Superparamagnetic dynamics and blocking transition in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> nanoparticles probed by vibrating sample magnetometry and muon spin relaxation

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