Quantitative magnetization measurements of magnetic particles with FePt standard samples

Micrometer-sized magnetic particles have been widely used in magnetic force microscopy, magnetic resonance force microscopy, and bio-sensing. To quantitatively interpret the data obtained with magnetic particles, it is important to know the magnetic properties of the particles. However, the magnetic moment of individual particle is usually too small to be measured by common instruments for samples with large volume. Here, we present a method to characterize magnetic microspheres using patterned FePt thin films as standard samples. The FePt thin film in the L10 phase has perpendicular magnetic anisotropy, and the patterned features can be magnetized to near single-domain magnets, which make them suitable standards for magnetic sphere calibration with magnetic force microscopy. Multiple linear regression is used to analyze the frequency shift images and obtain the effective dipole moment of the spheres. The position of the dipole moment is obtained by minimizing the residuals in multiple linear regression with a gradient descent algorithm. Three NdFeB spheres of different diameters were measured. It was found that the magnetization increases with the increase in the diameter of the sphere, possibly due to the weakening of ferromagnetism on the surface.