Understanding particle size and distance driven competition of interparticle interactions and effective single-particle anisotropy

Magnetic response of single-domain nanoparticles (NPs) in concentrated systems is strongly affected by mutual interparticle interactions. However, particle proximity significantly influences single-particle effective anisotropy. To solve which of these two phenomena plays a dominant role in the magnetic response of real NP systems, systematic study on samples with well-defined parameters is required. In our work, we prepared a series of nanocomposites constituted of highly-crystalline and well-isolated CoFe₂O₄ NPs embedded in an amorphous SiO₂ matrix using a single-molecule precursor method. This preparation method enabled us to reach a wide interval of particle size and concentration. We observed that the characteristic parameters of the single-domain state (coercivity, blocking temperature) and dipole–dipole interaction energy ($E_{\text{d}-\text{d}}$) scaled with each other and increased with increasing ${\left(d_{\text{XRD}}/r\right)}^3$, where d _XRD was the NP diameter and r was the interparticle distance. Our results are in excellent agreement with Monte-Carlo simulations of the particle growth. Moreover, we demonstrated that the contribution of $E_{\text{d}-\text{d}}$ acting as an additional energetic barrier to the superspin reversal or as an average static field did not sufficiently explain how the concentrated NP systems responded to an external magnetic field. Alternations in the blocking temperature and coercivity of our NP systems accounted for reformed relaxations of the NP superspins and modified effective anisotropy energy of the interacting NPs. Therefore, the concept of modified NP effective anisotropy explains the magnetic response of our concentrated NP systems better than the concept of the energy barrier influenced by interparticle interactions. (paper)