ELSEVIER Physica B 234 236 (1997) 1135-1137

Neutron reflectometry and SANS by neutron spin echo

M. Theo Rekveldt

lnterfacultair Reactor Instituut, Delft University of Technology, 2629 JB Delft, The Netherlands

Abstract

The application of neutron spin echo as a small-angle neutron scattering instrument (SESANS) using DC magnetic fields is discussed. Its principle is based on the difference in Larmor precession angle in a coil system with changing transmission angle. A scatterer between two identical coils with opposite precessions causes depolarisation. The latter as a function of the precession field yields a real space correlation function. A modification of this principle of SESANS implemented into a polarised neutron reflectometer using a linear position-sensitive detector, is proposed, which enables one to measure with a full divergent beam. From two measurements with zero and maximum spin-echo field, the fraction of off-specular reflection can be determined at each point of the detector. Moreover, from a field-dependent measurement the full correlation function of the roughness perpendicular to the sample plane causing the off-specular reflection can be determined, when desired also in a direction with the momentum transfer in the plane of the sample by rotating the spin-echo coils over 90 °. The sensitivity of SESANS is up to the micron range.

Keywords: Neutron reflectometry; Small-angle neutron scattering; Spin echo

1. Introduction

There is renewed interest in a very challenging application of spin echo in small angle neutron scattering (SESANS) due to Keller et al. [1] and Hank et al. [-2], who described SESANS by an inclination of the spin-echo resonance coil with respect to the passing neutron beam direction. Due to this inclination the transmission length difference through the coils by some scattering angle 0 occurring between the coils is linear in 0. This enables one to carry out SANS experi- ments with extremely high sensitivity without reducing the neutron intensity, as is required in conventional SANS instruments to achieve the same sensitivity.

Our description of SESANS using DC fields I-3] is similar and a modification of one echo coil by two prism shaped precession devices is even

advantageous if one is interested only in SANS measurements and not in inelastic effects in the signal.

In the present paper, the application of SESANS in a neutron reflectometer will be considered.

2. SESANS with reflectometry

A sketch of the proposed setup is given in Fig. 1. The beam polarisation in the z-direction is ob- tained by a polarising supermirror in the xz-plane. The beam passes in the x-direction through two sets of equally sized precession coils C1, C2 and Ca, C4 with equal magnetic fields B in the _+ y-direc- tions, respectively. In these fields the polarisation precesses in the xz-plane over the angles ~01 and ~o 2 in opposite directions. The precession angle in each field is proport ional to the time, i.e. the path

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1136 M. ~ Rekveldt / Physica B 234-236 (1997) 1135-1137

L d

p C 1 C 2 S C 3 (24 A PSD

Fig. I. Sketch of combined reflectometer and SESANS setup. The neutron beam is polarised in P in the z-direction and then passes through the four wedge shaped precession coils sand- wiched around the sample S. The opposite precessions in C1, C2 and C3, C, cancel each other for the neutrons which are specularly reflected. After the analysis of the z component of the polarisation in A, the beam is detected in D.

length which the neutrons travel in this field. The magnitudes of these angles differ by the transmis- sion directions through the coils and because the energy transfer at the sample causes a wavelength change AL

The precession angles in the case of scattering or off-specular reflection can be calculated from geometry and yields,

( - ~ ( d + 2 L ) otanOo) (1) q ) l - - q ) 2 = c2Bd + ~

where c = 4.63 x 1014 T-x m-2 and d is the trans- mission length through each set of two coils in the x-direction. 0o is the angle made by front of the coil with the z-axis. Using this, the polarisation of the beam behind C4, to be analysed by the analyser A, is given for SESANS (SESANS with reflectometry) by the weighted sum of polarisations of scattered (off-specularly reflected) and non-scattered (specu- lady reflected) neutrons.

( P'(B) ~ 1-- + ~ G(z), (2)

with the one-dimensional correlation function:

Qym, Q~m

G(z) = f d2Q S(Q)cos(zQz), (3)

-Q,m, -Qzm

where f = 1 - s + Sa and s is the fraction of neu- trons off-specularly reflected from the incident beam, while Sd is the same but with the extra con-

straint that they are reflected into the detector. Moreover, if A2 is assumed to be zero,

J,2B 2nO z - = c ~ ( d + 2 L ) t a n 0 o , Qz= 2 (4)

The quantity Qm is determined by the critical re- flection angle 0c of P and A in the xy-plane, the quantity Qzm is determined by the acceptance or opening angle 0, of the analyser plus detector in the xz-plane (0c ,~ 0a). S(Q) is the scattering power for off-specular reflection.

Eq. (2) is the sum of a B independent part (repres- enting the specularly reflected neutrons) and a B dependent part G(z) (corresponding to the off-specularly reflected neutrons) with z equiva- lent with B in the coils according to Eq. (4). The function G(z) approaches a Fourier trans- form of S(Q) w h e n f ~ 1. For SANS and SESANS with reflectometry G(z) represents a correlation function of the sample inhomogeneities, i.e. the roughness.

When one uses a linear position-sensitive de- tector (PSD), with a full-divergent beam, a given position z' on the PSD determines the reflection angle of the reflected beam. However, the intensity at that point is a mixture of neutrons reflected specularly and off-specularly. The combination of reflectometer and SESANS aims to separate these two fractions.

The intensity of the neutron beam measured at position z' in the PSD is

I(z', B) = Io(z')(1 _+ Po(B)P'(z', B)), (5)

where Io is the intensity of the fully depolarised beam with the sample in the beam, the _+ sign depends on the analysing direction and Po(B) is the polarisation of the beam without sample, which is obtained from a calibration. When the field in the echo coils is maximum, the neutrons off-specularly reflected will be fully depolarised. So the difference I(z,O)-I(z,B~,ax) represents the neutrons off- specularly reflected, while I(z, Bmax) itself represents the specularly reflected intensity. By measuring the full B dependence of the polarisation in that point, the G(z) or the angular distribution of neutrons off-specularly reflected is determined. When de- sired, the momentum transfer can be chosen also in

M.T. Rekveldt / Physica B 234-236 (1997) 1135 1137 1137

the plane of the sample by rotating the spin- echo coils over 90 °. From such information obtained simultaneously at all PSD positions, detailed information about the sample surface and interface conditions can be derived. From Eq. (4), we can calculate that the measurable roughness ranges from about 5 nm up to microns. This applies to the reflection plane and perpendicu- lar to it.

In conclusion, the SESANS reflectometry combi- nation makes an intensity gain of an order of mag- nitude possible by combining the full divergence of the neutron beam with a PSD. The roughness of the interfaces can be studied in two directions. This

combination may be applicable even for magnetic samples in not too strong magnetic fields which polarise the beam not too strongly.

References

[-1] T. Keller, R. G~ihler, H. Kunze and R. Golub, Neutron News 6 (3) (1995).

[2] P. Hank, M. K6ppe, R. G/ihler, T. Keller and R. Golub, in: Proc. 3rd Summer-school on Neutron Scattering; Magn. Neutron Scattering, Zuoz, Schwitzerland, Aug. 1995, ed. A. Furrer (World Scientific, Singapore, 1995) ISBN 981-02- 2353-6, p. 228.

['3] M. Th. Rekveldt, Nucl. Instr. and Meth., B 114 (1996) 366.