Magnetic nanoparticles

Let us consider a magnetic nanoparticle with a magnetic moment p = M_sV (where M_s and V are the saturation magnetization and MNP volume). We can represent a nanoparticle as a small, spherical magnet with diameter equal to 2 R, that is, the single domain MNP acts as a dipole with magnetic moment p. Magnetic induction and its gradient at the axis parallel to the magnetic moment direction are given by

Near the surface of the MNP, at r = R, the modulus of the radial magnetic gradient is , as follows from (15). The perpendicular component, B_⊥, is two times smaller than B_//. Thus, for the considered magnet geometry, close to the magnet surface (edge), the magnetic gradient is the same order of magnitude: , where r is the characteristic length scale of the task. We have analytically examined magnetic systems for producing high-gradient magnetic fields and calculated the magnetic flux and gradient distributions that might enable control of the cell shape and functions. The magnetic systems capable of generating HGMFs and formulas allowing rapid estimation of the magnetic field gradient are summarized in Table 1.