Physica B 267}268 (1999) 154}161 Polarized neutron re#ectometry } a historical perspective G.P. Felcher* Argonne National Laboratory, Building 223, Argonne, IL 60439, USA Abstract Born in the early 1980s to study magnetic "lms, polarized neutron re#ectometry (PNR) has enjoyed growing popular- ity as witnessed by the number of instruments assembled at neutron research centers. PNR has proved its usefulness by providing information as diverse as the penetration depth of the magnetic "eld in superconductors and the absolute value of the magnetic moments in ultrathin ferromagnetic layers; yet its widest application has become the study of the magnetic con"gurations in multilayers. Two types of re#ectometers have been constructed: time of #ight and crystal analyzer. The relative merits of the two types are discussed in the light of present and future applications. 1999 Published by Elsevier Science B.V. PACS: 75.70.!i; 07.60.Hv; 74.76.!w Keywords: Neutron re#ectivity; Polarized neutrons 1. How it started atories have become quite consistent. Goal of this report to give a current perspective focussing on the Polarized neutron re#ectivity (PNR) has reached work done during the past years. I discussed pre- a maturity perhaps surprising in view of its young vious accomplishments in an earlier review [1]; age. Born in the middle 1980s, it was devised as an several other reviews have since appeared [2}7]. analytic tool to measure the magnetic depth pro"le Neutron re#ectivity is an optical technique: the of thin "lms or in proximity of surfaces and interfa- interaction of neutrons with the medium through ces. Fortunately, its deployment was paralleled by which they propagate is described by a potential the evolution of techniques capable of producing whose magnitude is related simply to the scattering reliable magnetic "lms with novel magnetic proper- length density of the nuclei and the magnetic induc- ties. Maturity has come to PNR in two ways: its tion B in the material: role in research has become considerably better de"ned, and the results obtained by di!erent labor- 2  < "<#< " bN#B ' s, (1) m where b is the mean of the scattering lengths over * Corresponding author. Tel.: #1-630-252-5516; fax: #1- the N atoms occupying a unit volume and s is the 630-252-7777. neutron spin. The trajectory of the neutron in this E-mail address: felcher@anl.gov (G.P. Felcher) potential is obtained by solving the SchroKdinger 0921-4526/99/$ } see front matter 1999 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 0 5 3 - 8 G.P. Felcher / Physica B 267}268 (1999) 154}161 155 equation. If < is a function only of the depth from The coe$cients of the two exponentials are deter- the surface (as in a strati"ed medium) only the mined by the conditions of conservation of matter z-component of the motion perpendicular to the and #ux at each boundary. The spin-dependent surface is a!ected by it: the motion in the plane x, y re#ectivities are simply of the form R""r (parallel to the surface) is that of a free particle. Let ", where r us assume for simplicity that B is parallel to the  is the coe$cient of the second term in Eq. (3) for the region above the surface. In general the re#ec- neutron spin and parallel to the re#ecting surface. tivity is unitary for most materials up to values of After separating the variables, the SchroKdinger q equation along z reduces to X"2k of the order of 0.01 As\, and decreases rapidly beyond that limit with an asymptotic q\ f  X dependence. We have shown the simplest mag- !#[k!4 (bN$cB)] f!, (2) netic case } all magnetic "elds are collinear. Even in where k more complex cases it is straightforward to calcu- "2 sin / , and is the angle of the neutron beam with the surface, the neutron late exactly the re#ectivities from the potential. wavelength. This procedure is to be followed close to the critical For any layer n in the medium for which the value of qX: at larger qX the re#ectivities are well potential is constant the solution of Eq. (2) is given approximated by the scattering theory in the "rst by the sum of two exponentials, giving the #ow of Born approximation. When in the spinor equations neutrons in either direction of z: f>, f\ cannot be separated, spin-#ip processes take place. f!"t! exp (ik!z)#r! exp (!ik!z), (3) A re#ectometer is a simple instrument (Fig. 1) where [8]: a neutron beam of wavelength hits a sample surface at an angle and is re#ected from the k!  "(k!4 (bN$cB). surface at the same angle . The instrument is Fig. 1. Scheme of a crystal analyzer re#ectometer (Ref. [8]). 156 G.P. Felcher / Physica B 267}268 (1999) 154}161 practically a di!ractometer with resolution su$- parent, although it might be so in particular cases. cient to separate transmitted and re#ected beams at The intensities of the di!raction peaks can be ana- values of qX where the re#ectivity becomes unitary. lyzed in terms of the kinematical theory. For in- Re#ectometers have been constructed at both stance, the bottom "gure shows an AF peak at steady state and pulsed neutron sources. The re#ec- q tivity is solely a function of the momentum transfer X"0.045 As\. Its intensity is proportional to: along the z direction, q I>>"I\\""M X"4 sin / : a range of ,"; I>\"I\>""M,", (4) qX can be spanned either by changing the wave- where M length, and keeping "xed the angle of incidence, or ,, M, are the projections of the staggered magnetization parallel and perpendicular to the by changing the angle of incidence at "xed neutron quantization axis. After making a similar wavelength. In the former mode the wavelength is analysis on the ferromagnetic peak (at q selected by Bragg-re#ecting the beam from the X" 0.09 As\) the angle between the two sublattice moderator with a crystal analyzer (CA). In the magnetizations has been obtained. This kind of second mode the neutron beam is chopped in short analysis does not apply to smaller values of q pulses: the neutron wavelength is sorted out by the X. As it can be observed in Fig. 2, R>\ decreases with q time of #ight (TOF) from chopper to detector. X in the total re#ection region; it is easy to show analyti- Re#ectometers built at steady-state sources are of cally that R>\P0 when q both kind, while at pulsed sources only TOF re#ec- XP0. Since the relation- ship between spin-dependent re#ectivities and spin tometers are feasible. Both types of instruments structure is not transparent, details of the non- have distinct advantages. In a TOF instrument collinear structure are obtained by model "tting. a substantial region of qX is covered simultaneously, without changing the footprint on the sample, by the entire neutron spectrum. On the other hand, with a CA instrument one can use all available neutrons to measure the intensities at a selected value of qX. The choice of the best instrument is thus dictated by the experiment to be performed. Appropriate devices are added to the re#ec- tometer to polarize the incoming neutrons along an applied magnetic "eld or to analyze the polariza- tion of the re#ected beam (Fig. 1). Conventionally, the direction of initial polarization is "xed. The sample may change the polarization of the neutron; yet a conventional analyzer chooses, among the re#ected neutrons, those polarized along the same direction as the polarizer. Reversal of the neutron spin is obtained by energizing #ippers placed before and after the sample. The re#ectivities are then characterized by the sign of the neutron polariza- tion before and after re#ection with respect to the reference "eld: R>>, R>\, R\>, R\\. As an example, in Fig. 2 are presented the re#ectivities from a multilayer of Fe/Cr in which the magnetiz- ation of subsequent Fe layers was suspected to be non-collinear [9]. When spin-#ip occurs, the interpretation of the Fig. 2. Spin-dependent re#ectivities from two samples [Fe(52 As)/Cr(17 As)];5 grown at di!erent temperatures ¹ entire q %. For X range of spin-dependent re#ectivities in ¹ terms of a magnetic structure is not always trans- %"2503C the magnetization of subsequent Fe layers is at an angle of 503. From Ref. [9]. G.P. Felcher / Physica B 267}268 (1999) 154}161 157 Table 1 Polarized neutron re#ectometers in the world Instrum. Source Start up Mode Beam size Q range Pol. Comments (mm) As\ An. POSY I IPNS, Argonne 1984 TOF 3;40 0.5 Yes CRISP ISIS, Rutherford 1986 TOF 10;40 Yes BT-7 NIST Reactor 1990}1996 CA In con"nement building NG-1 NIST Reactor 1996 CA 7;50 2.2 Yes In guide hall AMOR SINQ 1998 TOF 50;50 Yes SPEAR LANSCE, 1991 TOF 8;50 Yes Part time in the polarizing mode Los Alamos ROG IRI, Delft 1988 TOF 5;30 No EVA ILL Grenoble 1987 CA 30;30 No For di!raction at grazing incidence SPN FLNP Dubna 1988 TOF 3;60 Yes G2-2 OrpheHe, Saclay 1995 CA ADAM ILL Grenoble 1997 CA 15;40 Yes REFLEX FLNP Dubna 1997 TOF No V6 HMI Berlin 1992 CA 10;50 1.5 Yes V14 HMI Berlin 1996 CA 4;50 1.5 Yes PORE KEK Tsukuba 1999 TOF 10;30 0.4 JAERI 1996 CA Interferometer D-17 ILL Grenoble 1999 Variable 30;70 1.0 Yes Eq. (4) indicates that polarizers and #ippers must inhomogeneous state is created (in type-II super- have very good e$ciency to de"ne accurately the conductors) with the magnetic "eld penetrating direction of the magnetization. For instance, if the along lines of #uxoids. With the magnetic "eld uncertainty in the polarization is 1%, from a purely applied perpendicularly to the surface, arrays of magnetic signal the direction of the magnetic mo- #uxoids terminating at the surface have been ob- ments is determined only within 63. It is also clear served by surface sensitive techniques. With the that good e$ciency is more di$cult to achieve for "eld parallel to the surface the #uxoids may be TOF instruments, which use an extended range of entirely within the material, and in this condition wavelengths. Yet the recent years has seen a sus- a penetrating probe (as neutron re#ection) needs tained e!ort in fabricating e$cient polarizers to be used. With regards to the penetration depth, [10}12] and #ippers [13]. Table 1 gives a compen- the results obtained by di!erent laboratories have dium of the polarized neutron instruments [14}16] been satisfactorily converging. This is not only true built up to now. The technical e!ort in constructing of conventional superconductors, like niobium them is paralleled by the expansion of the scienti"c [17,18], but also of the high ¹ program. superconductor YBaCuO\V where the measurements point to a penetration depth of the order of 1400 As [19,20], in good agreement with the results obtained by 2. Current research muon spin rotation and by neutron scattering from a #uxoid lattice perpendicular to the surface. 2.1. Penetration depth in thick superconducting The magnetic con"gurations above H ,lms  are still under discussion. From transport measurements it appears that the con"guration of #uxoids is not The penetration depth characterizes completely universal, but depends heavily on the anisotropy of the diamagnetism of a "lm for applied magnetic the coherent lengths, the thickness of the supercon- "elds below a critical "eld H , above which an ducting layers and the amount of the pinning 158 G.P. Felcher / Physica B 267}268 (1999) 154}161 centers. The anisotropy is reduced to shape anisot- altered from the bulk value in size, direction of ropy in a single "lm of niobium. Material anisot- magnetization and even type of magnetic order. ropy can be introduced by layering thin "lm of These new properties are the result of a complex set superconductor with metallic spacers (an extreme of circumstances, such as the incomplete quenching case is that of epitaxially grown high ¹ materials). of the orbital moments, the stretching (or com- In all cases pinning centers may give rise to a dis- pressing) of the lattice on the substrate, and the ordered distribution of #uxoids not aligned with transfer of electrons between magnetic "lm and the the "eld but straggling the "lm: the magnetic re- substrate. Polarized neutron re#ection has been sponse is then basically described by the Bean used to determine the absolute value of the mag- model [21]. In the absence of pinning centers netic moment per atom (notably in Fe and Co) in #uxoids should order into lattices. When the aniso- very thin "lms, and its increment compared to the tropy is extreme, the #uxoid currents are expected bulk values [24}28]. The results are in good agree- to be located principally within the superconduct- ment with those theoretically predicted as well as ing layers to minimize the tunneling through the those obtained by alternative techniques recently non-superconducting layers (Josephson vortices). developed [29,30]. For a less anisotropic medium a di!erent organiza- Magnetic bilayers have also been studied. When tion of #uxoids has been suggested [22]. Above in contact, the magnetization vectors of two layers, H  a single row of #uxoids is formed with spacing one of gadolinium, one of iron are oppositely alig- d at the center of the "lm to minimize the repulsion ned; however, in the presence of a magnetic "eld the from either surface; this splits into two rows above softer exchange interaction within the gadolinium a second critical "eld. layers gives rise to twisted states [31,32]. The inter- A one-dimensional lattice should give rise to an action between two layers of iron, interleaved with o!-specular di!raction line with exit angle : a metallic spacer, is strongly dependent on the (1/d)"(cos nature and the thickness of the spacer, as studied in !cos )/ , (5) Fe/Cr/Fe [33] and Co/Cu/Co [34]. If two mag- as derived from the conditions of conservation of netic layers are unequal in thickness, chemistry or energy and momentum for the neutrons. In prac- because one is anchored to an antiferromagnet, the tice, geometrical conditions severely restrict the system may behave as a spin-valve in the presence observable d spacings, and the intensity of the dif- of a magnetic "eld. PNR allowed the study of the fraction line is expected to be very weak anyway. layer by layer magnetization of such composites Up to now, the presence of a #uxoid lattice has [35,36]. been inferred only from the spin dependence of the re#ectivity [20,23]. The e!ect of #uxoids on the 2.3. Magnetic multilayers re#ectivities depends on their concentration as a function of z. If pinned at random, their e!ect First for very selected couples, then for a rapidly would be detected just close to the value of qX host of combinations of Fe, Co, Ni interleaved by corresponding to total re#ection. Instead, a line of most of the 3, 4, 5d non-magnetic metals it was #uxoids close to the center gives rise to a maximal found that the coupling between subsequent fer- spin dependence of the re#ectivity at qX&2 /(D/2) romagnetic layers oscillates from ferromagnetic (D is the total layer thickness). An array of Joseph- (FM) to antiferromagnetic (AF) as the thickness of son #uxoids in a multilayer should exhibit a maxi- the non-magnetic spacers is varied. Magnetic "elds mal spin dependence of the re#ectivity at the Bragg ranging from a few tens to a few thousand Oersteds re#ections of the multilayer. align the overall magnetization of AF multilayers, with a large change of magnetoresistance. The mag- 2.2. Very thin xlms netic structure of the AF state has been observed directly by PNR and found to be of the type For a "lm thickness below a few nanometers the #!#!, with a simple doubling of the chem- magnetization of a ferromagnet is signi"cantly ical periodicity. A number of papers have appeared G.P. Felcher / Physica B 267}268 (1999) 154}161 159 to con"rm this magnetic con"guration in several systems, study the pattern of antiferromagnetic do- mains, their evolution with the onset of a magnetic "eld and its correlation with the magnetoresistance [37}42]. Analysis of the polarization of the re#ec- ted neutrons has been used to determine the direc- tion of the magnetization as a function of depth. In this way it was con"rmed the presence of 903 mag- netic con"gurations for weak interlayer coupling, as justi"ed if biquadratric terms in the magnetic exchange become important [9,43}47]. Less studied, but of growing interest, are multi- layers with rare-earth spacers [48}52]. Multilayers of rare-earth/Fe or rare-earth/Co are inherently imperfect, in view of the large degree of mismatch of the lattice spacing of the two components. Such mismatch is, however, greatly reduced when the rare earth is hydrogenated. At the same time, the hydrogenation changes reversibly the band struc- ture and metallic character of the material contain- ing the rare earth, by an amount controllable with Fig. 3. Logarithmic contour plots of neutron intensities re#ec- ted from a cobalt "lm for an angle of incidence the hydrogen pressure. This line of research has just "0.443. The bottom and the top pictures represent plots for neutrons polariz- started; however for Nb/Fe, V/Fe superlattices it ed parallel and antiparallel to a magnetic "eld H"13 kOe has been shown [53,54] that hydrogenation can applied perpendicular to the surface. From Ref. [59]. switch reversibly the AF and FM states. was found by observing the magnetic satellites around the (0 0 1) di!raction line of chromium 3. The outlook [45,56]. Common to all these endeavors is the requirement that the intensity be measured at a few, Even from this incomplete review it becomes widely spaced points of q evident that the bulk of the experimental work X. To study these a re#ec- tometer/di!ractometer at "xed wavelength is the concerns the study of magnetic multilayers. To optimal instrument. determine the details of the magnetic pro"le of the Is there a future for the TOF re#ectometry? As single repeat unit a large qX region needs to be already stated, this instrument becomes preferable explored. At large qX the signal of the re#ected beam when the objective is to cover a substantial region is practically zero, except at Bragg re#ections of neutron momentum transfers. This is the case which, for a typical bilayer thickness of a few tens of when some magnetic scattering is o! the re#ection Asngstroms, appear at intervals qX&0.5 As\. line. Inhomogeneities in the plane of the "lm give Moreover, in epitaxially grown materials, di!rac- rise to scattering which appears in a two-dimen- tion lines due to the mean lattice spacing appear at sional counter at an angle q di!erent from and at X&6 As\. This line of research actually antedates an angle away from the plane of re#ection. If an the development of re#ectometry. For instance in FM or an AF multilayer is composed of in-plane superlattices of the type Gd/Y [55] large angle domains, the magnetism is no longer uniform in the di!raction lines have been measured in the middle plane of the "lm, and the "nite size of the domains 1980s to see the occurrence of magnetic dead layers gives rise to scattering around the direction of the at the Gd/Y interfaces. More recently, in studying re#ected beam. This has been repeatedly observed Fe/Cr superlattices, the link between the magneti- [1,57,58]; from the width of di!use scattering the zation of Fe and the spin density wave in chromium domain size has been deduced. As visually shown 160 G.P. Felcher / Physica B 267}268 (1999) 154}161 by A. Fermon in the following paper, patterned [5] B. Sarkissian, Vacuum 46 (1995) 1187. magnetic structures give rise to a rich spectrum of [6] C.F. 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