Superparamagnetic dynamics and blocking transition in Fe$_3$O$_4$ nanoparticles probed by vibrating sample magnetometry and muon spin relaxation

TL;DR

This study investigates the superparamagnetic and blocked states of Fe$_3$O$_4$ nanoparticles using magnetometry and muon spin relaxation, revealing size-dependent transition temperatures and microscopic magnetic parameters.

Contribution

It provides a detailed combined analysis of magnetic properties of Fe$_3$O$_4$ nanoparticles using both bulk and local magnetic probes, highlighting size effects on magnetic transitions.

Findings

Superparamagnetic to blocked transition occurs over broad temperature ranges.

Transition temperatures depend on nanoparticle size.

Microscopic parameters like activation energy and anisotropy are estimated.

Abstract

The magnetic properties of Fe$_3$O$_4$ nanoparticle assemblies have been investigated in detail through a combination of vibrating sample magnetometry and muon spin relaxation ($\mu$SR) techniques. Two samples with average particle sizes of 5 nm and 20 nm, respectively, were studied. For both samples, the magnetometry and $\mu$SR results exhibit clear signatures of the superparmagnetic state at high temperature and the magnetically blocked state at low temperature. The $\mu$SR data demonstrate that the transition from the superparamagnetic to the blocked state occurs gradually throughout the sample volume over a broad temperature range due to the finite particle size distribution of each sample. The transition occurs between approximately 3 K and 45 K for the 5 nm sample and 150 K and 300 K for the 20 nm sample. The magnetometry and $\mu$SR data are further analyzed to yield estimates of microscopic magnetic parameters including the nanoparticle spin-flip activation energy $E_A$, magnetic anisotropy $K$, and intrinsic nanoparticle spin reversal attempt time $\tau_0$. These results highlight the complementary information about magnetic nanoparticles that can be obtained by bulk magnetic probes such as magnetometry and local magnetic probes such as $\mu$SR.