The Anisotropy of the AC Susceptibility of Immobilized Magnetic Nanoparticles-the Influence of Intra-Potential-Well Contribution on the AC Susceptibility Spectrum

We have experimentally verified the ac susceptibility model by Shliomis and Stepanov which accounts for the anisotropy caused by the different directions of the easy axes of the magnetic nanoparticle (MNP) cores with respect to the applied ac magnetic field. To experimentally access the anisotropy, single-core MNPs were immobilized in the absence of a magnetic field, thus causing random orientations of easy axes, and in a static magnetic field of 170 mT, thus orienting the nanoparticles' easy axes either parallel or perpendicular to the ac field. In agreement with theory, the real part of the sample with easy axes aligned perpendicularly to the ac field is constant while the imaginary part is zero. In contrast, the real part of the sample with parallel-oriented easy axes decays with increasing frequency. The susceptibility spectra of the sample with random orientation of easy axes are in between the other two cases according to χ(ω) = (χ II (ω) + 2χ ⊥ (ω))/3. This anisotropic behavior also explains why the real part of suspensions of thermally blocked MNPs does not drop down to zero at high frequencies but to a finite value. This value allows one to independently estimate the effective anisotropy constant of MNPs.