Neutron Spin Echo - How IT Works

How It Works

Basically NSE is a time-of-flight technique. Concerning the neutron spins it has a strong analogy to the so-called Hahn echo, well known in the field of NMR. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation, that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of the nuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam. The Larmor precession of the neutron spin in a preparation zone with a magnetic field before the sample encodes the individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-called flipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated (provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron. If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of final polarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample. The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the scattering function S(Q,ω). The effect on the measured beam polarization is proportional to the cos-Fourier transform of the spectral function, the intermediate scattering function F(Q,t). The time parameter depends on the neutron wavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magnetic field in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field. For some further explanations pertaining the NSE principle with animations see: pathfinder.neutron-eu.net.

It is important to note: all the spin manipulations are just a means to detect velocity changes of the neutron, which influence—for technical reasons—in terms of a Fourier transform of the spectral function in the measured intensity. The velocity changes of the neutrons convey the physical information which is available by using NSE, i.e.

where and .

B denotes the precession field strength, λ the (average) neutron wavelength and Δv the neutron velocity change upon scattering at the sample.

The main reason for using NSE is that by the above means it can reach Fourier times of up to many 100ns, which corresponds to energy resolutions in the neV range. The closest approach to this resolution by a spectroscopic neutron instrument type, namely the backscattering spectrometer (BSS), is in the range of 0.5 to 1 μeV. The spin-echo trick allows to use an intense beam of neutrons with a wavelength distribution of 10% or more and at the same time to be sensitive to velocity changes in the range of less than 10−4.

Note: the above explanations assumes the generic NSE configuration—as first utilized by the IN11 instrument at the Institut Laue–Langevin (ILL)--. Other approaches are possible like the resonance spin-echo, NRSE with concentrated a DC field and a RF field in the flippers at the end of preparation and decoding zones which then are without magnetic field (zero field). In principle these approaches are equivalent concerning the connection of the final intensity signal with the intermediate scattering function. Due to technical difficulties until now they have not reached the same level of performance than the generic (IN11) NSE types.