Polarized beam operation of the Hybrid Spectrometer at the pulsed
Spallation Neutron Source![](media/image1.png){width="0.65in"
height="0.6666666666666666in"}![](media/image2.png){width="0.6729166666666667in"
height="0.8506944444444444in"}

I. Zaliznyak^a^[^1], V. Ghosh^b^, S. M. Shapiro^a,b^, L. Passell^b^

^a^Department of Physics, Brookhaven National Laboratory, 11973-5000,
Upton, NY, USA

^b^Center for Neutron Science, Brookhaven National Laboratory,
11973-5000, Upton, NY, USA

**Elsevier use only:** Received date here; revised date here; accepted
date here

Abstract

The concept of a neutron Hybrid Spectrometer (HYSPEC) combines the
time-of-flight spectroscopy with the focusing Bragg optics and
incorporates a polarized beam option. Here we describe the polarization
analysis scheme proposed for HYSPEC and quantify its performance via the
Monte-Carlo simulations. We find that the broadband supermirror-bender
transmission polarizers provide reasonably good polarization analysis
capability within a \~ 8-10 meV energy window for scattered neutron
energies in the thermal range, up to \~ 25 meV. © 1905 Elsevier Science.
All rights reserved

*Keywords*: polarization analysis; time-of-flight spectroscopy;
Monte-Carlo simulations

1.  Introduction

The neutron polarization analysis (PA) \[1\] is broadly recognized as an
important tool in neutron scattering studies. It allows distinguishing
between the spin excitations and phonons, separating magnetic scattering
from background and uncontrolled structural features ("Braggons",
"spurions", etc.), studying magnetic critical dynamics, etc. Recently,
PA was successfully applied to the doped strongly correlated oxides,
\[2,3\] quantum magnets, \[4,5\] studying phase transitions and novel
ordered phases in complex systems \[6,7\].

Traditionally, polarized neutron studies were performed on the crystal
(mainly triple axis) spectrometers at steady-state neutron sources and
by employing the polarization-dependent Bragg reflectivity of the
Heusler-alloy (Cu~2~MnAl) crystal. The time-of-flight (TOF) spectroscopy
in many cases offers significant advantages by surveying neutron
scattering events in a wide range of angles and energy transfers in a
single measurement. The superiority of the TOF approach is overwhelming
at the pulsed (spallation) neutron sources, where the incident neutron
beam is inherently time-modulated. However, development of the PA
techniques for the TOF instruments is still in its infancy and presents
an area of the expected future growth.

The main problem of using the traditional PA techniques in the TOF setup
is posed by the contradictory requirements of a large angular acceptance
on the one hand, and of the well-collimated beams on the other. Indeed,
a beam collimation is required both in the Heusler crystal PA setup
\[1,8\] and in the PA setup with the supermirror-bender transmission
polarizers (SBTP) \[9\]. One venue for the PA on the TOF instruments is
opened by the recent progress in developing the polarized ^3^He
transmission cells \[10\]. However, while the great potential of this
approach is unquestionable, it has not yet been established as a
reliable technique where the large angular apertures are required. An
alternative approach consists in using the multi-channel setup by
replicating the traditional, collimated-beam PA devices covering the
large range of scattering angles. Such scheme is currently employed on
the D7 spectrometer at the ILL \[10\]. Here we describe the
multi-channel PA setup with the transmission polarizers proposed for the
Hybrid Spectrometer (HYSPEC) at the pulsed Spallation Neutron Source
(SNS).

2.  The polarized beam setup on HYSPEC

HYSPEC is a direct-geometry, crystal/TOF Hybrid Spectrometer designed
for the SNS. It will operate in the thermal and sub-thermal neutron
range \[2.5, 90\] meV, have a resolution comparable to that of a
reactor-based triple axis spectrometer, or better, and will have a
polarization analysis capability. HYSPEC combines the time-of-flight
spectroscopy with the focusing Bragg optics by using the TOF for
selecting the neutron energy and the vertically-curved crystal
monochromator for concentrating the neutron flux on sample. In this
setup, a particular incident neutron polarization needed for the PA can
be selected by using the (111) Bragg reflection from a Heusler crystal.
This reflection has the property that the nuclear and magnetic
scattering lengths are equal so only one spin state is reflected.
Studies indicate that the polarization in excess of 95% is achievable
when the Mn moments are aligned, and the Bragg reflectivity can approach
that expected for an ideal mosaic crystal such as PG \[8\].

![](media/image3.wmf){width="3.0in" height="1.6541666666666666in"}

Figure 1. **Schematics showing (a) geometry of the HYSPEC's
multi-channel setup for the scattered beam polarization analysis and (b)
the operation of the analyzer in the polarized beam mode. Shading and
arrows illustrate how the supermirror benders split scattered neutrons
into beams with opposite polarizations.**

Large angular acceptance of the HYSPEC's analyzer (a 60º horizontal
coverage is currently planned) does not allow using a Heusler crystal
for determining the polarization of the scattered neutrons. Therefore, a
multi-channel array of equivalent, broadband, supermirror-bender
transmission polarizers (SBTP) is envisioned for the polarization
analysis of the scattered beam, Figure 1, (a). Nineteen-to-twenty
benders could be positioned in front of the analyzer vessel, at a
distance ≈ 0.5 m from the sample axis, and within the 60º angle
subtended by the detector array. For each PA channel this allows a ≈ 3º
sector, or a ≈ 24 cm long segment on the detector bank at 4.5 m from the
sample, containing 8-10 detector tubes.

3.  Performance and optimization of the transmission polarizer

![](media/image4.wmf){width="2.5083333333333333in"
height="3.941666666666667in"}

Figure 2. **(a) Setup of a single PA unit consisting of a collimator and
a transmission polarizer. The angular splitting of the two beams is
determined by the difference of the critical angles for the
corresponding neutron spin polarizations, *θ~c~*^↑^ - *θ~c~*^↓^ ≥
2.4*θ*~c~^(Ni)^**. **(b) Geometry of a single channel of the SBTP
showing the relevant parameters: the channel width, *d*, the angular
size, α, the radius of curvature, *R*, and the tilt angle, *θ*.**

Supermirror-bender polarization analyzer is a short, multi-channel
curved guide with magnetically aligned, polarization-sensitive Fe-Si
supermirror films on the channel walls. In practice, each channel is
made of a thin, supermirror-coated single-crystal silicon wafer bent to
the desired curvature \[9\]. The neutron critical reflection angle of
such (magnetically aligned) film is large, *θ~c~*^↑^ ≥ 3.0 *θ~c~*^(Ni)^,
for one spin state and is small, *θ~c~*^↓^ = 0.6 *θ*~c~^(Ni)^ ≈ 0, for
the other (here *θ~c~*^(Ni)^ ≈ 0.63º/*k~f~* is the critical reflection
angle for natural nickel, and *k~f~* is the scattered neutron's wave
vector in Å^-1^). Hence, the neutrons of one polarization will follow
the curvature of the guide, while those of the other will go essentially
straight through. The two polarizations will thus be spatially separated
at the detector bank \[10,12\] and can be measured simultaneously,
thereby optimally exploiting the spectrometer's detector coverage,
Figure 1, (b). With two SBTP arrays optimized for 10 meV and 20 meV it
would be possible to perform the PA of scattered neutrons for energies
from \~ 5 meV to \~ 25 meV.

Generic setup of a single transmission polarizer unit is illustrated in
Figure 2, (a). It consists of an up-stream collimator and a SBTP. The
collimator ensures that neutron beams with different ("up" and "down")
polarizations, corresponding to the neutrons "deflected" and
"transmitted" by the SBTP (respectively), do not overlap. Hence, the
collimation *η* should be smaller than the angular separation between
the two beams, Δ*θ*, introduced by the polarizer,

*η* \< Δ*θ* ≈ *θ~c~*^↑^ - *θ~c~*^↓^, or, *η* \< 2.4 *θ*~c~^(Ni)^ ≈
1.5º/*k~f~*. (1)

For a *η* = 20′ collimator considered here, Figure 2, (a), this
condition is fulfilled for neutron energies below ≈ 41 meV.

Parameters defining geometry of the individual bender-polarizer are
shown in Figure 2. Although there are a fair number of parameters, many
of them are coupled and/or constrained. In particular, *θ~c~*^↑^ and
*θ~c~*^↓^ are limited by the available technology, while the length of
the SBTP, *L*, must not exceed ≈ 5 cm if we require that neutron beam
attenuation in silicon is less than ≈ 10%. Furthermore, for a given
channel length, *L*, its bend angle, *α*, and its curvature radius, *R*,
are related through *α* = *L/R*, and are constrained by the mechanical
properties of the silicon wafers and the bending mechanics. Finally, the
channel width, *d*, (i. e. the thickness of an individual single-crystal
Si wafer) is limited by the requirement of closing the direct
line-of-sight through the channel,

*d* ≤ *R* (1- cos*α*) ≈ *Lα*/2. (2)

Therefore, the only parameter in the SBTP setup that is free from the
technological constraints and can be fully optimized is the polarizer's
tilt, or "rocking" angle, *θ* \[the angle between the polarizer and the
collimator's axis, Figure 2, (b)\]. Because the SBTP is rather short, it
is essentially a single-bounce device (i. e. the most probable neutron
passing through the channel is only reflected once). In this case a
simple analytical estimate for the tilt angle *θ* optimizing the SBTP
operation follows from matching the reflection condition for the most
probable neutron (i. e. the neutron that travels parallel to the
collimator axis) at the channel's end-point,

[]{#_Ref84236280 .anchor}*θ* + *α* = *θ~c~*^↑^ ≈ 3.0*θ~c~*^(Ni)^. (3)

Thus, the optimized bender's tilt angle is neutron-energy-dependent, and
decreases with the increasing energy.

Performance of the SBTP for 15 meV neutrons was experimentally studied
by C. Majkrzak in Ref. \[9\]. He has demonstrated that good polarization
sensitivity is achievable if the polarizer tilt angle is appropriately
tuned. Here we investigate the performance of the SBTP at different
neutron energies using the Monte-Carlo (MC) simulations with NISP
package \[14\]. In view of the above constraints, we adopt the same
values of the polarizer's bend angle, length, and the channel width as
used in Ref. \[9\] , *L* = 5 cm, *α* = 0.57°, and *d* = 0.025 cm. Also,
we use *θ~c~*^↑^ = 3.0*θ~c~*^(Ni)^ and *θ~c~*^↓^ = 0.6*θ*~c~^(Ni)^ for
the two critical angles.

![](media/image5.wmf){width="3.0in" height="2.363888888888889in"}

Figure 3. **Horizontal profile of the neutron intensity at the detector
placed 3.9 m behind the polarizer obtained using the Monte-Carlo
simulations with NISP package. The „up" (red) and „down" (green) spin
polarizations correspond to the deflected and the transmitted neutron
beams, respectively. Black symbols show the total intensity. Results for
three different values of the polarizer's tilt angle *θ* are shown for
three scattered neutron energies, E~f~ = 3.7 meV in (a) -- (c), E~f~ =
10 meV in (d) -- (f), and E~f~ = 20 meV in (g) -- (i). Scale on the
right is for the panels (d) -- (i).**

Our MC results for the horizontal distribution of the transmitted
(spin-down, shown in green), deflected (spin-up, shown in red), and
total (black) neutron intensities on the HYSPEC's detector bank at ≈ 3.9
m from the polarizer's rear face and for the three neutron energies, 3.7
meV, 10 meV and 20 meV, are shown in Figure 3. It is clear from the
figure that the optimized polarizer tilt is smaller at higher energy,
where a much finer tuning of this tilt is required. Multiple peaks in
the "deflected" channel appearing at higher SBTP tilt angles arise from
the consecutive neutron reflections from the channel's walls.

To quantify the PA efficiency of the SBTP setup we have divided the
detector in two parts with respect to the minimum of the total neutron
intensity which separates the two nearest peaks with opposite
polarizations. We then assigned the side containing the
straight-transmitted beam to measure the „down" polarization, and the
rest of the detector to measure the „up" polarization. The polarization
efficiency (PE) was then obtained by dividing the intensity of the
selected polarization on each side of the detector by the total neutron
intensity on that side.

Figure 4. **The „rocking curves" for the SBTP obtained using the NISP MC
simulations similar to those shown in Figure 3. For each *E~f~* and *θ*
we used the minimum in the total neutron intensity (black symbols in
Figure 3) which separates the two nearest peaks with different
polarizations to divide the detector in two parts that measure the
respective polarizations. The polarization efficiency (PE) was then
obtained by dividing the intensity of the selected polarization on each
side of the detector by the total neutron intensity on that side. The
relative intensity shows the relative contribution of „up" and „down"
polarizations over the entire detector. The horizontal bars show the
angular range where the PE \> 80% \[note the different x-axis scales in
the panel (a) and the panels (b), (c)\].**

The resulting SBTP "rocking curves" for the three neutron energies are
shown in Figure 4, (a) -- (c). For all three energies, the PE of ≈ 90%
can be achieved by tuning the SBTP tilt to its optimum value, *θ*~0~.
The optimum tilt thus obtained from our MC simulation agrees reasonably
well with the simplistic estimate of Eq. ([3](#_Ref84236280)), which
predicts that *θ*~0~ is 0.84°, 0.29°, and 0.04° for neutron energies of
3.7 meV, 10 meV, and 20 meV, respectively. The agreement is better at
lower energies, where the neutron critical angles are larger and the PA
setup is not very sensitive to the polarizer's alignment.

![](media/image6.wmf){width="2.75in" height="5.8125in"}With the
increasing SBTP tilt the PE of the deflected beam grows, but its
relative intensity decreases. The angular region where the PE is \> 80%
is shown by the horizontal bars in Figure 4, (a) -- (c). For the lower
neutron energy, *E* = 3.7 meV, this "working" region is quite large,
indicating that the setup is rather un-sensitive to the SBTP alignment.
However, this region shrinks rapidly with the increasing neutron energy.
At higher energies, above ≈ 10 meV, the PA setup proposed here would
require a fine tuning of the polarizer's rocking angle.

4.  Summary

We have described the polarized beam setup proposed for the Hybrid
Spectrometer at the SNS. In this setup the polarization analysis of the
scattered neutrons is carried out by a multi-channel array of the
supermirror-bender transmission polarizers. We have studied the
performance of such a polarizer for different neutron energies using the
Monte-Carlo ray-tracing simulations. Our results show that the
polarization efficiency of up to 90% is achievable for neutron energies
at least up to 20 meV with appropriate tuning of the SBTP rotation angle
with respect to the up-stream collimator. Furthermore, an acceptable PE
\> 80% is achievable within a rather broad energy window, ∆*E* \~ 8 --
10 meV, when this angle is appropriately aligned, optimizing the SBTP
performance for a particular neutron energy within this window.

**Acknowledgements**

We thank S.-H. Lee, T. Krist, and M. Hagen, for useful remarks and
discussions. This work was supported by the US DOE under the Contract
DE-AC02-98CH10886.

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[^1]: ^\*^ Corresponding author. Tel.: 1-631-344-3761; fax:
    1-631-344-2739; e-mail: zaliznyak@bnl.gov