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Neutron Spin Echo Spectroscopy europhysics BULLETIN OF THE EUROPEAN PHYSICAL SOCIETY news J.A. Volume 16 Number 4 April 1985 Neutron Spin Echo Spectroscopy F. Mezei, Grenoble / Budapest * (Institut-Laue-Langevin / Central Research Institute for Physics) Inelastic neutron scattering is poten­ nance (NMR) allows us to study local done by methods mobilizing a larger tially the ultimate tool for the investiga­ fluctuations at nuclear sites at an ade­ number of quanta. tion of atomic and magnetic dynamics quate rate, but does not allow us to make For a (neutron) experiment to be pro­ on the microscopic scale in condensed direct observation of correlations be­ ductive it is not sufficient to have the matter. This is because of the unique tween neighbouring atomic sites. right kind of probe, one has also to be feature that both the wavelength and Further very useful features of neu­ able to extract enough information. This the energy of thermal neutron radiation tron radiation are its interaction with the is the problem of experimental resolu­ fall within the range relevant to the dyna­ magnetic moments in the sample via the tion (which is, e.g. the essential reason mics of common solids and liquids viz. neutron spin and its large penetration why we cannot use X-ray scattering for 1-10 A and 1-100 meV ≡ 0.25 - 25 THz. into many materials. This latter is made the study of, say, phonons). Conven­ Neutron scattering is the only microsco­ use of in industrial applications like neu­ tional neutron scattering methods allow pic probe able to provide the whole pic­ tron radiography and testing for phase us to determine the energy changes of ture in space and time although there are homogeneity in welds by neutron dif­ the neutron radiation in the scattering a number of other methods, which yield fraction. process with a typical best resolution of partial information. For example, X-ray Inevitably, such outstanding advan­ 1 %. This limits the range of frequencies scattering is very powerful in the deter­ tages cannot occur in real life without which can be studied to about 10 GHz - mination of atomic structures, but since drawbacks ! For neutrons there are two : 20 THz. (Epithermal neutron beams X-ray quanta have energies in the 10 keV neutron sources are expensive and even which are becoming available with pro­ range, it is not practical (at least so far) to the best available beam fluxes are small per intensities at the so-called "spalla­ observe changes on the meV or µeV in absolute terms (i.e. compared with the tion sources", extend this range to scale associated with atomic motions. number of atoms in a sample). Thus, maybe 500 THz.) To a very rough approximation, the while in an NMR experiment we typical­ energy changes of the scattered radia­ ly have 1020 nuclear spins to act on, or a tion can be looked upon as Doppler laser can provide 1020 light quanta Contents shifts caused by the motions of the scat­ within reasonable time, the highest flux tering atoms. In contrast, with light scat­ neutron scattering instruments barely Neutron Spin Echo Spectroscopy 1 tering one can observe easily any energy provide 1013 neutrons over a day. Con­ New Members of EPS 4 change that might occur, but the basic sequently only relatively big samples Neutral Injection Heating in wavelength of several 1000 A restricts and/or strong scattering effects can be Fusion Devices 5 the space domain studied to one of simi­ studied with neutron scattering and the Nuclear Methods in Condensed lar size, i.e. to practically macroscopic statistical accuracy of the results is al­ Matter Physics Studies 9 regions. Or, to take an example at the ways limited. As a rule of thumb, neutron Hewlett-Packard Prize 11 and 16 other extreme, nuclear magnetic reso- scattering investigation, giving a detail­ Surface Studies of MBE-Grown ed, model-independent space-time pic­ Semiconductor Films 12 ture, is indispensable if we are not ab­ Council Decisions 15 * Present Address : solutely sure of the nature of a particular Changes to EPS Constitution Hahn-Meitner-Institut and phenomenon, whereas systematic stu­ and By-Laws 16 Technical University, dies on a large number of similar sys­ IOM Delegate to Council 16 Berlin (West) tems, including small samples, is better Europhysics News is published monthly by the European Physical Society. © 1985. Reproduction rights reserved. ISSN 0531-7479 1 Fig. 1 — Scheme of a neutron spin echo precession angle Φ1 The comparison spectrometer: IN11 at ILL, Grenoble. The between φo and φ1 is made by making length of the precession field solenoids is 2 the two precessions to occur (effective­ m and the maximum precession field is 750 ly) in the opposite sense, resulting in a 0e. For 8 A wavelength neutrons, this gives total precession angle (if Ho = H1 = H, rise to about 55000 rad precession. cf. Fig. 1) of: where δv = v1 - vo and we assume δv << v0. Remembering that the neutron energy is 1/2 mv2, we see that φ is just a measure of the neutron energy change in the scattering process, hω, which is what interests us : if v0 is rather well defined (in practice beams with about ± 10% variation of vo are used) the proportionality constant t = γLHl/mv03 is also. The important thing is that the obser­ vable quantity φ is directly related to the change of the neutron energy, and we do In order to study slower phenomena, gnetic field H conveniently lends itself to not have to proceed by the determina­ the energy resolution had to be improv­ its use as a time base : tion of the initial and final neutron ener­ gies in two separate steps. Therefore hω ed well beyond the 1% level. The main ωL = γLH (1) can be determined independently of the difficulty in doing this was not really where the constant γL = 2.916 kHz/Oe. scatter of the initial and final neutron technical but fundamental : the problem If a neutron with a velocity v crosses a energies, and, for the first time, the of low beam intensity. The production of magnetic field of strength H and length energy resolution becomes independent a highly monochromatic beam means l, the total Larmor precession angle φ of the monochromatization of the beam. selecting out a tiny portion from the will be a measure of its velocity : This means that we have managed to originally Maxwellian neutron energy φ = γlHl/v (2) distribution. Since low beam intensities In writing down this equation we impli­ side-step the normal reciprocal relation are the main limitation in neutron scat­ citly assume that the neutron can be between resolution and beam intensity. tering from the outset, the direct path to considered as a classical particle, is it is The fundamental practical point in higher resolution is basically limited by pointlike and thus has a well defined tra­ NSE is how to produce and analyse Lar­ the flux alone. The so-called "backscat- jectory and velocity, while its spin cor­ mor precessions. This can be done sur­ tering'' method, in which 0.01 - 0.1% responds to a classical vector and per­ prisingly easily with the help of a simple monochromatic beams are used, fol­ forms precessions in a field in the classi­ flat coil (Fig. 2), whose introduction in lows this conventional path. The price cal mechanical sense, like a top. This is 1972 at the Central Research Institute one has to pay for the gain in energy certainly at variance with the “popular" for Physics in Budapest was actually the (time) resolution (30-100 MHz lower picture, of the spin of a spin 1/2 particle starting point of NSE 1). If neutrons limit) is that in order to recover some of being able to occupy only discrete "up" enter the coil with spin S parallel to the the lost intensity, the momentum and "down" states. Such a picture is, of external field H, inside the coil they will (space) resolution has to be relaxed. course, an incorrect over-simplification, start to process around the field H' Logically, the method has proved to be but it was the reason nevertheless why which is the sum of the external field H extremely successful, primarily in the for a long time, little effort was made to and the field Hc produced by the coil. If, study of non-dispersive (wavenumber explore the full vectorial character of as shown, the neutrons leave the coil independent) phenomena, such as the spin polarization in particle beam ex­ after half a precession around H' which tunnelling motion of protons and other periments. Rigorous quantum mechani­ radicals between various local equili­ cal analysis shows 3), that in magnetic brium positions within the elementary fields where the gradients are not too cell of a crystal. strong (in the absence of the Stern- To overcome the fundamental intensi­ Gerlach quantum effect) the neutron ty barrier to higher resolution a radically spin motion can be treated classically, new approach was needed : the resolu­ i.e. by considering the Larmor preces­ tion had to be decoupled from the mono­ sions governed by the classical equa­ chromatisation. This apparent contra­ tion : diction is solved in the neutron spin echo dS/dt = γL [S x H] (NSE) method 1). The basic idea is that where S is the spin vector. instead of monochromatizing the beam In a neutron spin echo spectrometer impinging on the sample, we make each (Fig. 1) a first "precession" field is used neutron remember its initial velocity. In to allow each neutron to label its own ini­ order to do this, we use the natural in­ tial velocity vo by performing a preces­ Fig.
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