Screening effect of a magnetically soft shell of single-domain ferromagnetic nanoparticles

The possible manifestations of magnetic screening effects were theoretically investigated for a particle with a ferromagnetic single-domain core and a magnetically soft shell. The exact solution of the Laplace equation gave analytical formulas for the magnetic field created by the particle placed in a uniform external magnetic field. The system of non-interacting randomly oriented particles was investigated in the Langevin model. The effects of the shell on individual and thermodynamically averaged magnetic properties of the particles were described in a single way using the screening factor A. The screening effects are appeared in a decrease in: (i) the demagnetization factor of the particle core; (ii) the total dipole moment and, accordingly, the external magnetic field created by the particle; (iii) the effective magnetic moment in isothermal magnetization curves and in the Curie law. The magnetically soft shell of the particle also changes the behavior of the particle system in high magnetic fields: the magnetization does not reach saturation, and the differential magnetic susceptibility tends to a non-zero value.