Spin echo three-axes spectrometers for improved energy and momentum resolution

Journal of Physics and Chemistry of Solids 60 (1999) 1573–1578

Spin echo three-axes spectrometers for improved energy and momentum resolution C.M.E. Zeyen Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France

Abstract Optimised Field Shape [1] spin precession coils can be made sufficiently short, so as to be added to existing Three-Axis Spectrometers (TAS) without increasing the neutron flight paths significantly. Furthermore, homogeneity corrections can be applied in such a way as to feature uniform magnetic induction line integrals even for very divergent beams. This way, intense TAS with Spin Echo combinations can be built, the loss of luminosity with respect to the normal polarised mode being negligible. Based on the experience with resistive TAS and Spin Echo spectrometers (TASSE) on PONTA (ISSP) and a superconducting version on IN20 (ILL) used mainly for high momentum transfer quasielastic scattering experiments (meV– neV resolution), a variety of other applications will be made possible: inelastic scattering from excitations with meV resolution ˚ 21), a domain until now reserved for synchrotron radiation. The fields of and very high momentum transfer resolution (10 23 A application will include the extension of the accessible momentum transfer region with respect to cold neutron Spin Echo, for example in the study of glass and liquid dynamics phase transitions and slow dynamics in general. The advantage of thermal neutrons as well as of the TAS background spectrometer with a well-defined transmission function will allow addressing new subjects such as excitation lifetimes across the entire Brillouin zone. Dispersive excitations can be ‘ focused’ by the use of gradient coils that allow restoring the echo polarisation blurred by the dispersion. Another application of these gradient coils is improved momentum resolution for elastic scattering that allows TASSE to compete with synchrotron radiation facilities. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: C. Neutron scattering; D. Anharmonicity; D. Phase transitions; D. Phonons

1. Introduction The techniques developed for cold neutron NSE in the last 20 years cannot directly be transposed to thermal neutron NSE spectroscopy. If one aims at high resolution investigations of solid state excitations, the energy width of the transmission function should be of the order of DE/E ù 1–3%, much smaller than the 10–15% given by the velocity selectors on traditional NSE devices. This is because individual excitations have to be ‘singled out’ via the classical transmission function of the spectrometer. Three-AxisSpectrometers (TAS) with relaxed collimations can be tuned to display convenient background momentum and energy resolution to isolate for example a transverse phonon from another one. This is why we have undertaken to investigate the best precession magnet geometry for combined TAS and Spin Echo spectrometers (TASSE). Based on the ideas of Optimal Field Distribution [1] precession coils two

TASSE devices have been successfully developed; PONTA TASSE of the ISSP in Japan [2] and IN20-TASSE [3] at the ILL. The latter option uses superconducting OFS coils and is suitable for very high energy resolutions (neV) with thermal neutrons and therefore large momentum transfers. PONTA is better suited for medium resolution (quasielastic 0.15 and 1 meV for inelastic scattering). The same OFS concepts have also been applied to a cold neutron NSE spectrometer of the ISSP by a Hiroshima University group [4].

2. The optimised field shape approach to the thermal neutron spin echo OFS [5] is an analytical solution to the line integral homogeneity problem, the crux of all Larmor precession techniques. For cylinder symmetry (beam axis z) magnetic field distributions, the condition of equal line integral for all

0022-3697/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00176-6

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Fig. 1. Echo Polarisation with and without Spiral correction for 2.36 ˚ neutrons, elastic scattering from KDCO3, PONTA TASSE, FourA ier time of 0.15 ns corresponds to about 1000 Larmor precessions.

neutron trajectories can be written as: Z uBu d` ˆ constant: This variational problem has at least one useful solution, the OFS field shape of length L,

are that optimal precession coils can now be both short (coil length of order 80% of L) and presenting small diameters. This reduces their cost significantly as well as the strayfield levels. Using OFS coils on Three-Axis Spectrometers allows changing or scanning the sample scattering angle without the need for retuning the echo phase and/or polarisation. Further advantages are that in beam homogeneity corrections for path length effects due to significant beam divergence (several degrees!) can be calculated easily and analytically. This leads to optimal positions of 2, 3 or more spiral Fresnel coils, depending on the beam divergence used. The calculation which has also been extended to simple solenoids [5,6] and is applied on IN11 at the ILL [7]. Last but not the least, the OFS approach produces convenient line integral gradients that allow, by a suitable line integral, neutron propagation direction correlation, to remove the Echo blurring caused by finite dispersion of elementary excitations. This ‘phonon focusing’ technique which has previously [6,8] been addressed for the case of helium rotons by the so-called ‘Kjeller 8’ coils and by the ‘tilted magnet technique’. The latter technique proved to be experimentally unfeasible [8], the former is limited to low energy excitations and small sound velocities (dispersion slopes).

Bz ˆ B0 cos2 …pz=L†; which gives the best possible line integral homogeneity. It can easily be produced by superposing a number (the higher the number, the better the precision). Its main advantages

Fig. 2. IN20 TASSE with superconducting OFS coils: quasielastic scattering from critical slowing down of (DCO3)2 dimers in KDCO3 (Tc ˆ 353). The range of Fourier time corresponds to 1/3 of the design values and can be compared to PONTA TASSE.

3. Experiments with TASSE Compared to the cold neutron NSE, experience with TASSE is very restricted. This mainly stems from the fact that no dedicated thermal neutron TASSE has yet been built and that both PONTA and IN20 Spin Echo options are competing with intense ‘classical’ and ‘polarised’ use. TASSE requires precise geometrical and magnetic adjustments that apart from being tedious do not foster progress in the same way as a dedicated spectrometer does. IN20TASSE has been able to collect spin echo data for days and PONTA TASSE for weeks only. The PONTA resolution obtained is 0.15 meV and a Fourier time of 0.16 ns whereas the IN20 is designed for neV resolution and 6 ns Fourier time (14 meV neutrons). This extends the accessible resolution–momentum transfer range given by other techniques significantly. Talking about resolution, Fig. 1 gives the typical quality function data obtained during the first experiment on PONTA during which the energy width momentum transfer dependence of Huang and critical diffuse scattering were investigated in KDCO3. With a practically flat echo polarisation like this, resolution corrections are not needed. It can be added here that this Echo behaviour is stable in polarisation and phase when the scattering angle is changed within the range of the instrument. This is due to the very low strayfield pattern of OFS coils. The KDCO3 experiment has been repeated as a test on the IN20 TASSE up to 1/3 of its nominal performance. As can be seen in Fig. 2, the Fourier time domain is extended by an order of magnitude.

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Fig. 3. Lifetime of the 6.3 meV phonon in SrTiO3 measured on PONTA TASSE shown with simulation data. The wiggle in the latter is probably due to the simple triangular beam distributions used until now in the simulations.

In this first test, the quality of the Echo polarisation was marred by mediocre geometrical alignment of the coils. The IN20 superconducting coils can bring forth a line integral of about 1.5 T.m. They are well suited for very high-resolution quasielastic scattering and the study of low energy excitations. Their mobility would also allow using them on cold neutron beams yielding Fourier times in excess of the microsecond!

4. Phonon spectroscopy using TASSE This is at the same time the most enticing application and the most difficult one. It is difficult because of the low intensity of inelastic scattering and because dispersion blurs the echo polarisation. It is enticing because classical TAS resolution is sufficient only in sparse cases to allow the measurement of phonon lifetimes. Many open problems of phonon decay, electron–phonon or other couplings exist in solid state. Removal of dispersion blurring has been the object of consequential theoretical [1,6] and experimental effort [6,8]. The difficulty is of electromagnetic order: it is extremely difficult to produce a suitable relation between the direction of propagation of the neutron and the value of the line integral in the scattering plane. A theorem, showing that it is virtually impossible in the case of rot B ˆ 0, that is with only conductors outside the beam area, has been demonstrated [1]. The so-called ‘Kjeller 8’ type current sheets have been used on IN11 for the roton lifetime studies but they do not allow to match large dispersion as occurring in solids. The tilted magnet scheme proposed by the inventor

of NSE [6] only works for transverse precession fields and leads to very difficult experimental situations [8]. We therefore proposed a different winding scheme for in-beam gradient coils that operate in higher field areas. Delivering larger gradients, such coils can further be designed to match not only the local slope of the dispersion surface but also its local curvature[1]. Gradient coils of this kind have been wound and tested on PONTA. The optimal Gradient coil length is also the one giving minimal Echo depolarisation. Producing opposite gradients MI. and MF in the two spectrometer-arms can test the efficiency of the gradient coils. What is then observed are only the high order perturbations that attenuate Echo polarisation. The results obtained show that gradients sufficient to match dispersion slopes even for the hardest materials can be obtained. OFS coils with gradient coils accepting large angular divergences can produce phonon focusing in a way comparable to the tilted high frequency coils in the zerofield NSE technique. Since the gradient can be positive or negative in either of the two spectrometer-arms, TASSE in fact adds the possibility of four configurations for every TAS configuration (essentially two possibilities usually labelled U and W). For a given experiment, these configurations are not necessarily equivalent; some may be impossible, but there is usually one, which is expected to yield better data with good neutron economy. It is therefore beneficial to calculate the effect on the resulting Echo polarisation for each configuration in order to choose the best. We have developed simulation software to find the possible configurations, and among those finding the best one, for example the one

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Fig. 4. Simulation of momentum resolution obtained on TASSE for Q ˆ 0 and 10 000 precessions as a function of initial and final gradients MI and MF. (The straight line through the origin and joining the extrema of the gradient curves is a guide to the eye.)

that can match the phonon slope with the smallest gradient values. The simulation routines further allow calculating the expected Echo polarisation curve (as a function of Fourier time). For the determination of the lifetime of flat excitation branches gradient coils are not required. Fig. 3 shows such a measurement on an optical branch in SrTiO3. A simulation calculation also shown in Fig. 3 reveals that part of this depolarisation is due to high-order terms and that the phonon width is of the order of 50 meV (12 GHz). For serious inelastic work on phonons for example high resolution study of their lifetimes, optimisation of the Heusler polariser/analyser systems both on PONTA and IN20 are presently underway. The real solution will be a dedicated TASSE for meV energy resolution with an integrated design of short large beam cross section OFS precession, correction and gradient/coils. Following the experience gained with the completion of the first test, such a design is now possible. 5. Improved momentum (Q) resolution using TASSE Another interesting application of gradient coils is obtaining improved momentum resolution. This is particularly true for the presently available TASSE options for which the best luminosity conditions have not yet been achieved. Once the TAS is set to elastic scattering the effect of activating the gradient coils will be such that the constant Echo phase surfaces (normally parallel to the momentum transfer axis Q) will intersect the Q-axis in the scattering plane. The relative momentum resolution will be given by: DQ M 1 MF 1 ù I · ; Q a 2 MF b N I

where MI and MF are the initial and final gradients, a and b are configuration dependent and NI is the initial number of precessions. Note that an extra echo condition applies when gradients are applied. Despite the fact that scattering is elastic one may have NI ± NF. Obviously, resolution will improve both with increasing Fourier time t, proportional to the number of precessions N, and the value of the gradients MI and MF. In the case of small angle scattering (SANS i.e. Q t 0) NI ˆ NF and MI ˆ 2MF. Fig. 4 shows the obtained Q-resolution for given antisymmetric gradients and number of precessions. The ^ signs of the resolution refer to CW or CCW rotation of the line of constant echo phase with respect to the momentum component in the scattering plane. For finite Q values, the situation becomes more complex and an example, given in Fig. 5, shows the case of elastic ˚ 21 for the U (Fig. scattering for a momentum transfer of 3 A 5(a)) and W (Fig. 5(b)) TAS configurations. Resolutions of ˚ 21 can be reached in this case for moderthe order of 10 23 A ate field gradients and a precession number well within the range of IN20 TASSE.

6. Conclusions and perspectives Thermal Neutron Spin Echo in particular, in conjunction with Three-Axis spectrometers, is comparatively new if we compare it with the 20 years of test and user experiments with for example IN11. The potential should be at least as varied as for classical TAS with the extra capacity of very significantly improved energy resolution (up to five orders of magnitude for superconducting OFS coils and quasielastic scattering) or momentum resolutions comparable to what is presently obtained with synchrotron radiation. For

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˚ 21] and 10 000 precessions as a function of initial and final Fig. 5. Simulation of momentum resolution obtained on TASSE for Q ˆ 3 [A gradients MI and MF for the U (a) and W (b) TAS configurations. (The straight line through the origin and joining the extrema of the gradient curves is a guide to the eye).

inelastic spectroscopy, resolution is limited for intrinsic reasons from 0.1 to 1 meV for thermal neutrons. Very sensitive depolarisation experiments are also made possible. The first two TASSE options built for PONTA and IN20 allowed to test the OFS principle, the optimal positioning of the spiral-coil homogeneity corrections as well as the gradient coils for phonon focusing individually. The possibilities are now open to build dedicated and

specific TASSE, optimising the luminosity/ resolution compromise, and integrating OFS precession coils with spiral corrections and gradient coils. With experience this could be done with coils as short as 60–80 cm with large apertures allowing the best use of beam optics such as vertical focusing using variable curvature Heusler systems. One would aim at an energy resolution for inelastic scattering of the order of the meV; a typical neutron spectroscopy

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resolution which cannot be obtained by synchrotron radiation, while recent developments using the latter radiation now perform very well in the meV range resolution. Because of their ability to use small samples, they might push classical TAS out of business. Acknowledgements Collaborations with K. Kakurai on PONTA, R Cowley and J. Kulda on IN20 and M. Nishi on PONTA and IN20 are gratefully acknowledged. A. Bouvet and several students: Matthieu Giraud, Serge Richard, helped with the simulation. References [1] C.M.E. Zeyen, P.C. Rem, Meas. Sci. Technol. 7 (1996) 782 and references therein.

[2] C.M.E. Zeyen, K. Kakurai, M. Nishi, K. Nakajima, T. Sakaguchi, Y. Kawamura, S. Watanabe, M. Berneron, K. Sasaki, Y. Endoh, Neutron News 8 (4) (1997) 7. [3] T. May, C.M.E. Zeyen, private communication. [4] T. Takeda, H. Seto, Y. Kawabata, D. Okuhara, T. Krist, C.M.E. Zeyen, I.S. Anderson, P. Høghøj, Paper presented at the Seventh ISSP International Symposium on Frontiers in Neutron Scattering Research, and references therein. [5] C.M.E. Zeyen, in: G.J. Long, F. Grandjean (Eds.), The time domain in surface and structural dynamics, Kluwer Academic Publishers, Dordrecht, 1988, p. 213. [6] F. Mezei (Ed.), Neutron Spin Echo Lecture Notes in Physics 128 Springer, Berlin, 1980 and papers therein. [7] B. Farago, paper presented at the Seventh ISSP International Symposium on Frontiers in Neutron Scattering Research, and references therein. [8] C.M.E. Zeyen, Neutron Scattering 1981, in: J. Faber (Ed.), AIP Conference Proceedings No. 89 (1982) 101.