Physics of Functional Materials

Inverse Computational Magnetism

Principal Investigators

Dieter Suess, Florian Bruckner and Claas Abert

How must a magnetic material be structured so that a device performs a desired function? And what does the magnetization inside a sample look like when only the faint magnetic field it emits is known? Both are inverse problems: instead of simulating a known structure, we compute the structure itself. We develop simulation methods and open-source software to solve such problems – from the automated design of magnonic circuits to the reconstruction of magnetization from microscopy data.

Background and Motivation

Inverse Design

Micromagnetic simulations traditionally work in the forward direction: given the geometry and material parameters of a magnetic structure, they predict its magnetization dynamics and the resulting magnetic fields. Many of the most interesting questions, however, work in the opposite direction.

In inverse design, a desired functionality is prescribed – for example, a magnonic device that routes spin waves of different frequencies to different outputs. An optimization algorithm then determines a structure that realizes this function, often discovering non-intuitive geometries that outperform manually developed designs.

F. Vilsmeier et al., arXiv:2607.07324 (2026), Fig. 2, CC BY 4.0.

Design variables in inverse magnonics: device topology, local material parameters and external field landscapes are established design degrees of freedom, while input shaping and nonlinear effects offer further perspectives.

Magnetization reconstruction

In physics-informed magnetization reconstruction, the starting point is a measurement. Magnetic microscopy techniques such as magnetic force microscopy or nitrogen-vacancy magnetometry record the stray field outside a sample. The inverse problem is to infer the magnetization inside the material from this measured field.

Both inverse design and magnetization reconstruction are severely ill-posed problems: many different magnetic structures can produce nearly identical external fields. Solving them therefore requires carefully selected physical constraints, regularization methods and efficient gradient calculations.

Our group laid the foundations for gradient-based inverse magnetism through the development of adjoint methods for large-scale inverse magnetostatics and topology optimization of permanent magnets. These approaches were subsequently extended to hybrid finite-element and boundary-element formulations and to the optimization of heat-assisted magnetic recording write heads.

Computational Methods

The key to efficiently solving inverse problems is calculating the gradient of an objective function with respect to up to millions of design variables. We obtain these gradients using adjoint methods and, increasingly, through end-to-end automatic differentiation of complete micromagnetic simulations.

These capabilities are integrated into our open-source simulation frameworks magnum.np and NeuralMag. Both are based on machine-learning frameworks such as PyTorch and JAX and enable efficient calculations on graphics processing units.

Building on these simulation frameworks, we develop specialized inverse methods. These include level-set parameterizations that describe device topologies using smooth boundary functions, physics-informed reconstruction schemes that use micromagnetic energy as a regularizer, and Fourier-space propagation operators that allow even the unknown distance between a magnetic sample and a sensor to be optimized.

We also employ convolutional neural networks trained on synthetic micromagnetic data. Their predictions provide robust initial states for subsequent physics-based optimization.

A. Voronov et al., npj Spintronics 3, 19 (2025), Fig. 5, CC BY 4.0.

Inverse design of a spin-wave demultiplexer: a level-set function encodes the pattern within the design region that routes spin waves at 2.6 GHz and 2.8 GHz to different output ports.

Key Results and Applications

Inverse-designed magnonic devices

Using level-set topology optimization, we designed a sub-micrometre spin-wave demultiplexer that separates signals with frequencies of 2.6 GHz and 2.8 GHz into different output ports of a 300-nanometre-wide yttrium iron garnet conduit. This demonstrates how computational optimization can produce compact magnonic devices with precisely tailored functionality.

Physics-informed magnetization reconstruction

By combining U-Net neural networks with bias-field-constrained micromagnetic relaxation, we can reconstruct skyrmion textures and determine intrinsic material parameters such as saturation magnetization, exchange interaction, magnetic anisotropy and the Dzyaloshinskii–Moriya interaction from stray-field measurements.

Our Fourier-space physics-informed approach has also been applied to reconstruct magnetic domain structures in the van der Waals magnet Fe₃₋ₓGaTe₂ from experimental nitrogen-vacancy measurements. At the same time, the method determines the previously unknown distance between the magnetic sensor and the sample.

D. Suess et al., Scientific Reports 15, 42867 (2025), Fig. 1, CC BY-NC-ND 4.0.

Physics-informed magnetization reconstruction: a measured stray-field map is used to extract the magnetization texture inside the sample, shown here for a skyrmion lattice.

Outlook

Together with our research partners, we investigate the emerging field of AI magnonics, in which machine-learning methods design magnonic devices while magnonic hardware itself is used for neuromorphic computing.

These approaches pave the way towards quantitatively interpretable magnetic microscopy and a new generation of computer-designed magnonic and spintronic devices.