Use of Polarization Analysis in Inelastic Scattering

Neutron polarization can be used in two ways in inelastic scattering : (a) for the identification of scattering effects of magnetic origin, and (b) as a tool to measure the inelasticity itself, independently of the magnetic or non-magnetic character of the scattering. There are only few examples for the first kind of applications, but this number is expected to increase rapidly with the growing interest in diffuse scattering. On the other hand, various polarization modulation techniques, such as spin-flip chopping and, in particular, neutron spin echo became by now rather routinely used methods in inelastic scattering. The present review covers the principles of both types of utilization of polarized neutrons, together with a number of experimental results. • Introduction Before turning to the matter the title of this talk needs some explanation. Indeed, the expression "polarization analysis" is being used rather unprecisely and in more than one sense. Historically, the scattering of polarized neutrons on condensed matter was first considered as early as in 1937 by Halpern and Johnson, and in their amazing paper of 1939 they established the fundamental relation between the incoming and outgoing neutron polarization in scattering on. paramagnets [1] at a time when it was only a speculation that the neutron might have a substantial magnetic moment. In this pioneering work the neutron spin polarization was considered as a vector, and its change in the scattering process was described as a vector-vector relation. The term "polarization analysis" (PA) should therefore mean the determination of a polarization vector, as it is done in experiments more frequently referred to as "vector polarization analysis" or "three dimensional polarization analysis". This latter type of work is most often done in beam transmission studies of magnetic domain structure and kinetics, and it has been pioneered by the Delft and Leningrad groups as early as 1969 [2,3]. Alperin has demonstrated in 1973 in an ad hoc fashion the feasibility of vector PA in crystallography [4], and a general experimental technique for doing this has been described by the author at the same time [5]. A further project on vector PA is in progress at the ILL [6]. Finally, the Halpern and Johnson equation is the basis of the application of neutron spin echo [7] to paramagnetic samples, which in fact provided the first full experimental test of this vector relation, as it will be shown in the present paper. The most often used sense of the term "polarization analysis" is the one introduced in 1969 by the famous article of Moon, Riste and Koehler [8], in spite of these authors' warning of their improper use of these words : "(The title of the paper) Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982702 C7-10 JOURNAL DE PHYSIQUE is somewhat misleading, because we do not measure polarization at all". In fact, the method proposed and tested in this work consists of the investigation of the single component of the scattered beam polarization which is parallel to the incoming beam polarization, which in turn is parallel to the magnetic field on the sample. This restriction of both the incoming and outgoing beam polarization to a scalar quantity, i.e. the component parallel to the field direction (which will be referred to in what follows as the h-component) is a vast simplification of the experimental procedure and still provides a very powerful tool for the identification of magnetic scattering effects. Finally, if the scattering cross section depends on the h-component of the polarization one can either use a polarized incoming beam without analysing the polarization of the scattered beam or, alternatively, use an unpolarized beam and, analyse the h-component of the scattered beam. These procedures are most often referred to as "scattering of polarized neutrons:' rather than "polarization analysist'. In the present review I will consider all of these techniques in connection with inelastic scattering. In contrast to diffraction studies, in inelastic scattering the neutron polarization canbe utilised not onlyfor the unambiguous identification of the magnetic scattering effects but also as a powerful tool for measuring the scattering inelasticity itself. As a matter of fact, there are many more practical examples of this latter type of applications than of the first one. In many cases the investigated scattering is not at all of magnetic origin, in others the neutron polarization allows both the identification and the inelastic analysis of the magnetic effects. In what follows we will first consider the relations describing the scattering of polarized neutrons in various, experimentally relevant situations, and review the experiments in which practical use was made of these relations. The second half of the paper is devoted to the description of the various inelastic scattering methods based on various schemes of polarization modulation and their applications. With the exception of neutron spin echo and its applications, which alone represent by now a bigger volume than all of the other topics together and will therefore be only very briefly invoked, the present review was aimed to be fairly complete. 2. Scattering of polarized neutrons The most general case of scattering of polarized neutrons we are interested in both the scattering cross section and the polarization veztor ?' of the scattered beam for an incoming beam with an arbitrary polarization P. Since Halpern and Johnson derived their classical equation [ I ] -+ (where q is the neutron momentum transfer) for the scattering on ideal paramagnets, the theory has been gradually extended to samples of any complexity, in which the combination and interplay of magnetic, nuclear and nuclear spin scattering effects play an important role [ 9 ] . In the most general form the results become so complicated that only various simplified special cases are experimentally tractable. Much of the complexity comes from the interference between various types of contributions. In inelastic scattering these are generally small and do not provide too interesting information (in contrast to structural scudies), except for the magnetovibrational scattering, i.e. the magnetic contribution to the phonon cross section. This scattering effect has exactly the same polarization dependence as the Bragg scattering, and it is discussed in Ralph Moon's paper in this volume. Here I will only consider purely magnetic scattering, but in practice, the caution has to be kept in mind that the magnetovibrational cross section is often not negligible. The special cases which will be discussed below correspond to well defined experimental geometries and sample properties. I will use the code names "ferromagnetic" "paramagnetic" and "antiferromagnetic" situations, which evoke the fundamental features by the type of samples for which a given configuration and measuring procedure is the most typical. Nevertheless, as it will be shown below, with certain restrictions other kinds of samplescan also be investigated by each of these methods. A) Ferromagnetic situations Due to their high magnetization and domain structure, ferromagnetic samples tend to depolarize the impinging neutron beam unless they are magnetized to saturation [lo]. Thus a strong magnetic field has to be applied to such samples, which makes any precessing component of the neutron beam polarization (i.e. those perpendicular to the field direction) average very rapjdly to zero. Consequently the polarization of the beam impinging on the sample, P can only be parallel to $he magnetic field + H, and only the h component of the scattered beam polarization P ' will be maintained and can be measured. Due to these restrictions we can describe the beam polarization by a single scalar quantity P : where pt (p+) is the probability of occupation of the I.(+) state of the neutron magnetic moment with respect to the field direction taken as the z-axis. This is actually the con£ iguration introduced by Moon, Riste and Koehler [8] . In this particular case, in view of eq.(2) the scattered beam polarization P' = p+' p+' can be very simply evaluated by considering the partial cross sections describing the probabilities that the neutron is scattered into the same and into the opposite spin state. For the purely magnetic scattering we are interested in, and following standard algebra [Ill, both of these cross sections, called non-spinflip (nsf) and spin spin-flip (sf), can be given in extremely simple forms [I21 :