Combining of Neutron Spin Echo and Reflectivity: a New Technique For

ARTICLE IN PRESS

Physica B 336 (2003) 8–15

Combining of neutron spin echo and reﬂectivity: a new technique for probing surface and interface order

J. Majora,*, H. Doscha, G.P. Felcherb, K. Habichtc, T. Kellerd, S.G.E. te Velthuisb, A. Vorobieva, M. Wahla a Max-Planck-Institut fur. Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany b Argonne National Laboratory, Argonne, IL, USA c Hahn-Meitner-Institut, BENSC, Glienickerstr. 100, D-14109 Berlin, Germany d Max-Planck-Institut fur. Festkorperforschung,. Heisenbergstr. 1, D-70569 Stuttgart, Germany

Received 6 December 2002; accepted 2 March 2003

Abstract

The recently proposed spin-echo resolved grazing-incidence scattering (SERGIS) uses the well-known neutron spin echo effect for encoding the momentum transfer in reflectometry. By the application of tilted magnetic-field borders, SERGIS measures the scattering angle in grazing incidence experiments in absence of any geometrical beam-defining tool, such as slits. The main difficulty in such set-ups is the realization of geometrically flat field borders. The possibility of the application of neutron resonance spin echo (NRSE) for such a purpose is discussed, where the field borders are defined by current sheets. Prototype SERGIS experiments performed on holographically made optical gratings at a NRSE triple-axis spectrometer are shown. r 2003 Elsevier Science B.V. All rights reserved.

PACS: 61.12.Ha; 68.35.Ct; 68.47.Mn

Keywords: Neutron reﬂectivity; Grazing incidence diffuse scattering; Neutron spin echo; SERGIS; Neutron resonance spin echo; NRSE

1. Introduction semi-macroscopic lateral scales. Similar experiments using X-rays generated in modern synchro- Neutron reflectivity, or more generally, the tron-radiation sources have the benefit of a scattering of grazing incidence neutrons on flat brilliancy of the source considerably higher than sample surfaces, may provide unique information that available for neutrons. We will show how the not only about the depth-dependent, laterally application of neutron spin echo (NSE) can averaged structure of the sample, but also about partially remove this deficiency, making possible their in-plane correlations in microscopic to experiments exploiting the other advantages of neutrons, the low neutron absorption and the non- *Corresponding author. Tel.: +49-711-689-1264; fax: +49- monotonous dependence of the neutron scattering 711-689-1932. length on the number of protons and neutrons in E-mail address: [email protected] (J. Major). the nucleus.

J. Major et al. / Physica B 336 (2003) 8–15 9

The magnetic moment of the neutron, which is D coupled to its spin, makes the exploration of the P A F S E 1 magnetic structure with microscopical resolution 2 feasible, in both the bulk and the surface of 2 1 +B −B condensed matter. The existence of the neutron spin allows in addition to apply the NSE method which traditionally encodes the neutron-energy Fig. 1. The principle of an energy-transfer encoding (conven- transfer taking place in the scattering process [1]. tional) neutron spin echo spectrometer. P and A: neutron spin This paper discusses the application of NSE in off- polarizer and analyser; F: first precession area, B: magnetic field, S: sample, E: second (echo) precession area, D: neutron specular reflectivity experiments as first proposed detector. The arrows denote the polarization of the neutron by Rekveldt [2]. The method, dubbed as SERGIS spin. The measured quantity is the polarization P of the (spin-echo resolved grazing-incidence scattering neutron beam at the exit site from E; as a function of B: In the [3]), encodes the momentum change of the neutron neutron path 1, no energy transfer takes place at the sample and during its scattering at the sample as a rotation of the initial polarization is restored, while path 2 corresponds to events, in which the velocity of the neutrons is different in F the neutron spin in the absence of any geometrical and E; i.e. the neutrons become depolarized (the thicker line beam-defining tool, such as slits and a position denotes the path with altered speed). sensitive detector. The advantage of SERGIS is obvious: for the price of polarizing the neutrons (50% intensity loss), and of analysing the polarization, we can the neutrons does not change during the scatter- resolve a component of the scattering vector along ing, the polarization will be restored due to the a direction in which the beam is not collimated. symmetry of the magnetic-field arrangement for NSE was invented three decades ago by Mezei any neutron speed (echo condition). In the case of for encoding the velocity (energy) change of the an energy exchange at the sample, however, the neutrons during scattering into the rotation of the neutrons will be depolarized at the exit position neutron spin [4]. In this method, a sensitive from E: The measured quantity is the polarization discrimination of the neutron-energy transfer P of the neutron beam at this site. The function becomes possible without the corresponding nar- P ¼ PðBÞ provides us with the time-dependent row energy windows upstream and downstream of correlation function, i.e. the intermediate scatter- the sample, i.e. without the usual substantial ing function of the sample [6]. intensity penalty. General discussion on the NSE In traditional NSE equipments (energy-transfer can be found, e.g. in Ref. [5]. Shortly after the encoding; longitudinal field set-up, i.e. the mag- exploration of the NSE, the possibility of the netic field is parallel to the neutron beam) one of momentum-transfer encoding was also proposed the main difficulties wasR to solve the following [6,7]; however, the construction of the necessary problem. The integral B dx along the neutron magnetic-field set-up was technically not yet path is a quantity which defines the number of possible at that time. precessions of the neutron spin in the magnetic- The principle of conventional (energy-transfer field regions. The field integral should be sym- encoding) NSE is sketched in Fig. 1. The polarized metric around the sample position: in other words, neutron beam traverses the first magnetic-field the echo condition should be fulfilled simulta- area ðFÞ where the spins rotate according to the neously for all possible neutron paths [5]. This was time they spend in the magnetic field determined a prerequisite for being able to use the full by their individual speed. After scattering on the available beam intensity in high-resolution NSE sample (S), in the second (echo) magnetic-field experiments. In particular, the construction of the area ðEÞ; the spins rotate in the opposite (echo) field borders at the entry and the exit positions of direction according to their possibly changed the neutron beam is not a trivial task, since velocity. E possesses the same geometry and the magnetic-field lines cannot be terminated magnetic-field magnitude B as F: If the speed of ðdiv B ¼ 0Þ: However, the application of different ARTICLE IN PRESS

10 J. Major et al. / Physica B 336 (2003) 8–15 compensation coils solved this problem for the be restored due to the symmetry of the magnetic- longitudinal-field instruments. field arrangement for any flight direction (echo condition). As for conventional NSE, the measured quantity is the polarization P of the neutron beam at the exit position from E as function of B: 2. The encoding of the momentum transfer The change of the neutron-path direction, which results in a depolarization, corresponds to an in- The principle of momentum-transfer encoding plane transverse momentum transfer (Fig. 2). reflectometry NSE is sketched in Fig. 2. It differs Since the time the neutron spends in the field from conventional NSE (Fig. 1) only in the areas depends only on its momentum components geometry of the borders of the magnetic-field parallel to nSE; the spin-echo encoding is per- regions. In this instrument, the magnetic fields are formed only for these components. If the encoded applied along the neutron path with well-defined momentum component is perpendicular to that parallel flat entrance and exit faces which are resolved by conventional scattering methods, the inclined by an angle of Z0 to the mean neutron SE spin echo and the conventional experiment can be direction. The unit vector n ; the spin-echo performed simultaneously. vector, is perpendicular to the bordering planes Let us use the system of Cartesian coordinates of the field areas. The polarized neutron beam as defined in Fig. 2. The density function f of the traverses the first magnetic-field area ðFÞ where the distribution of the scattering angles j can be spins rotate while the neutrons are passing through calculated from the scattering profile gðyÞ by the the magnetic field. After scattering on the sample Fourier power transformation (S), the spins precess in the opposite (echo) Z 2 direction while passing through the magnetic-field f ðjÞ¼ gðyÞ expðiqyyÞ dy ; ð1Þ area ðEÞ: We may assume that the scattering is elastic, consequently the time one neutron spends where qy ¼ k0 sin j ðk0 ¼ 2p=lÞ is the transverse in E will only be different from the time spent in F wave-number transfer and l is the neutron if the direction of the neutron has changed during wavelength. scattering in the plane of the figure. If the direction It is worthwhile introducing the so-called spin- of the neutron does not change during the echo length [8] according to scattering, the polarization of the neutrons will m g dSE ¼ n n BLl2 cot Z ; ð2Þ 2ph 0

D where L is the length of the areas F and E 2 P A measured along x; mn is the neutron mass, gn is the nSE F S E ϕ neutron gyromagnetic ratio, and h ¼ 2p_ the 2 1 Planck constant. In the energy-resolving NSE, 1 η +B y −B 0 the analogous quantity is the spin-echo time [8]. SE x d is proportional to B and will be used below instead of B to specify the magnetic field. Fig. 2. The principle of the momentum-transfer encoding NSE In the first-order approximation, the resulting instrument. The flat borders with the normal unit vector nSE of the magnetic-field areas are perpendicular to the plane of the phase F of the spin at the exit position from E is figure but not to the direction of the neutron beam. For the SE SE F ¼ d qy ¼ k0d j: ð3Þ meaning of the symbols, see the caption of Fig. 1. The neutron path 1 corresponds to events, in which the direction of the The magnetic-field dependent polarization is an neutron path, at least in the plane shown, does not change average ð/ySÞ for all neutrons in the experiment: during scattering and the initial polarization is restored at the exit of E: Path 2 illustrates the case, in which the direction of PðdSEÞ¼/f ðjÞ cos FðjÞS the neutrons are different in F and E (scattering angle j) and Z SE the neutrons may become depolarized. If applied to reflecto- ¼ f ðjÞ cosðk0d jÞ dj; ð4Þ metry, the sample flat lies in the figure plane. ARTICLE IN PRESS

J. Major et al. / Physica B 336 (2003) 8–15 11 which is the cosine transform of (1) and repro- B0 duces the symmetrical part of the scattering profile B B = 0 B gðyÞ; i.e. provide us directly with the time- 0 0 B ω independent pair-correlation function of the scat- 1 B1 B1 1 tering system. (a) (b) In the realization of a SERGIS experiment, the Fig. 3. Magnetic-field arrangement in a NRSE set-up. (a): The main difficulty is the construction of inclined field ‘precession area’, which corresponds to area F or E in Fig. 2,is borders, which enclose the areas where the neutron field free except of two relatively thin layers at the neutron entry spins perform Larmor precession, that are rigor- and exit faces. (b): The fields in these thin layers lie in the layer ously flat. The application of specially formed plane; B0 is a constant field, B1 a sinusoidal (radio frequency, RF) field of angular frequency o ; which is perpendicular to B : correction coils [9] seems to work only for small 1 0 inclination angles ðZ0 > 82 Þ: A possible alternative consists in the usage of thin, flat neutron spin flippers, which—in a magnetically homogeneous Since in NRSE the crucial magnetic-field bor- area—‘switch on’ or ‘switch off’ the Larmor ders are accomplished by current sheets, large precession by the fast rotation of the spin out of magnetic-field gradients can be realized very or back to the field direction [10–12]. In such accurately. experiments, B can be longitudinal or transverse; a transverse-field set-up with the application of thin ferromagnetic sheets as spin-flipper devices is 3. ‘‘Proof of principle’’ experiments reported in the present volume [13]. For the first experiments, a neutron resonance In order to test the SERGIS principle, we used spin echo (NRSE) set-up has been used for the commercial optical gratings as samples, since those realization of the inclined magnetic-field borders. possess strong and well-known surface corruga- In NRSE [14–16], a combination of in-plane tions. The samples were holographically made magnetic fields are present in relatively thin border sinusoidal gratings with 3600 grooves=mm; #1 had sheets at both ends of the areas F and E shown in an aluminium surface with an amplitude of the ( ( Fig. 2, and the internal parts of the ‘precession grooves of 80 A [18], #2 had a 8000 A thick gold areas’ are free of magnetic fields (this technique is surface and the grooves’ amplitude was 150 A( [19]. sometimes called ‘zero-field NSE’). The usual set- It is well known from the literature [20,21] that up is constructed in a way that the level of such gratings give strong diffraction effects in magnetic stray fields are very low (bootstrap coils neutron-reflectivity experiments. The present sam- [17]). The magnetic-field arrangement in the ples were tested at the conventional reflectometer NRSE is sketched in Fig. 3. The resonance EVA (Institut Laue-Langevin, Grenoble, France) conditions for the parameters of the magnetic [22,23]. The results obtained on sample #2 are fields are shown in Fig. 4. The sample was oriented with grooves nearly parallel to the mean direction of the o1 ¼ gnB0; ð5Þ neutrons and the Bragg diffraction peaks corresponding to the longitudinal periodicity of the surface corrugations are well reproduced in the gnB1t1 ¼ 2p; ð6Þ results. In the reflection pattern (Fig. 4), we see where t1 is the neutron precession time in the layer Bragg reflections of at least three different orders. of the field B1: If the parameters of the set-up fulfil The surface of the sample #2 was also tested by the resonance conditions (Eqs. (5) and (6)), such atomic-force microscope as shown in Fig. 5. device works identical to a static-field set-up as in We performed the spin-echo tests at the FLEX Fig. 2, if the geometry is the same and B ¼ 2B0; or (V2) three-axis spectrometer at the Berlin Neutron in the case of the bootstrap set-up, B ¼ 4B0: For Scattering Center (BENSC) of the Hahn-Meitner- details see Ref. [17]. Institut (Berlin, Germany), equipped with a NRSE ARTICLE IN PRESS

12 J. Major et al. / Physica B 336 (2003) 8–15 set-up [25,26] and aligned in the geometry of a dence angle of a fraction of a degree. Horizontally simple (but rather limited) reflectometer. The the beam was fully open, its divergence was sample was mounted horizontally and the verti- approximately 1 (FWHM) according to the cally collimated polarized neutron beam ðl ¼ parameters of the neutron guide and of the 5:92 A( Þ impinged the surface in a grazing-inci- pyrolytic graphite monochromator crystals. In experiments made on sample #1, the detector was simply a large single detector, while for sample #2, a scintillation counter with a 2D CCD was used. The beam was polarized by a magnetized supermirror in the transmission mode, the scat- tered beam by a stack of magnetized supermirrors in front of the detector. As in the EVA experiment (Fig. 4), the grooves of the gratings were approximately along the x-axis (mean beam direction). Fig. 6 shows the patterns of neutrons recorded at the detector, with no magnetic field applied in the precession areas. The upper stripe represents the strongest diffracted beam. This does not give rise to an isolated spot, because of the divergence of the incoming beam. The same divergence causes the diffraction stripe to be tilted with respect to the specularly reflected beam. The SERGIS results, i.e. the magnetic-field- dependent polarization values, are presented in Figs. 7 and 8. Here the periodicity of the samples is well revealed. The horizontal axes in these figures SE Fig. 4. Diffraction pattern of the optical grating #2 at the EVA depict the spin-echo length ðd Þ; which is propor- (ILL, Grenoble) reflectometer ðl ¼ 5:5 A( Þ: The horizontal axis tional to the effective magnetic field in the Larmor- is the grazing incidence angle ðaiÞ; the vertical is the grazing final precession areas (cf. Eq. (2)). A peak in the SE angle ðaf Þ: The line inclined by 45 is the specular ridge. The polarization occurs when d is a multiple of grooves of the grating were nearly parallel to the direction of the periodicity of the grating. As a reference, the the neutron beam (azimuthal angle E2). In this experiment, only those Bragg scattering events that occurred in the results of an experiment on the sample #1 with reflection plane could be resolved, since the beam was not propagation vector turned into the x direction are collimated in the plane parallel to the sample. also shown. In this case, the momentum transfer

Fig. 5. The corrugated surface of sample #2 as obtained by an atomic-force microscope [24]. The horizontal range of the picture is 5 Â 5 mm2; the height is scaled to 0–160 nm: ARTICLE IN PRESS

J. Major et al. / Physica B 336 (2003) 8–15 13

0.8

diffracted beam 0.6 reflected beam 0.4 Polarization

0.2 direct beam 0 Fig. 6. Typical read-out of the 2D position sensitive detector 0 2000 4000 6000 8000 obtained setting FLEX in the reﬂectivity mode for sample #2. Spin-echo length δSE [Angstrom] The vertical structure is due to the structure of the spin analyser supermirror stack. The direct, the reﬂected, and one of the Fig. 8. Results of the SERGIS experiments on the optical diffracted beams are easy to identify. Other diffracted beams grating #2 performed at the FLEX (V2, BENSC-HMI) are too faint to be observable in this image. instrument. The orientation of the grooves is almost parallel to the direction of the neutron beam.

1.2 not only at the ﬁrst, but also at the second spin- echo length (cf. Fig. 8). This seems to indicate that 1 the lateral coherence length in SERGIS-type experiments is far greater than that obtained in 0.8 conventional small-angle scattering.

0.6 In the usual reﬂectometry or small angle

Polarization neutron scattering (SANS) experiments with slit 0.4 defined momentum transfer resolution, the transverse correlation length of the detected neutron 0.2 wave field at the sample along the y-axis can be calculated from the divergence angle of the 0 0 1000 2000 3000 4000 neutron beam at the sample Oy according to Spin-echo length δSE [Angstrom] slit l Fig. 7. Results of the SERGIS experiments on the optical xy ¼ : ð7Þ grating #1 performed at the FLEX (V2, BENSC-HMI) Oy instrument. The orientation of the grooves is perpendicular This equation is based on the fact that in slit- (squares) or almost parallel (circles) to the direction of the neutron beam. geometry instruments the momentum transfer is defined exclusively by the slit geometry. Such due to the Bragg scattering is perpendicular to nSE consideration does not apply to SERGIS results and therefore the Bragg events are not resolved by (Figs. 7 and 8), where the momentum transfer is slit the SERGIS. The observed loss of polarization is obtained by NSE. The value xy ¼ l=Oy ¼ due to inhomogeneities in the field distribution or 5:92 A( =1 ¼ 350 A( is in contrast to the clearly due to stray-field effects. resolved periodicity of 2800A( : To estimate the lateral correlation length, the following considerations are made. In SERGIS 4. Analysis of the experiments experiments, the Bragg scattering angle j is determined by NSE with the application of Perhaps the most dramatic result of the experi- magnetic fields in the two precession areas up- ments conducted on optical gratings is the stream and downstream of the sample. The determination of the period of the optical grating ‘mistake’ in the resulting rotation (phase) of the ARTICLE IN PRESS

14 J. Major et al. / Physica B 336 (2003) 8–15 neutron spin at the analyser position is the 5. Future plans quadratic sum of the errors accumulated in the two precession legs. The error in the phase of In this paper we show how a combination of the first leg is SERGIS and NRSE can extend the capabilities of B neutron reflectometry. DF ¼ D g L ¼ DðcBÞ In SERGIS experiments the component of the 1 n v sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SE momentum transfer q parallel to n is encoded. Dc 2 DB 2 Usually this component is in the plane of the ¼ cB þ ; ð8Þ c B surface, for instance along the y direction (Fig. 2). The q component along z; perpendicular to the where v is the neutron velocity. Here we have surface, is measured by conventional reflectome- compounded the geometrical errors in c; separat- try. When q possesses a component also along the ing them from the error in the sweeping field B: If x-axis, this is detected in off-specular scattering in it is reasonable to assume that DB=B is a constant, the plane of reflection. Thus, a combination of for an instrumental geometry there is an upper spin-echo and conventional diffuse scattering can field B for which DF1 becomes unacceptably large provide a three-dimensional image of the structure ðDF1 ¼ 2pÞ; resulting in depolarization. Note that near the surface. at the first peak in the polarization in Fig. 8, A very special property of the NSE is that the F1E2p Â 500; which means that even after the correlation length of the radiation field, which neutron spin has made 500 precessions, it is still far probes the sample, depends only on the perfection from being depolarized. From the decay of the of the precession legs, but is not influenced by polarization between the first and the second peak parameters of the neutron source or of the in Fig. 8, the spin-echo length where depolariza- geometry of the beam-defining slits. This may be tion occurs is determined to be of order of 1 mm; the most important advantage of the NSE, because which is a measure of the lateral correlation the increase of the correlation length or the length. angular resolution does not result in intensity loss The form of the lines in Figs. 7 and 8 should during the experiments. reveal the scattering profile of the sample as a SERGIS-type experiments open new possibili- time-independent pair-correlation function of the ties in the study of surfaces and interfaces. Further neutron scattering length density as expressed by experiments on surfaces with well-characterized Eq. (4). This equation was derived within the first roughness should enable to provide a firm assess- Born approximation. When the validity of the ment of the boundary in the height–height approximation breaks down as is the case for our fluctuation below which the first Born approxima- sample, the optical transformation from the tion retains its validity. This, by previous estimates ( diffraction space to the real space is considerably [29] is lower than 100 A: This is a region where less straightforward. quite interesting physical phenomena take place, For this quasi-tridimensional modulation of the for instance in dewetting of polymers on a silicon surface, the real space profile cannot be obtained surface [30]. by a simple Fourier transformation as outlined in To prove the scientific case of SERGIS, the Eqs. (1)–(4). As well known in optics (cf. for construction of a dedicated SERGIS reflectometer instance for X-rays [27], for neutrons [28]), higher set-up is in progress at Stuttgart. While the design order Bragg reflections are obtained even if the includes at present the adoption of conventional grating profile is purely sinusoidal. As seen in NRSE circuits [17], it is possible that a better Fig. 4, this is the case for sample #2. The real space refinement includes permanent magnet elements profile can be recovered in this case by using the that are being concurrently tested [13,31,32]. Their correct optical transformation as obtained by adaption might overcome a difficulty encountered solving the Schrodinger. equation for a neutron by the usage of conventional NRSE coils: the wave impinging the sinusoidal surface. neutron beam crosses a few millimeters of oxidized ARTICLE IN PRESS

J. Major et al. / Physica B 336 (2003) 8–15 15 aluminium, and this gives rise to an amount of [10] M. van Oossanen, W.H. Kraan, W.G. Bouwman, M.Th. small angle scattering (before and after the sample) Rekveldt, Physica B 276–278 (2000) 134. that creates an unwanted and limiting back- [11] W.G. Bouwman, M. van Oossanen, O. Uca, W.H. Kraan, M.Th. Rekveldt, J. Appl. Crystallogr. 33 (2000) ground. 767. The eventual goal of this endeavour is to make a [12] M.Th. Rekveldt, W.G. Bouwman, W.H. Kraan, J. Appl. solid case and a concrete design for a SERGIS- Phys. 92 (2002) 3354. type instrument to be installed at the new [13] R. Pynn, M.R. Fitzsimmons, H. Fritzsche, J. Major, generation of neutron sources, like the European M.Th. Rekveldt, in these Proceedings (SXNS-7), Physica B 336 (1–2) (2003). Spallation Source or the Spallation Neutron [14] R. Golub, R. Gahler,. Phys. Lett. A 123 (1987) 43. Source, that are actively considered at present or [15] R. Gahler,. J. Felber, F. Mezei, R. Golub, Phys. Rev. A 58 already under construction. (1998) 280. [16] T. Keller, R. Golub, R. Gahler,. in: R. Pike, P. Sabatier (Eds.), Scattering, Academic Press, San Diego, 2002, p. 1264. Acknowledgements [17] M. Koppe,. M. Bleuel, R. Gahler,. R. Golub, P. Hank, T. Keller, S. Longeville, U. Rauch, J. Wuttke, Physica B 266 The authors are indebted to B. Farago! (ILL), (1999) 75. R. Golub (HMI), and F. Mezei (HMI) for useful [18] Type K43228, Edmund Industrial Optics, Barrington, NJ, discussions. The support of the management and USA. [19] Type 8306BK-520H, Thermo RGL, Rochester, NY, staff at the Berlin Neutron Scattering Center of the USA. Hahn-Meitner-Institut and at the Institut Laue- [20] A.E. Munter, S. Adenwalla, G.P. Felcher, X.L. Zhou, in: Langevin (Grenoble) is gratefully acknowledged. D.A. Neumann, Th.P. Russell, B.J. Wuensch (Eds.), Work at Argonne was supported by the Depart- Neutron Scattering in Material Science II, MRS, Pitts- ment of Energy, Ofﬁce of Science, under contract burgh, 1995, p. 199. [21] R.M. Richardson, J.R.P. Webster, A. Zarbakhsh, J. Appl. 31-109-ENG-38. The activity of one of us (G. P. Cryst. 30 (1997) 943. F.) was partially supported by the Humboldt [22] H. Dosch, K. Al Usta, A. Lied, W. Drexel, J. Peisl, Rev. Foundation. Sci. Instr. 63 (1992) 5533. [23] http://www.ill.fr/YellowBook/EVA. [24] Explorer Scanning Probe Microscope, Veeco/TM Micro- scopes, Cunnyvale, CA, USA. References [25] T. Keller, R. Gahler,. H. Kunze, R. Golub, Neutron News 6 (1995) 16. [1] F. Mezei, in: F. Mezei (Ed.), Neutron Spin Echo, Lecture [26] T. Keller, R. Golub, F. Mezei, R. Gahler,. Physica B 241– Notes in Physics, Vol. 128, Springer, Berlin, 1980, p. 3. 243 (1998) 101. [2] M.Th. Rekveldt, Physica B 234–236 (1997) 1135. [27] J. Daillant, A. Giboud (Eds.), X-Ray and Neutron [3] G.P. Felcher, S.G.E. te Velthuis, J. Major, H. Dosch, C. Reﬂectivity: Principles and Applications, Lecture Notes Anderson, K. Habicht, T. Keller, in: I.S. Anderson, B. in Physics, Vol. 58, Springer, Berlin, 1999. Guerard (Eds.), Advances in Neutron Scattering Instru- [28] F. Ott, P. Humbert, C. Fermon, A. Menelle, Physica B 297 mentation, Proceedings of SPIE, Vol. 4785, SPIE Optical (2001) 189. Engineering Press, Bellingham, WA, USA, 2002, p. 164. [29] U. Pietsch, Phys. Rev. B 66 (2002) 155430. [4] F. Mezei, Z. Phys. 255 (1972) 146. [30] P. Muller-Buschbaum,. J.S. Gutmann, M. Stamm, R. [5] F. Mezei (Ed.), Neutron Spin Echo, Lecture Notes in Cubitt, S. Cunis, G. von Krosigk, R. Gehrke, W. Petry, Physics, Vol. 128, Springer, Berlin, 1980. Physica B 283 (2000) 53. [6] F. Mezei, in: Neutron Inelastic Scattering, IAEA, Vienna, [31] R. Pynn, M.R. Fitzsimmons, M. Theo Rekveldt, J. Major, 1978, p. 125. H. Fritzsche, D. Weller, E.C. Johns, Rev. Sci. Instr. 73 [7] R. Pynn, in: F. Mezei (Ed.), Neutron Spin Echo, Lecture (2002) 2948. Notes in Physics, Vol. 128, Springer, Berlin, 1980, p. 159. [32] M.R. Fitzsimmons, H. Fritzsche, J. Major, R. Pynn, [8] R. Gahler,. R. Golub, K. Habicht, T. Keller, J. Felber, M.Th. Rekveldt, in: I.S. Anderson, B. Guerard (Eds.), Physica B 229 (1996) 1. Advances in Neutron Scattering, Proceedings of SPIE, [9] K. Abrahams, O. Steinsvoll, P.J.M. Bongaarts, P.W. de Vol. 4785, SPIE Optical Engineering Press, Bellingham, Lange, Rev. Sci. Instr. 33 (1962) 524. WA, USA, 2002, p. 143.