🔬 materials science

NuMagSANS: a GPU-accelerated open-source software package for the generic computation of nuclear and magnetic small-angle neutron scattering observables of complex systems

NuMagSANS is a GPU-accelerated, open-source software package that enables the flexible and rapid computation of nuclear and magnetic small-angle neutron scattering observables for complex systems by utilizing position-dependent density data, full rotational control, and a comprehensive library of response functions.

Original authors: Michael P. Adams, Andreas Michels

Published 2026-01-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Michael P. Adams, Andreas Michels

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out what a mysterious, complex object looks like, but you can't touch it or see it directly. Instead, you have to shine a beam of tiny particles (neutrons) at it and watch how they bounce off. This is called Small-Angle Neutron Scattering (SANS). It's like trying to guess the shape of a hidden sculpture by watching how raindrops splash against it.

The problem is that for complex materials—especially those with magnetic properties—figuring out exactly how those neutrons should bounce is a massive mathematical headache. It involves crunching billions of numbers to predict the pattern.

Enter NuMagSANS. Think of this software as a super-fast, high-tech "pattern predictor" built specifically for scientists who study these magnetic materials.

Here is a breakdown of what the paper says NuMagSANS does, using some everyday analogies:

1. The "Magic Translator" (Input Data)

Usually, scientists have data about a material's internal structure (where the atoms are) and its magnetic "personality" (where the magnetic forces point). This data is often in a format that's hard to use for scattering calculations.

The Analogy: Imagine you have a detailed 3D map of a city (the material) and a list of traffic directions (the magnetism). NuMagSANS is like a translator that takes these raw maps and directions and instantly converts them into a "traffic flow prediction" (the scattering pattern).
The Claim: The software lets users import their own specific data about nuclear density and magnetization, giving them huge flexibility to study almost any complex system they can imagine.

2. The "Speed Demon" (GPU Acceleration)

Doing these calculations on a standard computer (CPU) is like trying to count every grain of sand on a beach one by one with a single spoon. It takes forever.

The Analogy: NuMagSANS uses a GPU (a graphics card, usually found in gaming computers). If a CPU is a single spoon, a GPU is an army of 10,000 tiny shovels working at the same time.
The Claim: By using this parallel processing power, NuMagSANS performs these massive calculations incredibly fast. The paper notes that a simulation that might take hours on a normal computer can be done in about 60 seconds on a high-end GPU, even for systems with tens of millions of data points.

3. The "Rotating Stage" (Sample Control)

Materials often look different depending on which angle you look at them from.

The Analogy: Imagine a spinning top with a weird pattern painted on it. If you only look at it from the front, you miss half the picture. NuMagSANS allows the user to virtually "rotate" the sample in 3D space.
The Claim: The software supports full rotational control, letting scientists explore how the scattering pattern changes as the material turns, which is crucial for understanding magnetic materials.

4. The "Swiss Army Knife" of Outputs

Once the math is done, the software doesn't just give you one number; it gives you a whole toolbox of insights.

The Analogy: It's like a camera that doesn't just take a photo, but also gives you a 3D model, a heat map, and a breakdown of the colors.
The Claim: NuMagSANS can calculate about 100 different types of results, including:
- 2D Scattering Maps: Visual patterns showing how neutrons scatter.
- Correlation Functions: These tell you how far apart things are inside the material (like measuring the distance between friends in a crowded room).
- Spin-Flip Data: Special calculations for when the neutrons change their "spin" (a quantum property) upon hitting the material.
- Separation of Effects: It can mathematically separate the "shape" of a single particle from the "crowd effects" of how particles interact with each other. This helps scientists understand if a pattern comes from the object itself or from how the objects are packed together.

5. The "Reality Check" (Verification)

To prove it works, the authors tested the software against known mathematical puzzles.

The Analogy: Before trusting a new GPS, you test it on a route you already know perfectly.
The Claim: They tested NuMagSANS on:
- A perfectly uniform magnetic sphere (the "easy" test).
- A sphere with a "vortex" magnetic pattern (a "twisty" test).
- A group of 800 nanoparticles arranged in different ways (a "crowded" test).
- In every case, the software's results matched the known mathematical answers perfectly.

6. The "Open Source" Promise

The Analogy: Instead of selling a locked box of tools, the authors are handing out the blueprints and the tools for free.
The Claim: The software is open-source (free to download and modify) and written in standard programming languages (C++ and CUDA). It runs on Windows, Mac, and Linux, provided you have an NVIDIA graphics card.

Summary

NuMagSANS is a free, super-fast software tool that helps scientists predict how neutrons will scatter off complex magnetic materials. By using the power of modern graphics cards, it turns a task that used to be slow and difficult into a quick, routine calculation, allowing researchers to see the hidden magnetic and structural details of materials with unprecedented clarity.

Technical Summary of NuMagSANS

Problem Statement
Accurately evaluating nuclear and magnetic small-angle neutron scattering (SANS) observables in structurally and magnetically complex systems presents significant computational challenges. Existing software solutions, such as SASfit, mag2exp, or the generic calculators within SasView, often lack the flexibility to handle arbitrary, position-dependent nuclear density and magnetization data or the computational speed required for large-scale datasets. Specifically, there is a need for a tool that can seamlessly integrate with micromagnetic simulation outputs (e.g., from MuMax3) to compute two-dimensional SANS cross sections and correlation functions for complex magnetic textures, including those with chiral features and interparticle interference, without relying on simplified analytical form factors.

Methodology
The authors present NuMagSANS, a software package implemented in C++ and CUDA, designed to leverage the parallel processing capabilities of NVIDIA GPUs. The core methodology involves:

Input Handling: The software accepts user-defined real-space data for nuclear scattering-length density ( $N(\mathbf{r})$ ), magnetization vector fields ( $\mathbf{M}(\mathbf{r})$ ), and structural object positions. It supports both atomistic (discrete point objects) and micromagnetic (continuum voxel-based) simulation modes.
Theoretical Framework: The code computes SANS observables based on the Fourier transforms of the input real-space data. It explicitly calculates unpolarized, polarized (POLARIS), half-polarized (SANSPOL), and chiral cross sections, as well as nuclear-magnetic interference terms. The implementation accounts for various scattering geometries, including magnetic fields applied perpendicular ( $B_0 \perp k_0$ ) or parallel ( $B_0 \parallel k_0$ ) to the incident neutron beam.
GPU Acceleration: The discrete-space Fourier transforms (DSFTs) required to convert real-space data into reciprocal space are executed in parallel on the GPU. The software separates real and imaginary parts of the Fourier transforms to accommodate CUDA kernel constraints, utilizing discrete cosine and sine transforms.
Workflow: The process involves parsing a configuration file, loading real-space data into RAM, transferring data to GPU memory, performing high-speed summations for the scattering amplitudes, and computing cross sections, correlation functions, and pair-distance distribution functions.
Output: The software generates two-dimensional SANS cross sections, azimuthally averaged intensities, angular Fourier decompositions (modal intensities), and both one- and two-dimensional correlation functions in CSV format.

Key Contributions

GPU-Accelerated Performance: NuMagSANS delivers substantial performance improvements over conventional CPU-based approaches, enabling the rapid computation of SANS observables for datasets containing tens of millions of discretization cells.
Flexibility and Modularity: The software allows for the import of arbitrary position-dependent nuclear and magnetic data, providing flexibility to analyze complex systems that cannot be described by simple analytical form factors. It includes a library of approximately 100 response functions covering 2D cross sections, correlation functions, and azimuthally averaged quantities.
Integration with Micromagnetics: A key feature is the seamless integration with micromagnetic simulation tools like MuMax3, allowing researchers to directly compute magnetic SANS observables from simulated spin configurations.
Separation of Contributions: The software includes functionality to separate particle form factors from interparticle interference contributions, facilitating the analysis of structure factor effects in ordered or densely packed systems.
Comprehensive Observable Suite: It computes a wide range of observables, including chiral scattering terms ( $\chi$ ) and nuclear-magnetic interference, which are critical for analyzing systems with broken inversion symmetry or specific magnetic textures.

Results and Verification
The paper validates NuMagSANS through several benchmark cases with known analytical solutions:

Uniformly Magnetized Sphere: The software correctly reproduces the analytical SANS cross sections and pair-distance distribution functions for a sphere with uniform magnetization, including the characteristic four-fold symmetry in spin-flip scattering.
Linear Vortex Texture: NuMagSANS successfully models a spherical nanomagnet with a linear vortex texture, accurately capturing the non-zero chiral scattering terms and the specific angular anisotropy arising from the broken inversion symmetry.
Interparticle Interference: The software was applied to an ensemble of 800 iron nanoparticles in dilute, random, and ordered (simple cubic) configurations. It successfully demonstrated the transition from smooth form-factor oscillations in dilute systems to noisy signals with Bragg-peak-like features in ordered lattices, capturing collective effects.
Performance Scaling: Runtime experiments on an NVIDIA RTX 3090 GPU showed that execution time scales approximately linearly with the number of discretization cells over two orders of magnitude (from $\sim 4 \times 10^4$ to $\sim 10^8$ cells). A system with $\sim 3.38 \times 10^6$ cells was processed in approximately 60 seconds.

Significance
The authors claim that NuMagSANS provides a powerful and efficient tool for advanced SANS analysis, bridging the gap between desktop-scale simulations and large-scale high-performance computing approaches. Its ability to handle complex, user-defined real-space data and its integration with micromagnetic solvers allow for detailed insights into the structural and magnetic characteristics of samples, particularly magnetic materials with intricate spin textures. By enabling the systematic examination of how interparticle correlations influence scattering cross sections, NuMagSANS offers a versatile platform for advancing the understanding of scattering phenomena in purely magnetic and hybrid systems. The software is distributed as open-source under the MIT License to facilitate reproducibility and further development within the community.