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Larmor precession reflectometry
ARTICLE IN PRESS
Physica B 350 (2004) e759–e762
Larmor precession reflectometry H.J. Lautera,*, B.P. Topervergb, V. Lauter-Pasyuka,c,d, A. Petrenkod, V. Aksenovd a
Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France b PNPI, Gatchina, Russia c Physik Department, TU Munchen, D-85747 Garching, Germany . d Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
Abstract Larmor precession phase encoding is applied to modulate TOF reflection spectra measured from a polymer multilayer and from an Fe/Cr multilayer. It is proposed that decoding of the spectra can be used to extract the smallangle scattering signal from the polymer film-embedded nanoparticles. The second example is directed to demonstrate one of the plausible realizations of the vector polarization analysis in reflectometry of magnetic systems. This would allow to unambiguously reconstruct the transverse and lateral distribution of the magnetization vectors throughout the multilayered superlattices. r 2004 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 68.35.Ct; 75.70.Cn Keywords: Larmor precession; Encoding; Reflectometry; polarized neutrons
The idea to use spin–echo (SE) techniques for improving resolution of small-angle neutron scattering (SANS) experiments has recently received further development, being applied to reflectometry and SANS at grazing incidence (GISANS) [1]. SE-SANS is based on classical SE, on encoding of the incident beam by the Larmor precession (LP) phase by means of the polarization vector P and subsequent decoding by the ‘‘echo’’. Here we demonstrate how the LP device encodes time-of-flight (TOF) spectra and discuss how this encoding can be employed to achieve the aim of SE-GISANS. The wavelength encoding *Corresponding author. Fax: +33-4-76-20-71-20. E-mail address: [email protected] (H.J. Lauter).
becomes visible by intensity oscillations picking up intensity in reflectometry and GISANS. We also propose the way to expand the 3-dimensional (3D), or vector polarization analysis for polarized neutron reflectometry to study magnetic layered structures. Due to LP the polarization vector scans the angular range in 2p and is not restricted in the sample surface plane. The first studies of the LP device were carried out on the reflectometer REMUR [2] in TOF. The LP-device in Fig. 1a is placed inside the reflectometer set-up using polarized neutrons with velocity vn ðlÞ (l the neutron wavelength) and neutron-spin analysis A in (+) direction in front of the linear PSD D. The LP-device itself consists of two current sheets (CS) with a magnetic field
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.259
ARTICLE IN PRESS e760
H.J. Lauter et al. / Physica B 350 (2004) e759–e762
Fig. 1. Larmor precession set-up: (a) The neutrons precess with the Larmor frequency between the first and second CS. The Larmor precession is made visible by intensity oscillations in the detector D through the effects of the second CS and the analyser A (see Fig. 2). Guide fields are outside the LP device. (b) Reflectometry set-up. (c) Two beam case in reflectometry. (d) GISANS set-up.
HLP in between. The first CS starts the Larmor precession, providing spin rotation in the x–z plane. The CS-current is adjusted such that the effective magnetic field in front of the CS (being composed of the field from the CS and HLP) is at 90 to the one behind the CS and LP starts. The second CS, adjusted as the first CS, turns the rotation plane into the x–y plane for analysis. The wavelength encoding is given by the accumulated phase F between the CSs with F ¼ gHLP L=vn ðlÞ [1]. g is ð2pÞ2916:4 Hz/G and L is the distance between the CSs. A thin polymer multilayer film (PS-PBMA with nanoparticles [3]) was the sample and was positioned in front of the CSs. The 2-dimensional (2D) intensity map in Fig. 2 shows the intensity of the direct beam as well as the intensity from the reflected beam as f ðlÞ: The direct beam appears because of over-illumination. Off-specular scattering accompanies the reflected beam and crosses the high-intensity spots of the Bragg-peaks. The LP device is switched off in Fig. 2a and is active in Fig. 2b. So, Fig. 2b shows over all the intensity
Fig. 2. Two-dimensional intensity maps as a function of the linear PSD pixel position and the wavelength l in TOF. (a) The top map was obtained with the LP-device switched off and the bottom map with the active LP device (incoming beam with () polarization). The arrows indicate the direct beam and reflected beam position.
Fig. 3. Intensities from a reflectometry set-up with LP-device as a function of wavelength. Dotted curve: direct beam profile (with (+) polarization); Full line with oscillations—reflected signal from polymer sample. The part of the curve joining at large wavelength l the direct beam profile is the total reflecting region. Both curves show intensity oscillations due to LP. The third curve is the reflectivity obtained by division of the reflected intensity by the direct beam intensity. The critical ( wavelength lc is at B4.3 A.
map a modulation equidistant in l: The period F of this structure originates from the LP between the current sheets and represents the encoding of the ( using the wavelength, with period F ¼ 6:2 ð2pÞ=A; parameters of L ¼ 0:473 m and HLP ¼ B18 G, in agreement with the number of oscillations per unit wavelength in Fig. 2b.
ARTICLE IN PRESS H.J. Lauter et al. / Physica B 350 (2004) e759–e762
The intensity profiles of the direct and reflected beam are displayed in Fig. 3 (here HLP B20 Gs, so ( The division of the reflected that F ¼ 6:6 ð2pÞ=A). by the direct beam intensity leads to the reflectivity curve without oscillations. Thus, the LP has no influence on the scattering process, with the sample in front of the LP-device a fact that is of no surprise. The direct beam intensity equals the reflected beam intensity in the total reflecting ( reflectivity 1). region (l > B4:4 A, In the set-up shown in Fig. 2a the incoming polarization was chosen to be in the () state. Here, flipping the incoming polarization acts as a phase shift of p on the oscillations seen between Figs. 2b and 3. The sense of the LP-device is to encode the state of the incoming neutrons in the z-direction, which results in intensity oscillations. A very important application of the wavelength encoding in reflectometry (see Fig. 1b with direct and reflected beam) is outlined in the following. If aimed at a gain in intensity the incoming beam is focused onto the sample and then each direction of incidence results in its own reflectivity curve Rða; lÞ for each incident angle a: A simplification, the 2beam case, is shown in Fig. 1c. From the two incident directions two reflectivity curves are obtained. However, off-specular scattering will overlap (see Fig. 2a, if one considers here the 2 beams as the direct beam and reflected beam). Encoding shown in Fig. 2b can solve the problem of separation by the difference in the phase of the intensity oscillations due to a different path length in the LP field of the beams at a and a0 in Fig. 1c. In Fig. 2b the necessary phase shift between the two beams is not visible, because the path length difference was not sufficient. This can be achieved with inclined CSs, an additional triangular-shaped magnetic field [5] or other supporting devices. The unfolding in the 2-beam case or more generally the case of a focussing beam (here in the x–z plane) onto the sample can be performed either via numerical or analogous Fourier transformation. In the latter case one deals with the traditional SEspectrometer. Here we propose to apply a mathematical unfolding, so that the experimental set-up shows only an encoding, but no decoding part. Another promising application of the encoding method is envisaged for GISANS outlined in
e761
Fig. 1d. If a size distribution of the objects, from which the scattering originates in a film, is expected then the two ‘‘diffraction points’’ smear out to a distribution in the y-direction. The incoming beam has to be collimated along z and y to provide the necessary resolution. However, wavelength encoding can be used in the y-direction to collect intensity from an incoming beam spread in the y-direction like in Fig. 1b to gain an appreciable intensity in GISANS. The LP-device in Fig. 1d has to be turned by 90 in order to be sensitive in the y-direction. In the last proposed set-up the sample, a magnetic Fe/Cr multilayer [4], is placed inside the LP-device of Fig. 1a with the sample surface along HLP. The axis of the LP lies in the sample surface and the neutron spin is rotating in the x–z plane covering directions perpendicular and parallel to the sample surface. The obtained intensity along the reflected and direct beam is shown in Fig. 4 and also the division of the reflected intensity by the direct beam intensity. However, the oscillations do not disappear as in Fig. 3. So, the process in this set-up is intrinsically different from the one shown in Fig. 2. Here, the neutrons hit the sample in the x–z plane at an angle bðlÞ as a function of the wavelength l: So, the reflectivity curves Rðb; lÞ
Fig. 4. Intensities from a reflectometry set-up with LP-device as a function of wavelength, the sample is situated inside the LP( Notation device with its surface parallel to HLP. lc at B4.3 A. of curves as in Fig. 3.
ARTICLE IN PRESS e762
H.J. Lauter et al. / Physica B 350 (2004) e759–e762
depend on b and l: If b is varying then the neutron magnetic moment interacts with the film magnetic moment as a function of b and oscillation show up on the reflectivity curve. This shows on the other hand that the division of reflected beam by direct beam is not applicable any more. The deconvolution of the ‘‘reflectivity’’ curve in Fig. 4 has been performed [5]. The new feature is that a magnetic sample can be investigated with the neutron spin in all directions relative to the surface and magnetization of the sample. This new LP set-up provides new spin-configurations for 3-dimensional polarimetry in reflectometry [6] so that e.g. the sequence of the magnetization in magnetic multilayer samples can be determined layer by layer with high certainty.
Acknowledgements We acknowledge the help of S. Kozhevnikov and V. Progliado and the support by the BMBF (Grant no. 03DU03MU).
References [1] R. Pynn, et al., Rev. Sci. Instrum. 73 (2002) 2948. [2] Reflectometer REMUR at IBR-2 reactor. http://www. jinr.ru. [3] V. Lauter-Pasyuk, et al., Langmuir 19 (2003) 7783. [4] V. Lauter-Pasyuk, et al., Phys. Rev. Lett. 89 (2002) 167203. [5] H.J. Lauter, et al., to be published. [6] B. Toperverg, et al., Physica B 297 (2001) 169.
Physica B 350 (2004) e759–e762
Larmor precession reflectometry H.J. Lautera,*, B.P. Topervergb, V. Lauter-Pasyuka,c,d, A. Petrenkod, V. Aksenovd a
Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France b PNPI, Gatchina, Russia c Physik Department, TU Munchen, D-85747 Garching, Germany . d Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
Abstract Larmor precession phase encoding is applied to modulate TOF reflection spectra measured from a polymer multilayer and from an Fe/Cr multilayer. It is proposed that decoding of the spectra can be used to extract the smallangle scattering signal from the polymer film-embedded nanoparticles. The second example is directed to demonstrate one of the plausible realizations of the vector polarization analysis in reflectometry of magnetic systems. This would allow to unambiguously reconstruct the transverse and lateral distribution of the magnetization vectors throughout the multilayered superlattices. r 2004 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 68.35.Ct; 75.70.Cn Keywords: Larmor precession; Encoding; Reflectometry; polarized neutrons
The idea to use spin–echo (SE) techniques for improving resolution of small-angle neutron scattering (SANS) experiments has recently received further development, being applied to reflectometry and SANS at grazing incidence (GISANS) [1]. SE-SANS is based on classical SE, on encoding of the incident beam by the Larmor precession (LP) phase by means of the polarization vector P and subsequent decoding by the ‘‘echo’’. Here we demonstrate how the LP device encodes time-of-flight (TOF) spectra and discuss how this encoding can be employed to achieve the aim of SE-GISANS. The wavelength encoding *Corresponding author. Fax: +33-4-76-20-71-20. E-mail address: [email protected] (H.J. Lauter).
becomes visible by intensity oscillations picking up intensity in reflectometry and GISANS. We also propose the way to expand the 3-dimensional (3D), or vector polarization analysis for polarized neutron reflectometry to study magnetic layered structures. Due to LP the polarization vector scans the angular range in 2p and is not restricted in the sample surface plane. The first studies of the LP device were carried out on the reflectometer REMUR [2] in TOF. The LP-device in Fig. 1a is placed inside the reflectometer set-up using polarized neutrons with velocity vn ðlÞ (l the neutron wavelength) and neutron-spin analysis A in (+) direction in front of the linear PSD D. The LP-device itself consists of two current sheets (CS) with a magnetic field
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.259
ARTICLE IN PRESS e760
H.J. Lauter et al. / Physica B 350 (2004) e759–e762
Fig. 1. Larmor precession set-up: (a) The neutrons precess with the Larmor frequency between the first and second CS. The Larmor precession is made visible by intensity oscillations in the detector D through the effects of the second CS and the analyser A (see Fig. 2). Guide fields are outside the LP device. (b) Reflectometry set-up. (c) Two beam case in reflectometry. (d) GISANS set-up.
HLP in between. The first CS starts the Larmor precession, providing spin rotation in the x–z plane. The CS-current is adjusted such that the effective magnetic field in front of the CS (being composed of the field from the CS and HLP) is at 90 to the one behind the CS and LP starts. The second CS, adjusted as the first CS, turns the rotation plane into the x–y plane for analysis. The wavelength encoding is given by the accumulated phase F between the CSs with F ¼ gHLP L=vn ðlÞ [1]. g is ð2pÞ2916:4 Hz/G and L is the distance between the CSs. A thin polymer multilayer film (PS-PBMA with nanoparticles [3]) was the sample and was positioned in front of the CSs. The 2-dimensional (2D) intensity map in Fig. 2 shows the intensity of the direct beam as well as the intensity from the reflected beam as f ðlÞ: The direct beam appears because of over-illumination. Off-specular scattering accompanies the reflected beam and crosses the high-intensity spots of the Bragg-peaks. The LP device is switched off in Fig. 2a and is active in Fig. 2b. So, Fig. 2b shows over all the intensity
Fig. 2. Two-dimensional intensity maps as a function of the linear PSD pixel position and the wavelength l in TOF. (a) The top map was obtained with the LP-device switched off and the bottom map with the active LP device (incoming beam with () polarization). The arrows indicate the direct beam and reflected beam position.
Fig. 3. Intensities from a reflectometry set-up with LP-device as a function of wavelength. Dotted curve: direct beam profile (with (+) polarization); Full line with oscillations—reflected signal from polymer sample. The part of the curve joining at large wavelength l the direct beam profile is the total reflecting region. Both curves show intensity oscillations due to LP. The third curve is the reflectivity obtained by division of the reflected intensity by the direct beam intensity. The critical ( wavelength lc is at B4.3 A.
map a modulation equidistant in l: The period F of this structure originates from the LP between the current sheets and represents the encoding of the ( using the wavelength, with period F ¼ 6:2 ð2pÞ=A; parameters of L ¼ 0:473 m and HLP ¼ B18 G, in agreement with the number of oscillations per unit wavelength in Fig. 2b.
ARTICLE IN PRESS H.J. Lauter et al. / Physica B 350 (2004) e759–e762
The intensity profiles of the direct and reflected beam are displayed in Fig. 3 (here HLP B20 Gs, so ( The division of the reflected that F ¼ 6:6 ð2pÞ=A). by the direct beam intensity leads to the reflectivity curve without oscillations. Thus, the LP has no influence on the scattering process, with the sample in front of the LP-device a fact that is of no surprise. The direct beam intensity equals the reflected beam intensity in the total reflecting ( reflectivity 1). region (l > B4:4 A, In the set-up shown in Fig. 2a the incoming polarization was chosen to be in the () state. Here, flipping the incoming polarization acts as a phase shift of p on the oscillations seen between Figs. 2b and 3. The sense of the LP-device is to encode the state of the incoming neutrons in the z-direction, which results in intensity oscillations. A very important application of the wavelength encoding in reflectometry (see Fig. 1b with direct and reflected beam) is outlined in the following. If aimed at a gain in intensity the incoming beam is focused onto the sample and then each direction of incidence results in its own reflectivity curve Rða; lÞ for each incident angle a: A simplification, the 2beam case, is shown in Fig. 1c. From the two incident directions two reflectivity curves are obtained. However, off-specular scattering will overlap (see Fig. 2a, if one considers here the 2 beams as the direct beam and reflected beam). Encoding shown in Fig. 2b can solve the problem of separation by the difference in the phase of the intensity oscillations due to a different path length in the LP field of the beams at a and a0 in Fig. 1c. In Fig. 2b the necessary phase shift between the two beams is not visible, because the path length difference was not sufficient. This can be achieved with inclined CSs, an additional triangular-shaped magnetic field [5] or other supporting devices. The unfolding in the 2-beam case or more generally the case of a focussing beam (here in the x–z plane) onto the sample can be performed either via numerical or analogous Fourier transformation. In the latter case one deals with the traditional SEspectrometer. Here we propose to apply a mathematical unfolding, so that the experimental set-up shows only an encoding, but no decoding part. Another promising application of the encoding method is envisaged for GISANS outlined in
e761
Fig. 1d. If a size distribution of the objects, from which the scattering originates in a film, is expected then the two ‘‘diffraction points’’ smear out to a distribution in the y-direction. The incoming beam has to be collimated along z and y to provide the necessary resolution. However, wavelength encoding can be used in the y-direction to collect intensity from an incoming beam spread in the y-direction like in Fig. 1b to gain an appreciable intensity in GISANS. The LP-device in Fig. 1d has to be turned by 90 in order to be sensitive in the y-direction. In the last proposed set-up the sample, a magnetic Fe/Cr multilayer [4], is placed inside the LP-device of Fig. 1a with the sample surface along HLP. The axis of the LP lies in the sample surface and the neutron spin is rotating in the x–z plane covering directions perpendicular and parallel to the sample surface. The obtained intensity along the reflected and direct beam is shown in Fig. 4 and also the division of the reflected intensity by the direct beam intensity. However, the oscillations do not disappear as in Fig. 3. So, the process in this set-up is intrinsically different from the one shown in Fig. 2. Here, the neutrons hit the sample in the x–z plane at an angle bðlÞ as a function of the wavelength l: So, the reflectivity curves Rðb; lÞ
Fig. 4. Intensities from a reflectometry set-up with LP-device as a function of wavelength, the sample is situated inside the LP( Notation device with its surface parallel to HLP. lc at B4.3 A. of curves as in Fig. 3.
ARTICLE IN PRESS e762
H.J. Lauter et al. / Physica B 350 (2004) e759–e762
depend on b and l: If b is varying then the neutron magnetic moment interacts with the film magnetic moment as a function of b and oscillation show up on the reflectivity curve. This shows on the other hand that the division of reflected beam by direct beam is not applicable any more. The deconvolution of the ‘‘reflectivity’’ curve in Fig. 4 has been performed [5]. The new feature is that a magnetic sample can be investigated with the neutron spin in all directions relative to the surface and magnetization of the sample. This new LP set-up provides new spin-configurations for 3-dimensional polarimetry in reflectometry [6] so that e.g. the sequence of the magnetization in magnetic multilayer samples can be determined layer by layer with high certainty.
Acknowledgements We acknowledge the help of S. Kozhevnikov and V. Progliado and the support by the BMBF (Grant no. 03DU03MU).
References [1] R. Pynn, et al., Rev. Sci. Instrum. 73 (2002) 2948. [2] Reflectometer REMUR at IBR-2 reactor. http://www. jinr.ru. [3] V. Lauter-Pasyuk, et al., Langmuir 19 (2003) 7783. [4] V. Lauter-Pasyuk, et al., Phys. Rev. Lett. 89 (2002) 167203. [5] H.J. Lauter, et al., to be published. [6] B. Toperverg, et al., Physica B 297 (2001) 169.