Magnetic dipole fit to Gwyddion TTF of a MFM probe.

Approximate the stray field gradient of a MFM probe using a magnetic dipole and simulated annealing to find the best parameters.

This script is used to obtain the dipole approximation of a magnetic force microscope (MFM) probe. See as an example the supplementary material of [1] and [2].

NOTE: For this script to work, you need to have in the same folder the simulated annealing function. It can be found in [3].
NOTE: Simulated annealing is slow, typically the fitting takes about 5 min.

Outside of the script: Gwyddion is used to calculate the magnetic field gradient of the MFM probe, as shown in [2]. The TTF image is exported as a txt file including a header (an example of data is included as both a txt and a png files).
Then, in the script:
1) Takes the text file and extract the raw data and the size of the image from the header
2) Calculates the magnetic field generated by a dipole (in symbolic form).
3) Calculates the derivative of the z-component of the field along the z direction.
4) It is assumed that the dipole approximation is centred at x=0 and y=0. At the moment the script doesn't considers a dipole shifted from the origin in x and y. The magnetic moment is decomposed in mmx mmy and mmz, and is located at a height, called rrz, from the tip of the probe.
5) Simulated annealing script[3] is used to find the values of mmx mmy mmz and
rrz that minimize the least square error between the given data and the
dipole approximation.

References:
[1] Casiraghi, A., Corte-León, H., Vafaee, M. et al. Individual skyrmion manipulation by local magnetic field gradients. Commun Phys 2, 145 (2019). https://doi.org/10.1038/s42005-019-0242-5

[2] Corte-León, H., Volker, Neu, Manzin, Alessandra et al. Magnetic Force Microscopy: Comparison and Validation of Different Magnetic Force Microscopy Calibration Schemes. Small 11, (2020). https://doi.org/10.1002/smll.202070058

[3] Hector Corte, Simulated Annealing Optimization, Taken on the 12th of April 2020. https://uk.mathworks.com/matlabcentral/fileexchange/33109-simulated-annealing-optimization?s_tid=prof_contriblnk&s_tid=mwa_osa_a

This script was written by :
Dr. Héctor Corte-León
Higher Research Scientist
Quantum Materials and Sensors
National Physical Laboratory
Hampton Road
Teddington
TW11 0LW
Phone: [phone]
Email: [e-mail]