europhysics BULLETIN OF THE EUROPEAN PHYSICAL SOCIETY news J.A. Volume 16 Number 4 April 1985

Neutron Echo

F. Mezei, Grenoble / Budapest * (Institut-Laue-Langevin / Central Research Institute for Physics)

Inelastic 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 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 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 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 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 : 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. 2 — The key element of NSE spectro­ dividual clock each neutron possesses: sion of Φ0, and after scattering on the scopy: the spin flip coil (typically activated its spin. In effect, the Larmor spin pre­ sample a second precession field is used by 1-3 A DC current) and an example of spin cession frequency ωL in an external ma- to measure the final velocity v1 via the turn by Larmor precession inside the coil. 2 exploration of the time domain is some­ times a very useful additional feature of NSE. Note that in an NSE experiment PNSE is determined as a function of t, the latter being varied most simply by chan­ ging the precession field H, (cf eq. (3)). Evidently the name given to the me­ thod has little to do with the above con­ siderations, rather is it justified techni­ cally. Fig. 3 shows what we actually observe measuring the x component of Fig. 3 — NSE signal showing the echo ef­ the precessing polarization after the se­ fect as measured with an 18% FWHM velo­ cond precession field H1 as a function of city-selected beam. The dephasing and de­ that field 1). As we have seen, at Ho = crease of the precessing polarization on both sides of the H0 = H1, echo condition H1, φ will be the same, i.e. zero, for all reflect this 18% spread of neutron veloci­ neutrons with v1 = v0 . This is not the ties. case when Ho ≠ H1, and the distribution Fig. 4 — The relaxation rate measured in pig of vo (or v1) introduces a distribution of immunoglobulin G-D20 solution of 7.33 precession angles φ which ultimately wt.% concentration 4). The line corres­ is bisecting the directions of H and Hc, makes Px average to zero. Therefore the ponds to the Dq2 law with a diffusion cons­ the effect of the coil is to turn S from the "echo signal" in Fig. 3 can only be tant D = 2.74 x 107 cm2s-1. direction of H into that of Hc. This is how observed around H0 = H1 (if vo ≡ v1). It the Larmor precessions can be initiated is interesting to note that this echo determined by sedimentation. Observ­ by turning through 90° the neutron signal is just the image of how the neu­ ing that the q range of the NSE experi­ spins, originally parallel to the field (Fig. tron waves in the beam would look if we ment corresponds to the size of the con­ 2). The inverse procedure, turning a described them by quantum mechanical stituant subunits of the IgG molecule, component of the precessing polarisa­ (coherent) wave-packets as opposed to this difference can be interpreted as tion (i.e. perpendicular to the field) into a distribution of classical velocities v. evidence for intramolecular motion : on a the field direction and using a conven­ The two approaches lead to exactly the length scale smaller than the size of the tional spin analyser, allows us to observe same results, of course 3). molecule, the subunits move faster than Larmor precessions. It turns out that the Since the IN 11 NSE spectrometer the molecule as a whole. On the purely fields required to achieve such spin turns (built by the author in collaboration with technical side, on the other hand, note are rather modest: e.g. with 1000 m/s(~ Paul Dagleish and John Hayter) went that the neutron energy changes (cor­ 4 A wavelength) neutrons and a 1 cm into operation in 1978 at the ILL, many responding to the Γ values in the figure) thick coil, H and Hc have to be of 12.1 0e successful and significant experiments are on the neV (10-9 eV) scale compared in order to achieve a 90° spin turn (cf eq. have been performed on the dynamics with the incoming neutron energies that (2)). Moreover, neutron radiation will of polymers and biopolymers in solu­ traverse the single layer of Al wire win­ tions, on atomic and molecular diffusion dings that make up the coil without ap­ in liquids and solids, on critical fluctua­ preciable intensity loss. tions in structural and magnetic phase The analysis of the precessing polari­ transitions, on the nature of the spin sation in the beam does not mean in glass transition, on the decay of elemen­ practice the direct measurement of the tary excitations in superfluid helium, on angle φ, but the observation of one com­ soliton dynamics, etc. It is not our pur­ ponent (say x) of the polarization P. If φ pose here to consider in depth any of is measured with respect to the x axis, these results (an early summary can be we have found in Ref. 2). To illustrate the perfor­ Px = < cos φ > mance of the method only we shall look where the bracket stands for the ave­ at just two examples instead. rage over all neutrons in the beam. Thus, Fig. 4 shows the relaxation rate F of in view of eq. (3), in a NSE experiment correlations in a solution of pig immuno­ we determine globulin G (IgG) molecules as a function PNSE = < cos φ > ≡ ∫ S(ω) cos (tω)dω (4) of the wavenumber q 4). We expect Γ to where S(ω) is the probability distribution reflect diffusive motion: in time t the of Tito neutron energy changes in the molecules diffuse away on the average scattering. It is known from the funda­ by a distance r = √(Dt) (where D is the mentals of neutron scattering that S(ω) diffusion constant) and thus the lifetime is just the of the cor­ of r = 1/q wavelength correlations is relation function S(t) describing the Γ1 = r2/D or Γ = Dq2, Fig. 5 — Decay rate of the roton excitation in atomic motions in real time. Since eq. (4) which is the well known diffusion equa­ superfluid 4He at various temperatures 5). The NSE results (open circles) are compared implies a backward Fourier transforma­ tion. The results in the figure show this with indirect light scattering data (dots) and tion, it is S(t) that we measure directly. relation in a q and Γ domain, in practice conventional neutron scattering results Thus e.g. in a simple relaxation decay only accessible by NSE. The diffusion (other symbols) resolution limited to line process we have constant D corresponding to the straight widths above 0.5 K. The line represents the Pnse = S(t) = exp(-Γt) line in the figure was found to be 40% theoretical prediction for temperature well where Γ is the relaxation rate. The direct higher than that relevant to q = 0 as below the X point (2.17 K). 3 are around 1.2 x 10-3 eV with a scatter a resolution nearly two orders of magni­ facilities in Europe, namely that in of ± 10%. This is a fine illustration of the tude better than classical neutron scat­ Budapest, and which were then com­ independence of energy resolution and tering methods. The existence of light pleted and fully exploited at the most beam monochromatization, which is the scattering results for comparison (full powerful facility in Grenoble. This is cer­ essence of NSE. These results represent circles) is also quite exceptional : it is the tainly a rather fortunate, but never­ the present absolute resolution limits in appearance of two-roton bound states theless significant example of fruitful inelastic neutron scattering (10-9 eV cor­ with total q ≡ 0 that makes the high collaboration in Europe. responds to 0.25 MHz). wave number (q = 1.92 Å-1) roton exci­ The other example (Fig. 5) shows a tation accessible to investigation. rather more elaborate use of NSE: the These examples taken from amongst REFERENCES measurement of the lifetime of roton ex­ many demonstrate that by the applica­ 1. Mezei F. Z. Physik 255 (1972) 146. citation in superfluid 4He 5). In this case tion of a new approach, the domain of 2. Neutron Spin Echo, ed. F. Mezei (Springer the deviation of the neutron energy applicability of inelastic neutron scatter­ Verlag, Heidelberg) 1980. 3. See Mezei F., J. de Physique 45 (1984) change from a well defined value, ing, a fundamental tool in condensed C3-223, and references therein. hω0 = 8.61 K = 0.742 meV matter research, could be substantially 4. Alpert Y., Cser L., Farago B., Franek F., (the minimum roton energy) is observed extended. It is worth noting that the new Mezei F. and Ostanevich Y.M., Symposium by the NSE difference method. This is method is based on ideas and techni­ on Neutron Scattering, Berlin (West), 6-8 done by using a special Ho/H1 preces­ ques which were originally developed at August 1984. sion field ratio. NSE in this case provides one of the smallest neutron research 5. Mezei F., Phys. Rev. Lett. 44 (1980) 1602.

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