wavefunction can be described [4] by ~ ~ :~. ... 1/1+ = T ++ exp(ikF+z) , o~ ;.- (4) .1, = T 10-4 f '1'- + exp(ikF-z) , , , , , ., 0 U.Ul U.U;! 003 004 005 006 0.07 008 q(A-I) where Fig. 1. Polarized neutron reflectivity of a film of permalloy on Nio5CoO5O, at a temperature of 20 K. The abscissa i, k q = 2k:o The permalloy is magnetized in the direction of the applied field H. Full points: neutrons polarized parallel to (5) H (R + ). Open circles: neutrons polarized opposite to H (R -) (see ref. [5]). The conditions of continuity of the wave function and of its derivative at all values of z allow the determination of R + + , R + -, T + + , T + -, and of 12 = IR reflectivity, IR + I' which is an optical the reflectivities IR++12 and IR+-12, which are transform of B .J.(z). most directly compared with the experimental Figure 2 shows pictorially some of the cases quantities. that can be encountered [9] .The + and -signs If the sample magnetization is parallel to an refer to the relative polarizations of the neutron applied magnetic field H (which is also the spin with respect to the applied magnetic field H . quantization axis of the neutron) the two eqs. (2) which acts as a quantization axis for the polar- do not contain crossterms. The neutron spin in ized neutrons. When a ferromagnetic layer is its trajectory remains in its origina1 state, either magnetically saturated in the plane of the film parallel to H ( + ) , or opposite to it ( -) .Figure 1 along the direction of H, the neutrons remain shows a typical example [5] of spin-dependent polarized during the reflection process (fig. 2(a». reflectivities for a 300 A layer of permalloy on If instead the direction of the magnetization the top of an antiferromagnetic film of deviates from the quantization axis, the neutrons NiosCoo.sO. Basically the reflectivity IR+(kz)12 undergo a partial precession during the reflection is an optical transform of b(z)N(z) + cB(z) and process, so that the reflected beam appears as similarly IR-(kz)12 is an optical transform of partially depolarized (fig. 2(b». If the ferromag- b(z)N(z) -cB(z). Much work has been done netic film is not saturated, but for simplicity the recently [6,7,8] to find the optimal way to exe- magnetization is uniaxial, the sample is divided cute this transform which, for large values of kz , in magnetic domains aligned either parallel or reduces to a Fourier transform. To present in antiparallel to the applied field. In this case there more concise form the magnetic information of is no depolarization of the reflected beam, but the reflectivity quantities such as IR + 12! IR -12 the values of IR+12 and IR-12 represent a weight- have been introduced, conventionally named ed average over the reflectivities of the indi- 'flipping ratio'. More recently it has been pre- vidual domains (fig. 2(c». Finally, if H is applied ferred to present the data as p = (R+ -R-)! perpendicular to the film and is sufficiently large (R + + R -) ; this is called 'polarization' or 'spin to magnetize the sample in that direction, the asymmetry'. When B1- ¥ 0, analysis of the polari- neutron reflectivities become optical transforms zation of the reflected beam gives a spin-flip of the nuclear profile only (fig. 2(d)). This is G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection l1Q parallel to an applied magnetic field or opposite to it. Similar devices, if inserted in the neutron (a) path after reflection of the sample, allow polari- zation analysis. Reflectometers have been con- structed at both steady-state [10] and pulsed neutron sources [2,11,12,13]. At steady state sources the reflectivity as a function of kz = 27r sin 01},. is obtained in the following way. The neutron beam is monochromatized to a wave- length },.0. A suitable region of kz is spanned by (b) varying the angle 0 between beam and sample surface (and sample surfaceldetector). In con- trast. at pulsed sources all the neutrons contained in the source spectrum are utilized, and their wavelength is sorted out by the time of flight from source to detector. Here a substantial region of k" is covered without changing the ~ angle of incidence 0. In all cases the maximum (c) -~/ value of k" spanned determines the resolution 0-- ~ ..::-:- . ~ length ~z in direct space: k" -1 I ~z . Both types of instruments have distinct advan- ~ H tages. At a steady-state source one can choose the k: region of interest with great flexibility, taking data only where needed and with the desired statistics. The neutron wavelength may - be chosen at the top of the maxwellian which / (d) characterizes the neutron spectrum. The resolu- ~--*- ~ tion, ., k::12 = [/lOIO] I f.lk [~A/A]- ~ consists of two terms of comparable size which Fig. 2. Effccts of tho: film magl1ctizatio!l On thc ncutro!l do not vary greatly with angle. This means that rellectivity a!ltl p()larizati\\il In conliguratio!ls (a) and (h) the high resolution can be obtained at large angle. reflectivity is spin-dcpcndc!lt: ho\vcvcr, in (h) the spin of the On the other hand, the instruments at pulsed reflectctl hcam is partially rotatcd. For (c) thc rcflectivity is sources have their own advantages: they permit averagL' for that of the two !lCutro!l spin states while for co!lliguration (tI) the rcflectivity is duc only to nuclear the observation of the entire reflectivity pattern interactions (see rcf. [lJI). at ollce; the footprint of the beam on the sample is fixed; since Ilk / k .-IlA / A is constant the z . because B;: , the component of B normal to the resolution is excellent for k- values close to the surface, is continuous across the surface. region of total reflection. The choice of the 'best' Conceptually (and to a great deal even practi- instrument is thus dictated by the experiment to cally) a reflectometer is a very simple instru- be performed. ment. A narrow beam of neutrons of wavelength The review presented here covers only the A hits a sample surface at an angle () (of the order PNR work done in selected areas of research of one degree) and is reflected at the same angle where rapid development is taking place. The list () into the detector. Appropriate devices polarize is not all-inclusive. For instance, PNR has been the neutrons before the samnle in the direction used to study the effects of thermal and chemical G.P. Felcher Magnetic depth profiling studies by polarized neutron refieclion treatment on the surface magnetism of ferrites netism exist only in a shallow surface layer when [14]. It has also been used to study the magnetic the field is applied parallel to the plate. The depth profiles of relatively thin films, when latter state occurs between H c2 and a surface deposited either on grossly mismatched lattices nucleation field Hc3. (like strained layers of Fe and Co on GaAs) [15], Only a few experiments have been made on or on antiferromagnetic substrates (like permal- superconductors (mostly below Hcl) and yet loy on NiO) [5,9] which provide a unidirectional there is a fair amount of disagreement between bias. the results of different groups. The earliest PNR experiment was carried out on a Nb film, 5 IJ.m thick, deposited onto a polished silicon substrate 2. Superconductivity [19]. The superconducting properties of this film were found to be satisfactory, with Hcl = 1.0 kOe The magnetic state of a body is always per- at T = 5 K and a critical temperature T c = 9.2 K. turbed at the surface, and the perturbation From PNR a penetration depth A = 430 :t: 40 A extends over a thickness that depends on the at 4.6 K was obtained and the temperature range of the interaction forces. In a ferromagnet, variation of A was found to be consistent with a at T = O the magnetic moments are significantly zero-temperature value A(O) = 410 :t: 40 A. This different from the bulk value up to three atomic value is in excellent agreement with theoretical planes from the surface. Such distance is too calculations and most of other, less direct mea- short to be detectable by reflectivity at present surements. However. independent measure- day neutron sources. The thickness of the 'mag- ments from another group [20] gave different netic surface layer' increases with the tempera- o . results: at T = 4.9 K, for a film 7000 A thick the ture [16] and actually becomes infinite at the penetration depth was found to be A = 900 :t: magnetic transition temperature. However, in 100 A; for a second film, 2550 A thick, ,1 = practice the span of temperatures over which 1450:t: 150A. surface effects become visible is small and at- Even larger discrepancies marred the deter- tempts made up to now [ 17] have not provided mination of the penetration depth of the high- T " reliable values for the critical exponents. More superconductor YBa2CuJO7-,. The first mea- promising is the case of superconductors. surement, made on a syntered pellet [21], gave a As is well known [18], magnetic fields always penetration depth A = 225 A. a value unexpec- penetrate to some extent the surface of a super- tedly low for a material with a very short conducting material. For an applied field H less coherence length and hence a large penetration than a critical field ( the thermodynamic critical depth. For two other measurements the sample field Hc for type-I superconductors; the lower was a thin film deposited epitaxially onto a critical field Hcl for type-II superconductors) the substrate of SrTiO3. In both cases the c-axis of penetration is restricted to a depth of the order the YBa2Cu3O7-, lamellar structure was perpen- of a few hundred Angstroms. At higher field the dicular to the film and the penetration depth was penetration is more dramatic: for instance for measured with the magnetic field applied parallel type-II superconductors, in fields between Hcl to the surface. The two results, A = 1400 A [22] and H c2 ( the upper critical field) a mixed state of and A = 900 (+600, -250) A [23], are in sub- quantized vortex lattice has been observed both stantial agreement with each other and with the by small angle neutron diffraction and decora- values obtained by muon resonance. All the tion techniques utilizing small magnetic particles. measurements on superconductors were plagued There are two situations that are strictly surface by the presence of a sizeable surface roughness. effects and cannot be conveniently studied by the which not only causes the 'surface' to be ill- preceding techniques. These are the Meissner defined but that -at least in the extreme case - state, in which the field penetrates only a small may cause a shortcircuit of the magnetic flux. distance into the superconductor, and the surface What is the functional dependence of the sheath, in which superconductivity and diamag- magnetic field close to the surface of a supercon- G.P. Felcher I Ma,s;'netic depth profiling studies by polarized neutron reflection 141 ductor? Provided that electronic response is reason. In vacuum the magnetic induction B entirely local, the magnetic field decays exponen- reduces to H. Hence the discontinuity of the tially in the material [18]. Nonlocality is pre- interaction potential at the surface is /l.n .(BII - dicted to have visible effects only in the case of H): in a diamagnetic material, such as a super- 'extreme' type I superconductors. A careful conductor, the neutron sees a negative magnetic study of films of pure lead and Pb-Bi alloys was field. The polarization of the Pb(Bi) film at made to explore this point [24]. Pure lead is a 323 Oe is compared with the results of different type-I superconductor for which Hcl equals the calculations. If for a magnetic profile an ex- thermodynamic critical field Hc. Adding an im- ponential decay is adopted, certain features of purity level of 0.8% Bi brings the system to just the polarization are not satisfied: for instance, below the crossover point to type-Il, where Hcl with an exponential decay length of 260 A, the and Hc2 separate and the region in between is minimum is matched but not the values of the characterized by the mixed state. polarization for higher values of kz. Much better The polarization of Pb(Bi) at T = 6 K is pre- fit is obtained with a magnetization profile that sented in fig. 3. The sample, in a field H = decays from the surface first less rapidly, then 323 Oe, is in the Meissner state. The polarization more rapidly an exponential function (fig. 3). appears to be entirely negative, for the following Such behavior might be explained in terms of nonlocal effects; however it is hard to justify the persistance of these effects in such a 'dirty' superconductor. New independent measure- ments [25] are now in progress to verify these 0.02 i finding and also to expand earlier observations of ~ a superconducting surface sheath predicted to occur at the superconductor/vacuum interface in to these materials at higher magnetic fields. 3. Magnetic thin films Only for film thicknesses below a few nanome- , , I i i i i 0.12 ters the magnetization of ferromagnetic is sig- 0.003 0.004 0.005 0.006 0.007 0.008 0.009 nificantly altered from the bulk value, in size, k (;..01) . direction of magnetization and even type of magnetic order [26]. These new properties are the result of a complex set of circumstances. Free standing films, ideally one atomic plane thick, are expected to exhibit magnetic moments larger than the bulk: since the orbital compo- nents are less quenched, the moments are ex- pected to tend toward the free atom values. On the other hand, the lower dimensionality is , ~ expected to reduce, and even to suppress, the 00 --I temperature of magnetic order. Experimental 0 200 400 600 800 1000 1200 films have to be deposited on a substrate, which Depth from surface (A) perturbs the magnetization of the proximate Fig. 3. Above: polarization of a film of Pb(Bi) in a field of layer on two accounts. In the first place the 323 Oe and 5.5 K. The dashed line is calculated for an magnetic atoms which are deposited from vapor exponential decay of the magnetic field in the material, with a penetration depth of 300 A. The continuous line is obtained or from a plasma arrange themselves in a struc- for the parametric model profile shown below (see ref. [24]). ture, which tends to mimic that of the substrate. 14 G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection In comparison with the bulk material, the thin easier to take into account the weak magnetic film is expanded (or compressed): this may response of overlayer and substrate, even when change drastically the coupling of magnetic elec- they are much more massive than the magnctic trons. In the second place, if both magnetic film film. and substrate are metallic a transfer of electrons To perform a PNR experiment it is not neces- takes place. Numerous ab initio calculations sary that the thin film is at the surface: the film have been made for epitaxial films [27] ; table 1 may be covered with a nonmagnetic layer, which o . shows the magnetic moments predicted for one- could be a few hundred Angstroms thIck. Actu- atomic-Iayer-thick metals on several substrates ally such coverage enhances [30] the spin depen- dence of the reflectivity. However, the polariza- [28]. A wealth of experimental information has tion is proportional to the linear magnetic flux. been accumulated in recent years on the magnet- i.e. the product of the internal field and iron ism of thin films [29]. For instance, ultrathin thickness (8 dFe). To the extent that k= .dFe ~ 1. films of iron have been epitaxially deposited on the experiment is insensitive to the variation of B single crystal substrates of Cu, Ag, Au, Pd, W within the layer, or for that matter to the and MgO and studied by spin-polarized photo- thickness of the layer itself. Once known 8, the emission, Kerr effect, conversion electrons, mean magnetic moment per atom JiF can be Mossbauer spectroscopy and spin-polarized obtained with precision without detailed kno\\'- LEED. These studies have demonstrated the ledge of the number of magnetic atoms in thc presence of ferromagnetic ordering and perpen- layer or their density. This is because the optical dicular surface anisotropy in monolayer thick potential of eq. ( 1) can be shown [ 1] to be iron films [27]. However, the determination of proportional to (b ::!:: C'Jir )N , where c' is a con- the absolute magnetic moment per atom of an stant (c' =0.02695 x 10-'2cm/Jiu) and N is thc ultra-thin film is still a tremendous challenge for atomic density per unit volume. The simulta- experimentalists. Experiments were proposed neous fitting of II~+I~.IRI2 strongly constrains [30] and later successfully implemented [31-35] the ratio between atomic moment of an atom to determine by polarized neutron reflection and its well-known neutron scattering length. (PNR) the magnetic moments in Fe and Co films The first magnetic thin film studied by PN R as thin as two monolayers. Being an optical was face-ccntcred-cubic (FCC) cobalt on technique, PNR goes well beyond conventional Cu(001), overcoated with copper [31]. For a magnetometry. To start with, if the magnetic film 18 A thick it was found an in-plane mag- layer is covered, its depth in the sample is netization of 1.8Jiu /Co, slightly larger than the localized. At the same time, the optical signal bulk value ( 1.6JiB ). Subsequent measurements assures that iron is conformed as a film. and not [32,33] on even thinner films of FCC cobalt on (for instance) in an assembly of droplets having Ag indicated a moment enhancement up to equivalent thickness. Finally. in PNR is much 2.15JiB/Co. Although these measurements were taken at 4.2 K, the cobalt magnetization was found to be virtually unchanged up to room Table 1 temperature. The behavior of thin films of body- Magnetization of thin films: theory and PNR experiments. 0 centered iron was entirely different. A 14 A film Monolayer Calculated Experimental Magnetic moment sandwiched in copper was fitted [31] with JLI1 / atom JLB / atom in solid 2.2JiB /Fe, a value virtually undistinguishable Cr!Vacuum 12 :0.1 from that of the bulk. Even for a 4.3 A film (on a Cr!Ag :0.1 nonmagneti rather rough surface) the ferromagnetic moment Fe!Cu 23 2.2 2.97 2.2 did not exceed 2.35JiB /Fe at liquid helium tem- Fe!Ag Fe!MgO 3.07 2.2 2.2 perature [15]. A systematic study of BCC iron Co!Cu 1.79 1.8 1.7 films 4,6,8,16 A thick on MgO and capped with 1 '7 Co!Ag gold [35] showed a dramatic decrease of the G.P. Felcher / Magnetic depth profiling studies by polarized neutron reflection 143 ordering temperature, and a concurrent change of the perpendicular anisotropy for thicknesses ~6 A; however, the ferromagnetic moment at saturation remains (2.2:!: 0.2)JLB/Fe down to the thinnest sample ( figs. 4, 5) .Finally, films of Cr (down to sub monolayer thickness) [33], depo- sited on Ag(OO 1) , did not show any measurable induced magnetization, in fields up to 0.83 kOe. Table 1 shows a compendium of the ex- perimental results hitherto obtained and com- pares them with theore~ical predictions. The magnetic moments, as determined by PNR at different laboratories, are entirely consistent: however, they are very close to the bulk value and do not show the enhancement predicted for thin film materials. For Cr, the calculation is in the limit of the single atomic plane and the moments of a second plane are thought to be coupled antiferromagnetically to the first. How- ever, the discrepancy between theory and experi- ment is clear and strong in the casc of BCC iron, which should have enhanced magnetic moment in thin films on a number of different substrates. It is to he hoped that future experiments clarify this important point. Looking farther in the future, good ferromagnetic thin films may be- I:e ~ " 6 " tlJ I Fig. 5. Polarization functions for (bottom) 4 A. (middle) 6 A " and (top) sA Fe films at T=40K and H=5kOe. All fits used the same parameters except for the iron thickness (see MgO ~- ---1 ref. [35]). ~ !1 ? Fe come useful to test in detail the properties of the phase transition in truly two-dirnensional sys- u If~~ 0) 10 !;: 1 terns. 0) Surface ~ 4. Magnetic coupling in multilayers 10'~ The development of reliable and controlled deposition techniques has made possible the , , IO.'L-- fabrication of metallic multilayers formed by 000 001 002 003 004 005 006 007 008 interleaving ferromagnetic films with nonmag- q(A-I) Fig. 4. Spin-dependent reflectivity of a }6 A thick Fe film. netic spacers. The original goal of this research The data were obtained at room temperature in a magnetic was to manufacture materials with novel mag- field of 200 Oe. Solid dots indicate data for neutron spin netic properties just stacking conventional metals parallel to the applied field ( + ); open circles for spins in layers of controlled thickness. First for very anti parallel to the field ( -) .The insert is the schematic selected couples, then for a rapidly expanding diagram of the neutron potential for + and -spin neutrons through the sample (see ref. [35]). host of combinations it was found that the 144 G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection coupling between subsequent ferromagnetic layers oscillates from ferromagnetic to antiferro- magnetic to ferromagnetic again as the thickness of the nonmagnetic spacers is increased. The nature of the coupling, inferred from the mag- netization measurements, was first directly ob- served by neutron reflection. In all recorded cases the alignment of the magnetization of the subsequent layer was either ferromagnetic (F) or antiferromagnetic (AF) of the type + -+ -, with a simple doubling of the chemical period- icity. The first material to exhibit oscillatory mag- netic interaction was a gadolinium/yttrium superlattice, epitaxialy grown on tungsten with the hexagonal c-axis perpendicular to the sur- face. When the yttrium spacer is ten atomic layers thick the superlattice is AF, as confirmed by polarized neutron diffraction [36]. A weak magnetic field in the surface plane has the effect of slightly canting the AF structure, with the main AF component perpendicular to the field. When the yttrium thickness is increased to twen- ty atomic planes, or decreased to six, the materi- al becomes ferromagnetic. The oscillatory be- havior has been well explained in terms of a Ruderman-Kittel-Kasuya-Yosida (RKKY) Co/Ru [44], Ni/Ag [45], Co/Cu [46] and Fe/Nb model [37] .The basic assumption is that the [47]. In the case of Fe/Si, F to AF oscillations conduction electrons of Y provide an indirect were found to be present only for short Si coupling between the gadolinium layers. Since thicknesses, when silicon forms a crystalline . those first experiments, the studies have greatly metallic silicide. For thicknesses larger than :?0 A expanded to cover other rare earths and other silicon is deposited as an amorphous semicon- spacers [38]. ductor which, unless excited, does not pro\'ide The magnetic coupling is oscillatory also in magnetic coupling to the adjacent iron layers. multilayers of Fe. Co, Ni interleaved by most of In retrospect, polarized neutron reflection had the 3,4.5 d nonmagnetic metals. Among these. only a marginal role in the study of the magnetic the first to be studied were multilayers of iron/ multilayers formed by transition metals. Actually chromium [39,40,41 ]. The magnetic fields the presence of an AF or an F state is no\\' needed to saturate the samples were found to observable in direct space by means of scanning vary periodically with the chromium thickness. electron microscopy with polarization analysis The presence of an AF ground state for multi- [49] as well as by magnetooptic Kerr effect layers with high saturating fields was quickly microscopy. However, neutron measurements confirmed [42,43] by PNR. The only magnetic contain a wealth of information that reaches far structures found up to now in this system are of beyond proving the nature of the ground state. the F and the AF kind: the latter configuration is From the intensities of the series of superlattice destroyed by applying a sufficiently large mag- peaks up to large scattering angle, and of their netic field (see fig. 6). Similar findings were spin dependence, one can obtain a detailed found for other kind of multilayers, such as profile of the magnetization within the single G.P. Felcher / Magnetic depth profiling studies by polarized neutron reflection magnetic layer, with a resolution that might parallel to the field. Since the magnetic coupling approach the interatomic spacing [38]. While is weaker for the surface layer, it has been experiments at large kz are considered more suggested that the phase transformation in a properly in the area of conventional polarized magnetic field should initiate at the surface, and neutron diffraction, even observations at small its character should depend on the nature of the kz, i.e. in the region where the mean refractive surface layer [52]. Experiments now in progress index of the material cannot be neglected, yield [53,54] tend to confirm in real samples the main information that is far beyond the mere de- features of the mean field model. termination of the F or AF state. Up to now it was implicitly assumed that the As already discussed the analysis of the polari- sample is composed of a single domain. In this zation of the reflected neutrons can be used to case the reflected neutrons are not depolarized determine the direction of the magnetization at (even from nonuniaxial samples) but at most the any depth in the sample. The simplest arrange- direction of their spins change from the initial ment consists in analyzing the neutron spin in polarization axis. In principle the reference field reference to the quantization axis of the neutrons for polarization analysis can be rotated until before hitting the surface. The non-spin-flip parallel to the quantization axis of the exiting reflectivity is due to the projection of the sam- neutrons: the spin-flip components of the reflec- pie's magnetization on the quantization axis, tivity become identically zero. If a device ca- while the spin-flip reflectivity is due to the pable of pro\riding 'flexible' polarization analysis perpendicular component of the magnetization. were constructed [ 55] , it would also discriminate In this way the presence of a canted arrangement the case discussed above from that, in which of spins has been observed first in Gd/Y [36] and more than one magnetic domain is present in the later in Fe/Cr [42]. A more quantitative com- sample. Here, since different neutrons ex- parison of IR++12, IR+-12, IR-+12 and IR--12 has perience different magnetic pathways, the re- been done for Co/Cu [46]. Polarization analysis flected beam is truly depolarized. Magnetic do- is also been used [50] to search for direct mains have an additional effect: the magnetism is evidence of a magnetic state where two magnetic no longer uniform in the plane of the film, and layers of a sandwich are magnetized at a 90° the finite size of the domains gives rise to angle, rather than at 0° or 180°. The presence of scattering around the direction of the reflected such a state has been inferred from magnetic beam. measurements, and it is justified if biquadratic terms in the magnetic exchange become impor- tant [51]. s. Forward magnetic scattering Polarization analysis becomes important to sort out the structures of more complex artificial In order to measure the reflected beam suffices superlattices, as those made by the alternation of a single counter, poised at an angle 0 with the two magnetic metals. Prototype of this class is a reflecting surface, and 20 with the primary beam. Gd/Fe multilayer, a material for which model However, in several instruments a one-dimen- properties have been proposed [52] and pres- sional, position sensitive detector is used, with ently tested. This material is made of two the geometry sketched in fig. 7. Such detectors magnetic components, Gd and Fe, which are offer several practical advantages: the reflected anti parallel to each other but have in general beam is easily localized and both signal and different sizes. In an applied magnetic field the background are measured at the same time . magnetic structure is predicted to transform from More important, these detectors measure not a ferrimagnetic to a 'twisted' configuration. This only reflected neutrons, but also those scattered is composed of an antiferromagnetic component at grazing incidence. Notice that in the geometry perpendicular to the field and a ferromagnetic shown in fig. 7 a one-dimensional detector dis- component, unequal for the two components, criminates only neutrons leaving the surface at 146 """" important difference between the two cases, and ~ detect thus to avoid confusion I will name the scattering ,~ in the plane of reflection as 'for}1'ard scattering. + to distinguish it from the lateral scattering at /V grazing incidence. In both cases the scattering is due to dis- homogeneities in the plane of the film, which might be represented by a vector '7' with planar " projections 7x and 7\1 (fig. 8). In the for'vard ~ scattering ~t is obtained from the separation ~O / between the scattered and the reflected beam. In 9--\.-- sample the lateral scattering 7y is obtained from the angle ~<1> between the scattered beam and the reflection plane. When '7' is small in comparison Fig. 7. Geometry of forward and lateral scattering of neu. with the incoming wavevector, the laws of con- trons at grazing incidence. servation of energy and momentum in plane reduce to: an angle Of different from Oi; however, the Tx = Ikl sin (J .lfJ scattering always takes place in the plane of (6) reflection. In contrast, in the most common Tv = Ikl.lcp (lkl = 21T/A) geometry of scattering at grazing incidence [56], the observations are focussed on the neutrons For comparable elements ~(J. ~<1> the regions of scattered out of the reflection plane. There is an T, .T, are entirely different. For instance. if ~f) = 01 =02 a) I~ , k, r-- I~ ~ rosrnoN SENSmVE ~ Dt":=R ~ J ~ ~ ' po/arized nelltron reflection 147 e = ~<1> = 1°, and a neutron wavelength A = 10 A, has the form of a ridge centered around a value 4 A -1 2 ° -I 'Tx = 1.9 x 10- , while 'Ty = 1.1 x 10- A . of jql equal to the value of the maximum of the The difference is about of two ordcrs of mag- AF peak, i.e. where qz = Tz, Tz being the propa- nitude. This means that, if the lateral fluctua- gation vector of the antiferromagnetic structure. tions 'T are isotropic in the plane of the film In contrast, at the first Bragg reflection due to {'Tx = 'Ty) scattering might be present at a detect- chemical modulation of the multilayer no corre- able ~(} even when ~<1> is negligibly small. The sponding broadening is present. The forward size of the objects that give rise to lateral scattering is of magnetic origin: it is as if the scattering is the same as that giving rise to small antiferromagnetic domains had finite size. It is angle scattering in transmission geometry: it is of easy to form a picture of the configuration, by order of 100 A. The fluctuations that give rise to assigning to each domain a magnetization axis, observable forward scattering are instead of the which may point along a local crystallographic order of one micron . ax IS. Sizeable forward scattering has been observed It is easy to calculate the lateral dimensions of in several instances, when reflectivity measure- the domains observed for Co/Ru \\'ith the help ments were taken on magnetic multilayers. In of a simple formula. In the kinematic approxi- fig. 8 is shown an intensity contour pattern mation the intensity of the antiferromagnetic obtained for a Co/Ru multilayer [44], and in fig. peak [57] may he \\'ritten as 9 that for a Fe/Nb multilayer [47]. The measure- ments were done at a pulsed neutron source, sin2(N"ak sin (} cas a) = J. J, = where the intensity reflected at a given angle sin2(ak sin (} cas a) with respect to the primary beam, (}i + et' are measured for all neutron wavelengths. In this sin2(N,ak sin (j sin a) . 7 pattern, the reflected heam appears as a vertical sin~(ak sin (j sin a) line of intensity at e, = (}t. The visible scattering \\hcre we have neglected tluctuations along y. In eq. (7), a is the (Intiferromagnetic spacing and N= C! ~ is the numbcr of laycrs composing thc film. In -w !, .(1 is in reality a dummy parameter: what is of ~ intcrest is the total length IJx = N,(1 in the .r .:;; --- "':;b dircction. a is the (mgle between the sc(lttering ~ vcctor and the z-direction: (It the Br(lgg reflec- - tion a = O (lnd the arguments in J = are multiples 0 of 20. When the incident \Vavevector k = 21T / A is ch(lnged (but the (lngle of incidence O remains < ~ constant) the m(lximum of J = occurs for finite a : ;:;E it is easy to see that under this condition q = q=O.IO6A-l remains constant. At finite a, !, rapidly de- crcases; Lx m(ly be chosen by finding the value of a at which !t = 0. From fig. 8 it may be deduced that, for Co/Ru, L., = 4 fJ.m. In the case of Fe/Nb (fig. 9) the counter used is too limited to give an estimate of the size of Lt and only an ~I, -' I - , , I 4.4 4.2 4.0 3.8 3.6 upper limit can be given: L.1: < 0.6 fJ.m. In conclusion, in the past ten years PNR has ei +ef(degree) been developed into a mature technique which is Fig. 9. Forward scattering of a Fe/Nb multilayer (from ref. being employed to study a variety of magnetic [47]). The forward scattering is much broader than the dimension of the counter (2.5 cm, at 90 cm from the sample). phenomena in samples having lamellar geome- ~ tI 148 G.P. Felcher I Magnetic depth profiling studies by polarized neutron reflection try. At the same time, the development of (lateral) scattering at grazing incidence, as well as that of forward scattering, may open new and exciting areas of research. Acknowledgements The present work was supported by the US Department of Energy, BES-Material Sciences, under contract W-31-109-ENG-38. The author would like to thank Prof. W.G. Stirling for giving him the opportunity to present this work at the ILL-ESRF Workshop on Neutrons and X-rays in Magnetism. The author is also grateful to R. Goyette and Y.Y. Huang for their help in prepar- ing the figures, and to Hong Lin for a critical reading of the manuscript. References [1] D.J. Hughes. Pilc Neutron Research (Addison-Wesley. Cambridge.1953). [2] G.P. Felcher, R.O. Hilleke, R.K. Crawford. J. Haumann, R. Kleb and G. Ostrowski. Rev. Sci. In- strum. 58 (1987) 609. [3] S.J. Blundell and J.A.C. Bland. Phys. Rev. B 46 (1992) 3391. [4] G.P. Felcher, Proc. S.P.I.E. 983 (1989) 2. [5] G.P. Felcher. Y.Y. Huang, M. Carey and A. Berkowitz. in: Proceedings of the Symposium on Ultrathin Films Multilayers and Surfaces, Lyon, September] 992. J . Magn. Magn. Mater. 121 (1993) ]05. [6] J. Lekner. Theory of Reflection (Martinus Nijhoff, Dordrecht. 1987). [7) M. Klibanov and P.E. Sacks. J. Math. Phys. 33 (1992) 3813. [8] J.S. Pederscn. J. Appl. Cryst. 25 (]992) 129. [9) S.S.P. Parkin. V.R. Deline. R.O. Hilleke and G.P. Felcher, Phys. Rev. B 42 (1990) ]0583. [10] C.F. Majkrzak. Physica B ]73 (1991) 75. [1]] R. Felici, J. Pcnfold. R.C. Ward and W.G. Williams. Appl. Phys. A 45 ( 1988) 169. [12) M. Maaza, in: Proceedings of the International School of Physics Enrico Fermi, Course CXIV, eds. M. Fontana and F. Rustichelli (North-Holland. Amsterdam, 1992) p. 34]. [13] D.A. Korneev, V.V. Pasyuk, A.V. Petrenko and E.B. Dokukin, Springer Proc. Phys. 6] (1992) 213. [14] S.S.P. Parkin. R. Sigsbee, R. Felici and G.P. Felcher, App]. Phys. Lett. 48 (1986) 604. [15] J.A.C. B]and, A.D. Johnson, H.J. Lauter, R.D. G.P. Felcher / Magnetic depth profiling studies by polarized neutron reflection 149 J. [40] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen van [ 49] J. Unguris, R.J. Celotta and D. T .Pierce, Phys. Rev. Dau, F. Petroff, P. Etienne, G. Creuzet and A. Lett. 67 (1991) 140. Friederich, Phys. Rev. Lett. 61 (1988) 2472. [50] A. Schreyer, K. Brohl, Th. Zeidler, Ch. Morawe, N. [41] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Metoki, H. Zabel, J.A. Wolf, P. Griinberg, J.F. Ankner Lett. 64 (1990) 2304. and C.F. Majkrzak, presented at Intern. Workshop on vity [42] A. Barthelemy, A. Fert, M.N. Baibich, S. Hadjoudj, F. the Use of Neutrons and X-Rays in the Study of Petroff, P. Etienne, R. Cabanel, S. Lequien, F. Nguyen Magnetism, Grenoble, January 1993. rto van Dau and G. Creuzet, J. Appl. Phys. 67 (1990) 5908. [51] J.C. Slonczewski, Phys. Rev. Lett. 67 (1991) 3172. [43] S.S.P. Parkin, A. Mansour and G.P. Felcher, Appl. [52] J.G. LePage and R.E. Camley, Phys. Rev. Lett. 65 Phys. Lett. 58 (1991) 1473. (1990) 1152. 61 [44] Y.Y. Huang, G.P. Felcher and S.S.P. Parkin, J. Magn. [53] C. Dufour, Ph. Bauer, M. Sajieddine, K. Cherifi, G. Magn. Mater. 99 (1991) L31. c. Marchal and Ph. Mangin, J. Magn. Magn. Mater. 121 [45] B. Rodmacq, P. Mangin and C. Vettier, Europhys. Lett. (1993) 300. ; 15 (1991) 503. [54] M. Lowenhaupt, W. Hahn, Y.Y. Huang. G.P. Felcher B. ~ [46] A. Screyer, T. Zeidler, Ch. Morawe, N. Metoki, H. B and S.S.P. Parkin, J. Magn. Magn. Mater. 121 (1993) Zabel, J.F. Ankner and C.F. Majkrzak, J. Appl. Phys., 173. to be published. [55] P.J. Brown, Physica B 192 (1993) 14. B. f, [47] J.E. Mattson, E.E. Fullerton, C.H. Sowers, Y.Y. [56] H. Dosch, Physica B 192 (1993) 163. Huang, G.P. Felcher and S.D. Bader, in: 37th Conf. on [57] R.W. James, The Optical Principles of Diffraction of Magn. and Magn. Mat., J. Appl. Phys. 73 (1993) 5969. X-Rays (Cornell University Press, Ithaca. 1962). [48] E.E. Fullerton, J.E. Mattson, S.R. Lee, C.H. Sowers, Y.Y. Huang, G.P. Felcher, S.D. Bader and F.T. Parker, J. Magn. Magn. Mater. 117 (1992) L301.