  A way to test electromagnetic field and spacetime properties around black
holes is by considering the dynamics of test particles. In fact, in real
astrophysical scenarios, it is hard to determine spacetime geometry which is
dominating due to degeneracy gravitational effects in parameters of gravity
theories. In this work, we study for the first time the dynamics of spinning
particles that have magnetic dipole moments around Schwarzschild black holes
immersed in an external asymptotically uniform magnetic field using the
Mathisson-Papapetrou-Dixon (MPD) equation. There are two combined interactions:
gravitational interaction between the spin of the particle and
(electro)magnetic interaction between the external magnetic field and the
magnetic dipole moment of the particle to be taken into account. First, we
derive the effective potential of the test spinning magnetized particles in
motion around the black hole. We also study the combined effects of spin and
magnetic interactions on innermost stable circular orbits (ISCOs), the energy,
and angular momentum of the particles at ISCO together with superluminal
bounds. We investigated the collision of the particles and evaluated the
center-of-mass energy in the collisions. Finally, we consider various cases in
which neutron stars and rotating stellar mass black holes can be treated as
spinning magnetized particles, evaluating the effects of the spin and magnetic
moment of objects around supermassive and intermediate-mass black holes.
