Preamble

Polarization-analyzed small-angle neutron scattering with an in-situ ³He neutron spin filter at the China Spallation Neutron Source

Long Tian♮,1,2,3, Han Gao♮,1,2,3,4, Tianhao Wang♮,1,2,3, Haiyun Teng,1,2, Jian Tang,1,2, Qingbo Zheng,1,2, Taisen Zuo,1,2, Tengfei Cui,2,5, Bin Wang,3,6, Xu Qin,2,6, Yongxiang Qiu,1,2, Yuchen Dong,1,2,7, Yujie Zheng,1,2,3, Zecong Qin,1,2,7, Zehua Han,1,2, Junpei Zhang,1,2,3,†, He Cheng,1,2,‡, and Xin Tong1,2,3,§

1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
2Spallation Neutron Source Science Center, Dongguan 523803, China
3Guangdong Provincial Key Laboratory of Extreme Conditions, Dongguan 523803, China
4Center for Neutron Scattering and Advanced Light Sources, Dongguan University of Technology, Dongguan, Guangdong 523808, China
5Graduate School of China Academy of Engineering Physics, Beijing 100193, China
6Center for Neutron Science and Technology, Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
7University of Chinese Academy of Sciences, Beijing 100049, China

Polarization-analyzed small-angle neutron scattering (PASANS) is an advanced technique that enables selective investigation of magnetic scattering phenomena in magnetic materials and distinguishes coherent scattering obscured by incoherent background, making it particularly valuable for cutting-edge research. The successful implementation of PASANS in China was achieved for the first time at the newly commissioned Very Small Angle Neutron Scattering (VSANS) instrument at the China Spallation Neutron Source (CSNS).

This technique employs a combination of a double-V cavity supermirror polarizer and a radio frequency (RF) neutron spin flipper to manipulate the polarization of incident neutrons. The scattered neutron polarization is stably analyzed by a specially designed in-situ optical pumping ³He neutron spin filter, which provides spatially symmetric scattering angle coverage of about 4.8°. A comprehensive PASANS data reduction method, tailored for pulsed neutron beams, has been established and validated with a silver behenate powder sample, achieving a maximum momentum transfer coverage of approximately 0.25 Å⁻¹.

Keywords: neutron polarization analysis, small angle neutron scattering, ³He neutron spin filter

INTRODUCTION

Small-angle neutron scattering (SANS) is a powerful method for studying material structures on nano- to micro-scales, complementing X-ray and light scattering techniques. Neutrons exhibit high transmittance, sensitivity to magnetism and nuclei, making them particularly useful for materials research involving proteins, polymers, and magnetic nanoparticles \cite{1-5}. When neutron spins are polarized, SANS can further distinguish contributions from nuclear coherent scattering, incoherent scattering, and magnetic scattering due to the different interactions between polarized neutrons and materials \cite{6-8}. This capability benefits measurements requiring accurate structural parameter extraction or clarification of magnetic domain distributions in materials \cite{9-12}. This capability is critical for advanced applications such as resolving spin textures in skyrmion materials or quantifying hydrogen/deuterium exchange dynamics in biomolecules. Consequently, polarized neutron small-angle scattering instruments are essential facilities worldwide.

The development of the ³He neutron spin filter (NSF) \cite{13-17} overcame the challenge of analyzing the polarization of scattered neutron beams for the polarization-analyzed small-angle neutron scattering (PASANS) method. Traditional polarization analyzers, such as polarizing supermirrors, suffer from limited angular coverage and require precise angular alignment, whereas ³He NSF provides a tunable, wide-angle solution adaptable to both reactor and spallation sources. The properties of a ³He NSF can be customized for a specific neutron wavelength band by optimizing the geometrical parameters and ³He gas pressure, enabling analysis of neutron polarization after scattering for both pulsed and single-wavelength neutron beams. Furthermore, the ³He NSF offers better accessibility for scattered neutrons in a SANS instrument compared to polarizing supermirror arrays by increasing the analyzing angle coverage. This is crucial for SANS experiments as it affects the range of reciprocal space that can be measured and the available sample scale in PASANS experiments.

The ³He NSF has primarily been used on neutron beamlines in ex-situ mode, such as the Very Small Angle Neutron Scattering (vSANS) diffractometer at the National Institute of Standards and Technology (NIST) Center for Neutron Research \cite{18}, the KWS-1 instrument at the Heinz Maier-Leibnitz Zentrum (MLZ) \cite{19}, and the D33 instrument at the Institut Laue-Langevin (ILL) \cite{20}. The ex-situ ³He NSF is shielded from spatial stray magnetic fields by a cylindrical µ-metal casing. Its compact size makes it feasible for deployment in SANS experiments as it occupies minimal space between the sample and detector array. However, powerful neutron sources and longer polarization decay lifetimes of the NSF are required due to the intrinsic decay of ³He polarization in ex-situ mode. Additionally, continuous calibration of the ³He polarization prior to or during sample measurements is necessary to ensure accurate corrections for each dataset when switching to a new NSF, which inevitably increases data reduction complexity.

As a complement to ex-situ mode, the in-situ ³He NSF maintains constant ³He polarization through in-situ optical pumping, greatly simplifying measurement procedures and making PASANS available at pulsed neutron sources \cite{21-25}.

At the China Spallation Neutron Source (CSNS), years of dedicated efforts in developing polarized neutron techniques have resulted in capabilities encompassing both instrumentation design and methodology establishment for polarized neutron experiments \cite{13,14,21,26-29}. Notably, the polarizing ³He capability at CSNS has been validated in both ex-situ and in-situ modes, allowing customized designs tailored to specific neutron instruments \cite{14,21,29}. In accordance with CSNS's pulsed neutron characteristics, geometry-optimized optical-pumping cells (OPC) can be produced internally to meet various requirements for neutron wavelength ranges and scattering angle coverage \cite{13}. Following extensive technological development and verification tests at CSNS, the polarized neutron technology is now ready for implementation in neutron instruments with small-angle scattering capabilities.

In this paper, we report the design and first successful application of the PASANS technique in China by utilizing polarized neutron instruments, including an in-house customized in-situ NSF at the Very Small Angle Neutron Scattering (VSANS) instrument at CSNS. Additionally, we established a comprehensive method for correcting polarized neutron data for PASANS measurements with a pulsed neutron beam, which has been validated through measurements using silver behenate powders.

II. EXPERIMENTAL INSTRUMENTS

A. PASANS Setup on the VSANS Beamline

The VSANS instrument at CSNS was designed to accommodate studies requiring polarized neutron scattering techniques. As shown in Fig. 1 [FIGURE:1], a rotational exchange drum is mounted upstream of the VSANS beamline, enabling precise switching among three channels: neutron guide, flight tube, and polarizing supermirror. This mechanized drum system achieves mode switching within several seconds with precise positional repeatability, allowing continuous measurements switching between polarized and unpolarized modes. The polarizing supermirror is specifically designed to polarize cold neutrons in the range of 2.2 Å to 11 Å by employing a double-V cavity composed of m = 5 Fe/Si supermirrors, optimized based on Monte Carlo simulation results for polarizing efficiency and transmission ratio \cite{30}. The vertical neutron polarization guide field, which maintains neutron polarization after the supermirror, is generated by a combination of permanent magnet bars and iron plate yokes mounted on downstream flight tubes. The magnet assembly is optimized to generate a field strength of 40-70 G with field direction uniformity better than 1° within the 4 cm × 4 cm central area, making it suitable for experiments requiring larger beam sizes or scattered beam angle coverage.

Furthermore, a radio frequency (RF) neutron spin flipper manufactured by SwissNeutronics Inc. is utilized to flip the polarization of incident neutrons by a π angle. The static magnetic field environment adjacent to the flipper (Fig. 1) was optimized using finite element simulations in COMSOL Multiphysics software \cite{31} to achieve a compatible gradient field distribution satisfying the magnetic resonance condition. This optimized field configuration enables the RF spin flipper to attain 98% flipping efficiency at 2.2 Å, significantly simplifying subsequent polarized neutron data reduction procedures.

An in-situ ³He NSF system is specially designed for VSANS as the analyzer, which is essential for PASANS since the neutron absorption cross-section of ³He is spin-dependent and the ³He NSF can be tailored to provide larger neutron scattering angle coverage for the scattered beam. Additionally, neutron polarization must be manipulated adiabatically by customized guide fields along the beam path \cite{27,32}, indicated by colored arrows in Fig. 1, rotated by 90° before the analyzer to be parallel or antiparallel to the polarized ³He neutron polarization analyzing direction. The in-situ pumping method for maintaining the ³He NSF on the beamline ensures stable and continuous analyzing capability throughout measurements. As shown in Fig. 2(a) [FIGURE:2], the PASANS experimental setup at VSANS was developed based on the design described above.

B. In-situ ³He Neutron Spin Filter

The in-situ ³He NSF at CSNS was first developed and delivered to neutron beamlines in 2021 \cite{21} and has been successfully utilized as a neutron spin polarizer and analyzer for neutron imaging and reflectometry measurements at CSNS \cite{28}. To accommodate the geometry of the conically scattered neutron beam for the SANS instrument, a new generation of in-situ ³He NSF, termed in-situ-SANS, was developed based on our innovative prototype designs. This specialized analyzer system was engineered to maintain the high polarization performance of standard in-situ filters while overcoming geometric constraints imposed by small-angle scattering measurements.

The OPC features an inner diameter of 72 mm and a length of 80 mm, as shown in Fig. 2(b), facilitating a scattering angle of approximately 4.8° (corresponding to θ in the yellow cone) and a maximum q value of about 0.24 Å⁻¹ when the cell is positioned 37 cm from the sample. Notably, the dimensions of the optics, oven windows, magnetic shielding cavity, and box on their exit sides have been enlarged to allow the analyzed scattered neutron beam to pass through the NSF setup unimpeded. The significant changes, especially the asymmetric magnetic shielding configurations and higher heat dissipation from the sapphire window, pose challenges in improving and maintaining the ³He polarization. To address these challenges, the system incorporates modifications to improve field and temperature spatial uniformity at the OPC position. This includes a revamped magnetic field sub-system featuring four distinct gradient compensation coils with optimized input currents, improving field homogeneity to the level of 10⁻⁴/cm at the OPC position. Furthermore, a proactive air cooling mechanism has been installed at the top of the box to mitigate thermal effects resulting from heat dissipation of the large window on the magnetic shielding materials.

Additionally, neutron-absorbing materials were attached to the exit side of the NSF box to minimize scattering interference beyond the cell coverage area. The figure of merit (FOM) of the OPC produced for PASANS measurements is optimized to be 11.01 bar·cm, which balances ³He neutron polarization and transmission ratio to maximize neutron polarization analysis capability across the instrument's wavelength range of 2.2 Å to 6.7 Å. The Free Induction Decay (FID) method is employed to track the evolution of ³He polarization, validating a saturated polarization level of 62.3% with the Electron Paramagnetic Resonance (EPR) method, corresponding to a ³He polarization of 61.1% calibrated through neutron transmission measurements (see Fig. 3 FIGURE:3 and (b)). As shown in Fig. 2(a), the new in-situ-SANS also allows for flexible experimental configurations. The main ³He NSF box can be moved in or out of the beam path by operating the support cart's motor \cite{29}. In combination with the switchable polarizing supermirror at the rotational exchange drum, the entire polarized neutron setup at VSANS enables quick switching between half-polarized SANS, PASANS, and unpolarized SANS. These features underscore the exceptional suitability of in-situ-SANS for PASANS applications and provide convenient user control over measurement modes.

III. POLARIZED DATA REDUCTION

In neutron scattering theory, the total scattering amplitude comprises distinct contributions \cite{33,34}: (1) nuclear coherent and isotope incoherent scattering, represented by term N, which are independent of neutron polarization; (2) nuclear spin-incoherent scattering I, which depends on neutron polarization and has an approximate 2:1 probability for flipping or not flipping neutron spins; and (3) the magnetic scattering term M⊥, which depends on both neutron spin and scattering vector, and can be further separated into M⊥∥ and M⊥⊥, where subscripts indicate that the sample magnetization component is perpendicular to the scattering vector (q) and can be either parallel or perpendicular to neutron polarization depending on whether the neutron spin flips. Concerning neutron spin dependence, total scattering can be divided into non-spin-flip (NonSF) and spin-flip (SF) scattering components, represented by red and blue arrows in Fig. 1, respectively. The NonSF scattering comprises terms N, 1/3·I, and M⊥∥, while SF scattering consists of 2/3·I and M⊥⊥.

In a typical polarized neutron scattering process, information about NonSF and SF scattering in a sample is collected by manipulating the polarization of incident and scattered neutrons. Additionally, polarized neutron data must be corrected for unintended scattering leakage from incorrect spin states in raw data due to inefficiencies of polarized neutron instruments. To extract absolute sample scattering amplitude, derivation based on instrument efficiencies is required \cite{35-37}. For SANS measurements at a pulsed neutron source, scattering intensity S(x, y, λ) is a function of two-dimensional position within the scattering plane (x, y) and neutron wavelength λ, which will be simplified as S hereafter. NonSF scattering S++, S−−, and SF scattering S+−, S−+, where subscripts indicate whether the spin of incident or scattered neutron is parallel (+) or antiparallel (−) to the guide field direction, in PASANS are typically given as follows:

$$
\begin{align}
S_{++} &= \frac{\zeta_{sm}^+\zeta_{3He}^+\sigma_{++} + \zeta_{sm}^-\zeta_{3He}^-\sigma_{--}}{\zeta_{sm}^+\zeta_{3He}^+ + \zeta_{sm}^-\zeta_{3He}^-} + \frac{\zeta_{sm}^+\zeta_{3He}^-\sigma_{-+} + \zeta_{sm}^-\zeta_{3He}^+\sigma_{+-}}{\zeta_{sm}^+\zeta_{3He}^- + \zeta_{sm}^-\zeta_{3He}^+} \
S_{--} &= \frac{\zeta_{sm}^-\zeta_{3He}^+\sigma_{++} + \zeta_{sm}^+\zeta_{3He}^-\sigma_{--}}{\zeta_{sm}^-\zeta_{3He}^+ + \zeta_{sm}^+\zeta_{3He}^-} + \frac{\zeta_{sm}^-\zeta_{3He}^-\sigma_{-+} + \zeta_{sm}^+\zeta_{3He}^+\sigma_{+-}}{\zeta_{sm}^-\zeta_{3He}^- + \zeta_{sm}^+\zeta_{3He}^+} \
S_{+-} &= \frac{\zeta_{sm}^+\zeta_{3He}^-\sigma_{++} + \zeta_{sm}^-\zeta_{3He}^+\sigma_{--}}{\zeta_{sm}^+\zeta_{3He}^- + \zeta_{sm}^-\zeta_{3He}^+} + \frac{\zeta_{sm}^+\zeta_{3He}^+\sigma_{-+} + \zeta_{sm}^-\zeta_{3He}^-\sigma_{+-}}{\zeta_{sm}^+\zeta_{3He}^+ + \zeta_{sm}^-\zeta_{3He}^-} \
S_{-+} &= \frac{\zeta_{sm}^-\zeta_{3He}^-\sigma_{++} + \zeta_{sm}^+\zeta_{3He}^+\sigma_{--}}{\zeta_{sm}^-\zeta_{3He}^- + \zeta_{sm}^+\zeta_{3He}^+} + \frac{\zeta_{sm}^-\zeta_{3He}^+\sigma_{-+} + \zeta_{sm}^+\zeta_{3He}^-\sigma_{+-}}{\zeta_{sm}^-\zeta_{3He}^+ + \zeta_{sm}^+\zeta_{3He}^-}
\end{align}
$$

where σ±± refers to the simplified description of sample scattering cross sections σ±±(x, y, λ) with different neutron spin states, and ζ∗∗∗ represents the probability that a spin-up (+) or spin-down (−) neutron can pass through a polarized neutron instrument. ζ∗∗∗ can also be expressed in terms of wavelength-dependent instrument polarization parameters P∗(λ) and transmission ratio T∗(λ), simplified as:

$$
\begin{align}
\zeta_{sm/3He}^+ &= \frac{1 + P_{sm/cell}}{2}T_{sm/3He}^{Pol} \
\zeta_{sm/3He}^- &= \frac{1 - P_{sm/cell}}{2}T_{sm/3He}^{Pol} \
\zeta_{smf/3He}^+ &= \frac{1 - P_{smf/cell}}{2}T_{smf/3He}^{Pol} \
\zeta_{smf/3He}^- &= \frac{1 + P_{smf/cell}}{2}T_{smf/3He}^{Pol}
\end{align}
$$

where Psmf = PsmPf and Tsmf = TsmTf. Psm/cell/f refers to the polarizing or analyzing efficiency of a supermirror (Psm), ³He spin filter (Pcell), and the flipping efficiency of the neutron spin flipper (Pf). Tsm/3HePol/f refers to the transmission ratio of an unpolarized neutron beam passing through polarized neutron devices. However, both Tsm and Tf are reduced in our case since experimental data (S∗∗) are normalized by the primary beam measured with the supermirror in place. In addition, Tf = 1 as an RF flipper is utilized.

According to these equations, to extract sample scattering cross sections, instrument parameters P∗ and T∗ must be calibrated in advance through direct transmission measurements with an unpolarized neutron beam. Benefiting from the time-independent ³He polarization of an in-situ ³He NSF, the polarizing efficiencies of the instruments can be determined as:

$$
P_{cell} = \sqrt{1 - \frac{T_{3He}^{Depol}}{T_{3He}^{Pol}}}
$$

$$
P_{sm} = \frac{I_{++} - I_{+-}}{I_{--} - I_{-+}}
$$

where T3HePol and T3HeDepol represent transmissions of an unpolarized neutron beam passing through a polarized or depolarized ³He cell, and I∗∗ refers to the neutron transmission ratio for different neutron spin states. All P∗ and T∗ parameters are calibrated before each experimental cycle on the beamline.

Furthermore, measurements of blocked-beam (Sbk, spin-independent), sample transmission ratio (Ts), and scattering from the sample holder (Sh∗∗) are also necessary to determine absolute scattering intensity of the sample. Since a typical sample holder is always non-magnetic, its spin-independent scattering measurements can be reduced when Pf is assumed to be 1. Both Sh∗∗ and Ss∗∗ must be normalized to remove effects of incident neutron flux and Tsm before polarization correction. The absolute scattering intensity of the sample in reciprocal space can then be expressed as:

$$
\sigma_s^{++}(q) = \frac{B_1S_{cor}^{++} + B_4S_{cor}^{+-} + A_3S_{cor}^{-+} + A_2S_{cor}^{--}}{C}
$$

$$
\sigma_s^{--}(q) = \frac{B_3S_{cor}^{++} + B_2S_{cor}^{+-} + A_1S_{cor}^{-+} + A_4S_{cor}^{--}}{C}
$$

$$
\sigma_s^{+-}(q) = \frac{B_2S_{cor}^{++} + B_3S_{cor}^{+-} + A_4S_{cor}^{-+} + A_1S_{cor}^{--}}{C}
$$

$$
\sigma_s^{-+}(q) = \frac{B_4S_{cor}^{++} + B_1S_{cor}^{+-} + A_2S_{cor}^{-+} + A_3S_{cor}^{--}}{C}
$$

where

$$
S_{cor}^{\ast\ast} = \frac{S^{\ast\ast}}{T_s} - T_sS_h^{\ast\ast}
$$

$$
A_1 = (P_{cell} + 1)(P_{sm} + 1)
$$

$$
A_2 = (P_{cell} - 1)(P_{sm} - 1)
$$

$$
A_3 = (P_{cell} + 1)(P_{sm} - 1)
$$

$$
A_4 = (P_{cell} - 1)(P_{sm} + 1)
$$

$$
C = 2P_{cell}P_{sm}(P_f + 1)T_{3He}^{Pol}
$$

Tsh and Th refer to transmission ratios of the sample with holder and an empty holder, respectively. B₁ to B₄ are obtained by replacing Psm with Psmf in A₁ to A₄ in equation (13). For non-magnetic materials such as polymers and proteins, M⊥∥ = M⊥⊥ = 0, which further simplifies equation (12) to σs+− = σs−+ = I and σs++ = σs−− = N + I.

IV. RESULTS AND DISCUSSION

A. Performance of the PASANS Setup

The polarized neutron efficiencies of the instruments were calibrated through neutron transmission measurements without samples on VSANS at CSNS. The procedure involved systematic measurement of transmission ratios for both spin states under various instrument configurations, ensuring comprehensive characterization of the polarization system. Neutron data from PASANS measurements were collected with a wavelength range from 2.2 Å to 6.7 Å, employing a collimation length of 8.31 m. The #3 detector array was positioned 12.2 m downstream from the sample to collect transmission data, while a 2 mm pinhole B₄C slit was mounted before the sample position to define the beam size.

Figure 3(a) shows the wavelength dependence of T3HePol and Pcell, where the latter is derived from equation (9). To verify the stabilization of the polarization analyzing capability of the in-situ-SANS, we measured T3HePol approximately every 30 hours. A difference of less than 0.4% in T3HePol was observed, corresponding to a fluctuation of P3He of less than 1.2%, and the weighted average difference in Pcell was approximately 0.5% based on the primary beam flux distribution. These results demonstrate the exceptional stability of the in-situ optical pumping system, a crucial advantage over conventional ex-situ ³He analyzers that typically require frequent recalibration. It also indicates that in-situ-SANS can be used as a stable analyzer at the beamline, allowing Pcell and T3HePol to be treated as constants during polarization correction. The corresponding saturated ³He polarization P3He was also fitted to 61.1% ± 0.1% during the experiment \cite{14,21} (Fig. 3(b)). This high polarization level, maintained consistently throughout measurements, validates the effectiveness of modifications to the ³He NSF sub-systems.

The polarizing efficiency (Psm) of the supermirror was calibrated according to equation (10) by flipping the ³He polarization while keeping the flipper off. As shown in Fig. 3(c), Psm exceeds 95% at 2.6 Å and reaches about 97.5% at longer wavelengths, similar to our simulation result of Psm > 95% at 2.4 Å; the difference may arise from collimation accuracy during installation. The spin-dependent transmission ratio (Tsm) of the supermirror also exceeds 32% across the experimental wavelength range. Moreover, the flipping efficiency (Pf) of the RF flipper mounted at the VSANS beamline was optimized to be over 98% for neutron wavelengths above 2.2 Å, with optimization involving careful balancing of RF frequency, power, and static magnetic field gradient to achieve maximum flipping efficiency across the entire wavelength band. The excellent flipper performance allows us to simplify the polarized neutron data reduction process during experiments.

B. Sample Measurement

Silver behenate (AgBE) has been well established as a standard sample for wavelength calibration in SANS instruments \cite{38}, as its first three Bragg reflection peaks are accessible within the SANS scattering angle range. Since it is non-magnetic and hydrogen-rich, its nuclear scattering components N and I can be effectively distinguished through NonSF and SF measurements. The PASANS experiment at VSANS was performed with a silver behenate powder sample encased in a quartz cell with an optical path length of 2 mm, placed 4.5 m and 12 m away from the middle-angle (#2) and small-angle (#3) detectors, respectively. Considering the compact design of the ³He NSF and the increased cross-section of the in-house fabricated ³He OPC, the polarization-analyzed scattered neutrons are detected by the entire #3 detector and part of the #2 detector (Fig. 1).

Fig. 4 [FIGURE:4] shows the comparison between NonSF and SF results measured over a neutron wavelength range of 2.2 Å to 6.7 Å. A distinct symmetrical ring at q ∼ 0.11 Å⁻¹ was observed in both two-dimensional patterns in the reciprocal space of the #3 and #2 detectors, corresponding to nuclear coherent scattering at small q. Additionally, the second Bragg peak at q ∼ 0.22 Å⁻¹ was captured by the inner part of the middle-angle detector. The q-range coverage discussed here is influenced by both the distance separating the detector and OPC cell, as well as the cross-sectional area of the cell. SANS instruments at other neutron sources choose compact ex-situ ³He NSF to minimize this distance, such as vSANS at NIST \cite{18,39} and D33 at ILL \cite{20}, allowing them to access a maximum q value of 0.1 Å⁻¹ to 0.28 Å⁻¹, but at the expense of time-independent analyzing capability. TAIKAN at J-PARC \cite{40}, on the other hand, employs the in-situ ³He NSF as the analyzer, effectively observing the second Bragg peak of AgBE with a maximum q value of around 0.25 Å⁻¹ by offsetting the OPC cell. Figures 3(b) and 4 illustrate the PASANS achieved at CSNS compared to other facilities, showing a balance between competitive, spatially symmetrical q coverage and constant analyzing efficiency.

As shown in Figs. 4(a) and (b), compared to NonSF, SF also exhibits weak isotropic scattering at the same q positions. These unexpected scattering signals result from leakage of scattered neutrons with incorrect spin states due to imperfect efficiency of the polarized neutron instruments. By implementing the polarized data correction method introduced above, scattering intensity corresponding to each spin state is allocated to the correct scattering state. Figs. 4(c) and (d) illustrate the corrected NonSF and SF information in reciprocal space, where nuclear coherent scattering in SF has been removed, making the SF scattering information, which is mostly contributed by hydrogen in the AgBE, homogeneous and independent of q. This successful separation validates the effectiveness of the polarization correction algorithm, particularly its handling of instrument efficiency factors and background contributions.

The azimuthally averaged absolute intensity of the corrected NonSF and SF curves is displayed in Fig. 5 FIGURE:5. Two peaks stand out in the NonSF curve, dominated by nuclear spin-coherent scattering, in contrast to the flat SF curve, which is contributed solely by nuclear spin-incoherent scattering. The peak positions at q = 0.107 Å⁻¹ and 0.216 Å⁻¹ match well with unpolarized neutron scattering results for silver behenate, confirming proper wavelength calibration of this polarized neutron instrument. To estimate the effect of multiple scattering in a hydrogen-rich thick sample, the contribution weight of I in the SF curve is denoted as m, which can be determined by fitting the ratio of σs−+ to σs++ in the low q range, where the N contribution in the NonSF curve can be neglected. Our measurements yield a ratio of m = 0.569, consistent with strong multiple scattering occurring in a thicker sample, which has been evidenced by Monte Carlo simulation \cite{39}, providing additional validation of data interpretation. Fig. 5(b) also presents the comparison of calculated N and I based on equations (14-15):

$$
\sigma_s^{++}(q) = \sigma_s^{--}(q) = N + (1 - m)I
$$

$$
\sigma_s^{-+}(q) = \sigma_s^{+-}(q) = mI
$$

where nuclear spin-coherent and spin-incoherent scattering are well separated in silver behenate below q ∼ 0.25 Å⁻¹.

V. CONCLUSION

In this paper, we report the first successful implementation of the PASANS technique at the newly commissioned VSANS instrument at CSNS. Polarized neutron equipment has been deployed along the neutron path to accomplish the complete process of neutron spin polarizing, flipping, and analyzing in PASANS. The integrated system achieves 97.5% polarization efficiency at λ > 2.6 Å and maintains 61.1% ³He polarization stability with <1.2% fluctuation over 75 hours of operation \cite{30,41}, setting a new benchmark for polarized SANS instruments at pulsed neutron sources. By utilizing the in-situ ³He NSF as the neutron spin analyzer, large symmetric scattering cross-section coverage was achieved in both real and reciprocal spaces, with a maximum q value of approximately 0.25 Å⁻¹ under an incident neutron wavelength range of 2.2 Å to 6.7 Å. This q-range coverage indicates state-of-the-art performance with the time-independent PASANS technique compared to other neutron facilities.

It enables studies focusing on characteristic length scales larger than 2.5 nm, making it particularly suitable for investigating magnetic nanostructures in condensed matter systems or obtaining macromolecular information in polymers. The efficiencies of the polarizing supermirror, spin flipper, and in-situ ³He NSF have been calibrated, demonstrating highly efficient and stable neutron polarization capability on VSANS. Moreover, a detailed process for polarized neutron data reduction is introduced, considering a pulsed neutron beam as the incident beam. Silver behenate powder served as a standard sample during PASANS commissioning, highlighting clear differences between its nuclear spin-coherent scattering and spin-incoherent scattering. This distinction allows its smeared-out Bragg peak at larger q to be differentiated from background.

The PASANS capability at VSANS opens new opportunities for studying complex magnetic orders in quantum materials and magnetic correlations in nanoparticles. Building on interfaces developed initially for upgrading the in-situ ³He NSF, future enhancements will focus on integrating the PASANS method with integrated sample environments, including multi-axis magnetic fields with strong field strength. This integration is expected to broaden scientific applications in magnetic materials with complex magnetic orders, such as magnetic skyrmions, by utilizing polarized neutrons on VSANS.

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