Micromagnetic Tomography (MMT) is a technique that combines X-ray micro
tomography and scanning magnetometry data to numerically invert the
surface magnetic signal for the magnetic potential of individual
magnetic grains via their spherical harmonic expansion . The
dipole and higher order multipole moment solutions are uniquely
determined, which has been proved in . As a result, this method
has allowed to analyze the signal of individual grains in rock samples
and synthetic samples, thus providing a new pathway to study the rock
magnetic properties of the remanent magnetization carriers .
Furthermore, the higher order multipole signals in the magnetic
particles are an indication that the grains carry more complex magnetic
orderings, such as multi-domain or vortex states. Therefore, these
higher order moments can be used to constrain the magnetic configuration
of the magnetic particles. In this work we review the multipole
expansion method used by MMT. In addition, we show three dimensional
micromagnetic modelling results to predict the multipole signal of
magnetic particles in different local energy minimum magnetization
states. We show that for certain grains it is possible to uniquely infer
the magnetic configuration from the inverted magnetic multipole moments.
This result is crucial to discriminate single-domain particles from
grains in more complex configurations. Our investigation proves the
feasibility to statistically select ensembles of magnetic grains with
similar properties, such as the magnetic state, which is a step forward
to find stable paleomagnetic recorders.  L. V. de Groot, K.
Fabian, A. Béguin, P. Reith, A. Barnhoorn and H. Hilgenkamp. Determining
Individual Particle Magnetizations in Assemblages of Micrograins.
Geophysical Research Letters, 45(7):2995–3000, 2018.  K. Fabian
and L. V. de Groot. A uniqueness theorem for tomography-assisted
potential-field inversion. Geophysical Journal International,
216(2):760–766, 2018.  D. Cortés‐Ortuño, K. Fabian and L. V. De
Groot. Single particle multipole expansions from Micromagnetic
Tomography. Geochemistry, Geophysics, Geosystems, 22:e2021GC009663,