FunMaP: Functional Magnetic Particles analysis pipeline for FePt thin films on spherical SiO₂ substrates

Natalia Gonzalez-Vazquez · Andrew K. Schulz

FunMaP workflow integrating experimental and micromagnetic simulation pipelines for FePt Janus particles.

An open-source research repository for micromagnetic simulations, SQUID magnetometry analysis, and XRD visualisation of FePt thin films on spherical SiO₂ substrates. This repository is tied to the soon to be pre-print and submitted publication entitled, "Ordering, not curvature provides means for magnetic tunability for FePt based Janus particles" by Natalia Gonzalez-Vasquez, Eylül Suadiye, Eberhard Goering, Ruben O. Miranda-Rosales, Hilda David, Frank Thiele, Julia Unangst, Andrew K. Schulz, and Gunther Richter.

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Overview

This repository contains three independent Python-based modules developed for the characterisation of FePt thin films on spherical SiO₂ substrates. Together they provide the full computational workflow for micromagnetic simulations, XRD visualisation, and SQUID magnetometry analysis presented in the associated thesis and manuscript.

• Part 1: Micromagnetic simulations of hemispherical FePt caps (ubermag/OOMMF)
• Part 2: Automated visualisation of X-ray diffraction (XRD) data
• Part 3: SQUID magnetometry analysis and SQUID–simulation comparison

Each module is self-contained but designed to function within a unified research workflow.

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Preview

Magnetization states along a full hysteresis loop for a 10 µm FePt cap with radial anisotropy and a 15% A1 soft fraction, at 0 K. Left: the loop with a marker at the current field. Centre: XZ central slice through the cap. Right: XY top view. Colour is m_z/M_s; white is outside the magnetic shell.

More example outputs, including the underlying state files, are in results/.

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Repository Structure

FunMaP/
│
├── analysis/                                                  # Experimental data analysis
│   ├── SQUID_analysis_Caps.ipynb                              # Batch averaging & background correction
│   ├── SQUID_analysis_Caps_v2.ipynb                           # + QD filling factor, absolute units, demag, IP/OOP
│   ├── SQUID-OOMMF-analysis.ipynb                             # SQUID vs simulation overlay
│   ├── OOMMF-analysis.ipynb                                   # Simulation hysteresis + SFD plots
│   └── XRDplot.ipynb                                          # XRD masked/naked plotting
│
├── simulations/                                               # Micromagnetic simulation scripts
│   ├── FePt_L10_A1_MultipleCaps_HystLoop_radial_merged.ipynb
│   ├── FePt_L10_MultipleCaps_HystLoop_DiameterSweep.ipynb
│   ├── FePt_real_magnetization_snapshots.ipynb
│   └── SIMULATIONS_GUIDE.md
│
├── results/                                                   # Example outputs (see results/README.md)
│   └── snapshot_10um_radial_15pctA1/                          # Loop animation, summary figure, state files
│
├── sample_data/                                               # Synthetic demo data (not real measurements)
│   ├── squid/
│   │   ├── sample_3um_measurement_A.dat
│   │   └── sample_3um_measurement_B.dat
│   ├── simulations/
│   │   ├── data_sphere_1.0um_synthetic.csv
│   │   ├── data_sphere_3.0um_synthetic.csv
│   │   ├── data_sphere_5.0um_synthetic.csv
│   │   ├── data_sphere_8.0um_synthetic.csv
│   │   └── data_sphere_10.0um_synthetic.csv
│   └── xrd/
│       └── sample_FePt_SiO2_on_Si.xy
│
├── environment.yml                                            # Conda environment (ubermag_env)
├── .gitignore
└── README.md

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Notebook Guide

Goal	Notebook	Main output
Run mixed-phase FePt cap simulations	simulations/FePt_L10_A1_MultipleCaps_HystLoop_radial_merged.ipynb	Hysteresis data for multiple diameters and phase fractions
Run pure L1₀ diameter-sweep simulations	simulations/FePt_L10_MultipleCaps_HystLoop_DiameterSweep.ipynb	Hysteresis data for pure L1₀ caps
Generate real magnetization snapshots	simulations/FePt_real_magnetization_snapshots.ipynb	XZ/XY state maps, selected-state PNG/SVG exports, interactive HTML viewer
Read the simulation workflow guide	simulations/SIMULATIONS_GUIDE.md	Simulation-only usage notes, parameters, outputs, and troubleshooting
See example outputs without running anything	results/README.md	Loop animation, summary figure, and representative state files
Analyse SQUID batches	analysis/SQUID_analysis_Caps.ipynb	Averaged loops, statistics, corrected plots, .csv export
Analyse SQUID batches in absolute units (IP/OOP)	analysis/SQUID_analysis_Caps_v2.ipynb	Magnetization in A/m and Tesla, demagnetization-corrected loops, IP–OOP comparison
Compare SQUID and simulation results	analysis/SQUID-OOMMF-analysis.ipynb	Two-panel SQUID–simulation overlay
Analyse converted OOMMF simulation files	analysis/OOMMF-analysis.ipynb	Overlay plots, swifting field distribution (SFD) analysis, per-file reports
Plot XRD files	analysis/XRDplot.ipynb	Publication-ready XRD .PNG/.SVG plots

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Pipeline

SQUID measurements (.dat)
        │
        ▼
SQUID_analysis_Caps.ipynb
  → background correction (diamagnetic slope subtraction)
  → per-batch averaging + statistics (Hc, Mr/Ms, W_hyst)
  → Averaged_Data_{diam}um_{ts}.csv
        │
        └──────────────────────────────┐
                                       ▼
Simulations (ubermag/OOMMF)     SQUID-OOMMF-analysis.ipynb
        │                         → overlay: SQUID mean vs sims
        ▼                         → two-panel: raw A·m² / M/Msat
[Simulation scripts]
  → CONVERTED CSVs
    (B_ext, Mz/Ms, Moment_Am2)
        │
        ▼
OOMMF-analysis.ipynb
  → multi-file overlay plot
  → per-file hysteresis + SFD + report

XRD measurements (.xy)
        │
        ▼
XRDplot.ipynb
  → masked / naked mode
  → reference markers: FePt, Si, SiO₂, Fe–O phases

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Sample Data

This repository includes synthetic example files in sample_data/ for testing the plotting and analysis workflow without requiring access to unpublished experimental data.

Folder	Contents
sample_data/squid/	Demo SQUID-style .dat files (Quantum Design format)
sample_data/simulations/	Synthetic converted simulation CSVs
sample_data/xrd/	Example .xy diffractogram

These files are intended only for workflow demonstration and code testing — they do not represent the original experimental datasets used in the thesis.

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Dependencies

All scripts run in a single conda environment based on ubermag.

Dependency	Version	Purpose
Python	≥ 3.9	Core execution
Ubermag	Latest stable	Micromagnetic simulation interface
OOMMF	≥ 1.2	Micromagnetic solver backend
NumPy	≥ 1.20	Numerical operations
pandas	≥ 1.3	Data I/O and tabulation
Matplotlib	≥ 3.5	Visualisation
scipy	≥ 1.7	Signal processing

git clone https://github.com/nagova/FunMaP.git
cd FunMaP
conda env create -f environment.yml
conda activate ubermag_env
jupyter notebook

Verify OOMMF is available:

oommf.tcl +version

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Quick Start

After installation, open Jupyter Notebook inside the ubermag_env environment and choose the notebook matching your task:

• Run micromagnetic hysteresis simulations
  • simulations/FePt_L10_A1_MultipleCaps_HystLoop_radial_merged.ipynb
  • simulations/FePt_L10_MultipleCaps_HystLoop_DiameterSweep.ipynb
• Generate real magnetization snapshots / interactive loop viewer → simulations/FePt_real_magnetization_snapshots.ipynb
• Analyse SQUID measurements → analysis/SQUID_analysis_Caps.ipynb
• Analyse SQUID measurements in absolute units (IP/OOP) → analysis/SQUID_analysis_Caps_v2.ipynb
• Compare SQUID data with simulations → analysis/SQUID-OOMMF-analysis.ipynb
• Plot XRD diffractograms → analysis/XRDplot.ipynb
• Analyse converted simulation files → analysis/OOMMF-analysis.ipynb

Recommended order for first-time users:

1. Create and activate the conda environment
2. Verify OOMMF is available (oommf.tcl +version)
3. Open Jupyter Notebook
4. Start from the notebook matching your workflow goal

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Part 1 — Micromagnetic Simulations

Click to expand

Scientific Scope

This module models the intrinsic magnetic switching behaviour of hemispherical FePt shells deposited on diamagnetic SiO₂ spheres. The SiO₂ substrate is treated as magnetically inactive (Ms = 0) and is excluded from the computational mesh.

The simulations explicitly account for:

• Curvature-dependent demagnetising effects
• Competition between exchange and magnetocrystalline anisotropy energies
• Phase composition (ordered L1₀ vs mixed L1₀/A1 FePt)
• Size-dependent discretisation for numerical convergence

Simulation Scripts

FePt_L10_A1_MultipleCaps_HystLoop_radial_merged.ipynb
Hysteresis loops for diameters 1, 3, 5, 8, 10, 20 µm (60 nm cap thickness). Mixed L1₀/A1 phase with radial anisotropy. Runtime prompts select temperature (MinDriver at 0 K / TimeDriver at T > 0 K). Supports checkpoint-based resume.

FePt_L10_MultipleCaps_HystLoop_DiameterSweep.ipynb
Same diameter sweep (1, 3, 5, 8, 10, 20 µm) but pure L1₀ phase — no A1 soft fraction. Runtime prompts select temperature and anisotropy mode (Radial or Uniaxial_Vertical). Supports checkpoint-based resume.

FePt_real_magnetization_snapshots.ipynb Runs one selected cap with a lighter field schedule and saves real spatial magnetization states from system.m. The notebook can render selected XZ side-view states as PNG/SVG and build an interactive Plotly/HTML viewer from a folder of saved state files.

For a simulation-only walkthrough, see simulations/SIMULATIONS_GUIDE.md.

Key Parameters

Note on notation: Throughout this repository, L10 in file names and code refers to the L1₀ (L1-zero) ordered intermetallic phase of FePt.

Parameter	Value	Units
Ms (saturation magnetisation)	1 × 10⁶	A/m
A (exchange stiffness)	1 × 10⁻¹¹	J/m
Ku (L1₀ hard phase)	6.6 × 10⁶	J/m³
Ku (A1 soft phase)	1 × 10⁴	J/m³
Bmax (field sweep range)	±18	T
Cap thickness	60	nm
Sphere diameters	1, 3, 5, 8, 10, 20	µm

Modelling Assumptions

• Single isolated hemispherical FePt cap; no inter-particle dipolar coupling
• Zero-temperature approximation for static driver (no thermal activation)
• Open boundary conditions; self-consistent magnetostatic field within the cap
• Homogeneous material parameters within each defined phase

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Part 2 — XRD Data Visualisation

Click to expand

Scientific Purpose

Automated visualisation of Cu Kα XRD diffractograms of FePt films on SiO₂ sphere monolayers, enabling rapid structural phase assessment and L1₀ ordering evaluation.

Script: XRDplot.ipynb

• GUI file selector → one or more .xy files
• Terminal prompt: masked (apply angular masks) or naked (raw data)
• log₁₀ intensity axis by default (switchable to linear)
• Colour-coded vertical reference markers with (hkl) + 2θ labels in an external legend:
  • FePt L1₀ — orange
  • Si substrate — gray
  • SiO₂ amorphous hump — blue
  • Fe–O phases (magnetite / hematite / maghemite) — green (togglable)
• Angular masks configurable via MASKS list at the top of the script
• Outputs: PNG (600 dpi) + SVG per file → xrd_outputs/

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Part 3 — SQUID Magnetometry Analysis

Click to expand

Scientific Purpose

This module bridges experimental SQUID magnetometry data and micromagnetic simulation results, enabling direct comparison between ensemble-averaged experimental hysteresis loops and single-cap simulated loops.

Script: SQUID_analysis_Caps.ipynb

Processes raw SQUID .dat files (Quantum Design format) for a single particle batch.

• GUI file selector → ≥2 .dat files per batch
• Prompts: sphere diameter [in µm], cap thickness [in nm], substrate area [in mm²]
• Optional diamagnetic background subtraction (slope fitted to ±95% saturation tails independently, then averaged)
• Averaging by branch (descending and ascending separately) → proper closed mean loop
• Extracts: H_c [in T], M_r/M__s [unitless], hysteresis loss W_hyst [in J/kg]
• Outputs: PNG + SVG two-panel plot, .txt statistical report, averaged CSV

Plot layout:

• Top panel: raw emu — individual curves + mean ± 1 SD
• Bottom panel: background-corrected M/Msat — individual curves + mean ± 1 SD

Averaged CSV columns: Field_T, M_norm_desc, M_norm_asc, M_emu_desc, M_emu_asc

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Script: SQUID_analysis_Caps_v2.ipynb

Version 2 of the batch workflow. It keeps v1's averaging and background subtraction and adds four corrections needed to report absolute magnetization, following processing notes from Prof. E. Goering (MPI-FKF).

SQUID_analysis_Caps.ipynb (v1) is unchanged and remains the validated single-geometry path. Use v2 when you need magnetization in physical units, or an in-plane / out-of-plane comparison.

Correction chain

raw m (emu), H (Oe)
  → 1. divide by the Quantum Design filling factor   → instrument-corrected emu
  → 2. subtract linear diamagnetic slope             → ferromagnetic emu
  → 3. divide by magnetic volume                     → emu/cm³, A/m, µ₀M in T
  → 4. shear by demagnetizing factor                 → µ₀H_int = µ₀H_app − N·µ₀M
  → 5. (optional) scale OOP to the IP saturation

Step 2 (a substrate correction, acting on the moment axis) and step 4 (a field-axis correction) are physically distinct and are easy to conflate; v2 applies both.

What v2 adds over v1

Feature	Why it matters
QD filling-factor correction	Sample shape and VSM amplitude change the measured EMU; v1 applies no instrument correction
Absolute units (emu/cm³, A/m, T)	Lets µ₀M be compared directly with the simulated µ₀Ms ≈ 1.26 T
Demagnetizing (shearing) correction	Removes the apparent easy-axis steepening caused by sample shape
IP / OOP pairing	Enables anisotropy comparison and OOP→IP saturation rescaling
Sweep-rate estimation	Recovers the true ramp rate from MPMS timestamps
Closed-cycle trimming	Removes virgin curves and park-at-zero tails that corrupt Hc and Mr

Important: the filling factors and demagnetizing factors are sample-specific. The defaults shipped in the notebook describe the foil disc used to validate it, not FePt caps. A sphere monolayer of hemispherical caps has no single rigorous demagnetizing factor, so the choice (thin-film limit N⊥ = 1, or compact-particle N = 1/3) is a modelling decision that must be stated explicitly. The notebook prints a critical value N_crit = 1 / max|d(µ₀M)/d(µ₀H)| and warns when the requested shear exceeds it, because beyond N_crit the corrected loop becomes multivalued.

Conventions: Hc is identical in applied and internal field, since the shear term vanishes at M = 0. Mr/Ms is quoted at zero applied field.

Outputs: four-panel PNG + SVG (corrected moment, absolute magnetization, internal-field loops, OOP rescaled to IP), a .txt report recording every correction factor used, and averaged + per-file metric CSVs.

Validation: the correction chain reproduces Prof. Goering's independently computed results for a 4.95 mm × 0.56 mm foil disc to machine precision (field 1×10⁻¹⁶, µ₀M 5×10⁻¹⁰, internal field 4×10⁻¹² relative deviation), and returns metrics consistent to ~1% across sweep rates from 10 to 700 Oe/s.

Anisotropy (COMPUTE_ANISOTROPY, on by default). Effective anisotropy is obtained by the area method on the anhysteretic mid-curve — the average of the descending and ascending branches at each field, which is single-valued and approximately reversible, so H(M) can be inverted legitimately:

K_eff = ∫₀^(m_frac·Ms) (µ₀H_hard − µ₀H_easy) dM

evaluated on internal field, with both geometries rescaled to a common Ms, the easy axis identified from squareness rather than assumed, and K_eff kept signed so an inconsistent assignment is visible instead of hidden.

Verified against an analytic Stoner–Wohlfarth pair with a known K_u: it recovers K_u to 0.09%, recovers µ₀H_K from the hard-axis slope exactly, and reproduces the predicted m_frac² truncation scaling to <1×10⁻³ over m_frac = 0.5–0.99.

Two independent anisotropy-field estimates are reported — one from the integrated area (2K/Ms), one from the hard-axis slope (Ms / dM/dµ₀H). They agree only when the sample really is uniaxial, so their ratio is a built-in validity check, alongside r2_hard (linearity of the hard axis) and a monotonicity check on the mid-curve. For curved FePt caps expect r2_hard well below 1: the easy axis is distributed over the cap surface, so K_eff is an ensemble-effective descriptor rather than an intrinsic anisotropy constant.

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Script: SQUID-OOMMF-analysis.ipynb

Two-panel overlay of averaged SQUID data and simulation results.

• Step 1: select averaged SQUID CSV (output of SQUID_analysis_Caps)
• Step 2: select one or more CONVERTED simulation CSVs
• Outputs: PNG + SVG → Comparison_Results_{ts}/

Plot layout:

• Top panel: physical moment [A·m²] — SQUID (emu → A·m² converted) + sim Moment_Am2
• Bottom panel: normalised M/Msat — SQUID M_norm + sim Mz/Ms

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Script: OOMMF-analysis.ipynb

Multi-file simulation overlay and per-file SFD analysis.

• GUI file selector → any number of CONVERTED simulation CSVs
• Terminal prompt: sphere diameter + cap thickness per file
• Outputs per session:
  • Overlay_{ts}.png/.svg — all files on one two-panel figure
  • Per-file {name}_{ts}.png/.svg + _report.txt (H_c, M_r/M_s, SFD FWHM)

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Citation

If you use this repository, please cite:

@misc{gonzalezvazquez_funmap_2026,
  title  = {FunMaP: Customizable simulations for Janus particles' magnetic properties
            with associated visualizations},
  author = {Gonzalez-Vazquez, Natalia and Schulz, Andrew K.},
  year   = {2026},
  note   = {In preparation},
}

For thesis citation or exact reproducibility, users are encouraged to reference a tagged repository release when available.

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Known Limitations

This repository was developed as a research workflow accompanying a thesis and associated manuscript. The notebooks are intended for transparent scientific analysis rather than as a general-purpose software package.

• Micromagnetic models treat the SiO₂ substrate as magnetically inactive (Ms = 0)
• Simulations represent isolated hemispherical caps — no inter-particle dipolar coupling
• Static simulations use a zero-temperature approximation unless thermal drivers are explicitly selected
• Material properties are homogeneous within each defined phase region
• Sample files included in the repository are synthetic demonstration data only

These assumptions should be considered when comparing simulation outputs with ensemble-averaged experimental measurements.

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License

This project is licensed under the GNU General Public License v3.0.
See the LICENSE file for details.

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Copyright

Copyright © 2026 Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V.
Copyright © 2026 University of Stuttgart

Authors: Natalia Gonzalez-Vazquez, Andrew K. Schulz

FunMaP is free software distributed under the GNU General Public License v3.0 or later.

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Acknowledgements

We thank G. Richter for scientific feedback and discussion.

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Contact

Authored and maintained by:

• Natalia Gonzalez-Vazquez — https://github.com/nagova
• Andrew K. Schulz — https://github.com/Aschulz94

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