We report on magnetic orderings of nanospins in self-assemblies of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ nanoparticles (NPs), occurring at various stages of the magnetization process throughout the superparamagnetic (SPM)-blocking transition. Essentially driven by magnetic dipole couplings and by Zeeman interaction with a magnetic field applied out-of-plane, these magnetic orderings include a mix of long-range parallel and antiparallel alignments of nanospins, with the antiparallel correlation being the strongest near the coercive point below the blocking temperature. The magnetic ordering is probed via x-ray resonant magnetic scattering (XRMS), with the x-ray energy tuned to the $\mathrm{Fe}\text{−}{L}_3$ edge and using circular polarized light. By exploiting dichroic effects, a magnetic scattering signal is isolated from the charge scattering signal. We measured the nanospin ordering for two different sizes of NPs, 5 and 11 nm, with blocking temperatures $T_B$ of 28 and 170 K, respectively. At 300 K, while the magnetometry data essentially show SPM and absence of hysteresis for both particle sizes, the XRMS data reveal the presence of nonzero (up to 9%) antiparallel ordering when the applied field is released to zero for the 11 nm NPs. These antiparallel correlations are drastically amplified when the NPs are cooled down below $T_B$ and reach up to 12% for the 5 nm NPs and 48% for the 11 nm NPs, near the coercive point. The data suggest that the particle size affects the prevalence of the antiparallel correlations over the parallel correlations by a factor $\sim 1.6$ to 3.8 higher when the NP size increases from 5 to 11 nm.

• Received 22 November 2022
• Revised 14 July 2023
• Accepted 29 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.104415