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concept of neutron mirrors / supermirrors

The concept of neutron supermirrors was initially proposed by Turchin [1] and Mezei [2,3] aiming to extend the range of neutron reflection from smooth surfaces beyond the regime of total external reflection. There high reflectivity is obtained from continuous Bragg reflection from a multilayer with a depth-graded variation of the layer thickness. A proper formalism to compute the thickness profile was provided by Hayter and Mook [4]. The following describes the concept of neutron supermirrors and its extension to polarizing supermirrors.

total external reflection

Neutrons (thermal, cold) can be reflected from smooth surfaces when they impinge at grazing incidence. Most materials have a refractive index, which is slightly smaller than one. Hence, neutrons are totally reflected up to a critical angle θc, which depends on the material and on the neutron wavelength λ, e.g. θc,Ni ≈ 0.1°/Ĺ · λ for natural Ni. The material property is generalized, i.e. independent of λ in terms of the momentum transfer q (perpendicular to the surface):


(eq. 1)


with θ being the angle of incidence. For example the critical momentum transfer of natural Ni is at
qc,Ni = 0.217nm-1.

supermirror reflection


Figure 1


Beyond θc, qc respectively, the neutron wave propagates in the material and is partially reflected at smooth interfaces (Figure 1) between layers of different materials having usually a different scattering length density (SLD). Multilayers represent an artificial one-dimensional lattice and Bragg reflection occurs at an appropriate momentum transfer similar to the Bragg reflection from the lattice planes of a crystal. Neutron supermirrors exploit this property and provide a regime of continuous Bragg reflection from a depth-graded multilayer (Figure 2).

Neutron supermirrors are essentially characterized by their reflectivity and the m value. The latter defines the range of the supermirror regime in multiples of qc,Ni. It is also common to refer to the m value as the critical edge of the supermirror according to the critical angle θc (in general momentum transfer) for total reflection.


Figure 2: Theoretical supermirror reflectivity


polarizing supermirrors

So far the nuclear interaction is concerned but for magnetic materials the magnetic interaction contributes in addition to the neutron scattering properties. In the following, the discussion about nuclear and magnetic interactions is rather simplified, addressing only those aspects, which are most relevant for the discussion on polarizing supermirrors.
The magnetic interaction adds in terms of the magnetic scattering length p to the nuclear b, dependent on the relative orientation of the neutron spin to the magnetization, i.e. (b ± p) with (+) for spins parallel to magnetization and (-) for vice versa. As the critical momentum transfer depends on the total scattering length, the regime of total reflection depends on the relative orientation between neutron spin and magnetization: (b + p) has an enhanced critical momentum transfer, whereas it is reduced for (b - p).
Considering a supermirror with one type of the layers being magnetic and their magnetization commonly aligned, neutrons with spins either parallel or antiparallel to the layer magnetization have a different reflectivity in the supermirror regime. For the state of the neutron spin parallel to the magnetization the total SLD of the magnetic layers is enhanced, thus having high reflectivity. For the antiparallel configuration the total SLD is reduced, ideally it matches the SLD of the non-magnetic layers. In the latter case the SLD is constant throughout the supermirror and the neutrons do not see the interfaces. The supermirror is transparent. These properties are illustrated in Figure 3.

Figure 3: Illustration of the spin dependent depth profile of the SLD of a multilayer comprising magnetic and non-magnetic layers: a) neutron spin parallel to layer magnetization, b) neutron spin antiparallel to layer magnetization

measurement of the reflectivity of supermirrors

The reflectivity of a supermirror is a function of the momentum transfer q (eq. 1). Hence it can be either measured in a wavelength or an angular dispersive mode. Besides specific features the information is the same obtained from the different techniques. However, most of the instruments used for reflectivity measurements operate in the angular dispersive mode i.e. using a neutron beam at a constant wavelength and scan the reflectivity by varying the angle of incidence. This mode is also applied at the instrument NARZISS (PSI, SINQ), which is available for SwissNeutronics.

  1. V. F. Turchin, Deposited Paper, At. Energy 22, 1967
  2. F. Mezei, Novel polarized neutron devices: supermirror and spin component amplifier, Communications on Physics 1, 81…85, 1976
  3. F. Mezei, P. A. Dagleish, Corrigendum and first experimental evidence on neutron supermirrors, Communications on Physics 2, 41…43, 1977
  4. J. B. Hayter, H. A. Mook, Discrete Thin-Film Multilayer Design for X-Ray and Neutron Supermirrors, J. Appl. Cryst. 22, 35...41, 1989