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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 experi- ments 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. 0921-4526/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4526(03)00264-3 ARTICLE IN PRESS 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 mea- sured 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.
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