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

• Core-shell nanoparticle is an example of magnetic screening effects at the nanoscale. • The magnetic soft shell screens both an external space from a core and a core from an external field. • Magnetic screening alters the superparamagnetic properties of nanoparticles. • Screening effects may be useful to control the magnetic properties of nanoparticles. Manifestations of magnetic screening effects were theoretically investigated in the framework of a model of a particle with a ferromagnetic single-domain core and a magnetically soft shell. The exact solution of the Laplace equation provided 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 studied in the framework of 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 emerged as decreasing 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. The results obtained for the idealized model can be useful for analyzing the properties of real nanoparticles.